Small Gain Theorems for Large Scale Systems and Construction of ISS Lyapunov Functions

Authors: Sergey N. Dashkovskiy, Björn S. Rüffer, and Fabian R. WirthAuthors Info & Affiliations

https://doi.org/10.1137/090746483

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Abstract

We consider interconnections of n nonlinear subsystems in the input-to-state stability (ISS) framework. For each subsystem an ISS Lyapunov function is given that treats the other subsystems as independent inputs. A gain matrix is used to encode the mutual dependencies of the systems in the network. Under a small gain assumption on the monotone operator induced by the gain matrix, a locally Lipschitz continuous ISS Lyapunov function is obtained constructively for the entire network by appropriately scaling the individual Lyapunov functions for the subsystems. The results are obtained in a general formulation of ISS; the cases of summation, maximization, and separation with respect to external gains are obtained as corollaries.

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References

1.

V. Andrieu, L. Praly, and A. Astolfi, Asymptotic tracking of a state trajectory by output-feedback for a class of non linear systems, in Proceedings of 46th IEEE Conference on Decision and Control, CDC 2007, New Orleans, LA, 2007, pp. 5228–5233.

2.

A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York, 1979.

3.

A. L. Chen, G.-Q. Chen, and R. A. Freeman, Stability of nonlinear feedback systems: A new small-gain theorem, SIAM J. Control Optim., 46 (2007), pp. 1995–2012.

4.

F. H. Clarke, Y. S. Ledyaev, R. J. Stern, and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer, New York, 1998.

5.

S. Dashkovskiy, B. Rüffer, and F. Wirth, A small-gain type stability criterion for large scale networks of ISS systems, in 44th IEEE Conference on Decision and Control and European Control Conference, CDC/ECC 2005, Seville, Spain, 2005, pp. 5633–5638.

6.

S. Dashkovskiy, B. Rüffer, and F. Wirth, An ISS small-gain theorem for general networks, Math. Control Signals Systems, 19 (2007), pp. 93–122.

7.

S. Dashkovskiy, B. Rüffer, and F. Wirth, A Lyapunov ISS small gain theorem for strongly connected networks, in Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems, NOLCOS2007, Pretoria, South Africa, 2007, pp. 283–288.

8.

S. Dashkovskiy, B. S. Rüffer, and F. R. Wirth, An ISS Lyapunov function for networks of ISS systems, in Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, 2006, pp. 77–82.

9.

S. N. Dashkovskiy, B. S. Rüffer, and F. R. Wirth, Numerical verification of local input-to-state stability for large networks, in Proceedings of 46th IEEE Conference on Decision and Control, CDC 2007, New Orleans, LA, 2007, pp. 4471–4476.

10.

S. N. Dashkovskiy, B. S. Rüffer, and F. R. Wirth, Applications of the general Lyapunov ISS small-gain theorem for networks, in Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008, Cancun, Mexico, 2008, pp. 25–30.

11.

B. C. Eaves, Homotopies for computation of fixed points, Math. Program., 3 (1972), pp. 1–22.

12.

L. C. Evans, Partial Differential Equations, Grad. Stud. Math. 19, American Mathematical Society, Providence, RI, 1998.

13.

S. Gaubert and J. Gunawardena, The Perron-Frobenius theorem for homogeneous, monotone functions, Trans. Amer. Math. Soc., 356 (2004), pp. 4931–4950 (electronic).

14.

L. Grüne, Input-to-state dynamical stability and its Lyapunov function characterization, IEEE Trans. Automat. Control, 47 (2002), pp. 1499–1504.

15.

D. Hinrichsen and A. J. Pritchard, Mathematical Systems Theory I: Modelling, State Space Analysis, Stability and Robustness, Springer, New York, 2005.

16.

D. Hinrichsen and A. J. Pritchard, Composite systems with uncertain couplings of fixed structure: Scaled Riccati equations and the problem of quadratic stability, SIAM J. Control Optim., 47 (2009), pp. 3037–3075.

17.

.28em plus .1em minus .1em Z.-P. Jiang, I. M. Y. Mareels, and Y. Wang, A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems, Automatica J. IFAC, 32 (1996), pp. 1211–1215.

18.

Z.-P. Jiang, A. R. Teel, and L. Praly, Small-gain theorem for ISS systems and applications, Math. Control Signals Systems, 7 (1994), pp. 95–120.

19.

Z.-P. Jiang and Y. Wang, A generalization of the nonlinear small-gain theorem for large-scale complex systems, in Proceedings of the 7th World Congress on Intelligent Control and Automation, IEEE, 2008, pp. 1188–1193.

20.

I. Karafyllis and Z.-P. Jiang, A vector small-gain theorem for general nonlinear control systems, IEEE Trans. Automat. Control, submitted.

21.

H. G. Potrykus, F. Allgöwer, and S. J. Qin, The character of an idempotent-analytic nonlinear small gain theorem, in Positive Systems, Lecture Notes in Control Inform. Sci. 294, Springer, Berlin, 2003, pp. 361–368.

22.

D. M. Raimondo, L. Magni, and R. Scattolini, Decentralized MPC of nonlinear systems: An input-to-state stability approach, Internat. J. Robust Nonlinear Control, 17 (2007), pp. 1651–1667.

23.

N. Rouche, P. Habets, and M. Laloy, Stability Theory by Liapunov's Direct Method, Springer, New York, 1977.

24.

B. S. Rüffer, Monotone Dynamical Systems, Graphs, and Stability of Large-Scale Interconnected Systems, Ph.D. thesis, Fachbereich 3, Mathematik und Informatik, Universität Bremen, Germany, 2007; available online athttp://nbn-resolving.de/urn:nbn:de:gbv:46-diss000109058.

25.

B. S. Rüffer, Monotone inequalities, dynamical systems, and paths in the positive orthant of Euclidean n-space, Positivity, (2009), DOI 10.1007/s11117-009-0016-5.

26.

D. D. Šiljak, Decentralized Control of Complex Systems, Math. Sci. Eng. 184, Academic Press, Boston, MA, 1991.

27.

E. Sontag and A. Teel, Changing supply functions in input/state stable systems, IEEE Trans. Automat. Control, 40 (1995), pp. 1476–1478.

28.

E. D. Sontag, Smooth stabilization implies coprime factorization, IEEE Trans. Automat. Control, 34 (1989), pp. 435–443.

29.

E. D. Sontag and Y. Wang, On characterizations of input-to-state stability with respect to compact sets, in Proceedings of IFAC Non-Linear Control Systems Design Symposium, (NOLCOS '95), Tahoe City, CA, 1995, pp. 226–231.

30.

E. D. Sontag and Y. Wang, On characterizations of the input-to-state stability property, Systems Control Lett., 24 (1995), pp. 351–359.

31.

E. D. Sontag and Y. Wang, New characterizations of input-to-state stability, IEEE Trans. Automat. Control, 41 (1996), pp. 1283–1294.

32.

A. R. Teel, A nonlinear small gain theorem for the analysis of control systems with saturation, IEEE Trans. Automat. Control, 41 (1996), pp. 1256–1270.

33.

A. R. Teel, private communication, 2005.

34.

M. Vidyasagar, Input-Output Analysis of Large-Scale Interconnected Systems, Lecture Notes in Control Inform. Sci. 29, Springer, Berlin, 1981.

35.

L. Wang and X. Zou, Exponential stability of Cohen-Grossberg neural networks, Neural Networks, 15 (2002), pp. 415–422.

36.

G. Zames, On input-output stability of time-varying nonlinear feedback systems I. Conditions derived using concepts of loop gain conicity and positivity, IEEE Trans. Automat. Control, 11 (1966), pp. 228–238.

Information & Authors

Information

Published In

cover image SIAM Journal on Control and Optimization

SIAM Journal on Control and Optimization

Volume 48 • Issue 6 • January 2010

Pages: 4089 - 4118

DOI: 10.1137/090746483

ISSN (online): 1095-7138

Copyright

Copyright © 2010 Society for Industrial and Applied Mathematics.

History

Submitted: 14 January 2009

Accepted: 24 March 2010

Published online: 12 May 2010

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Keywords

Authors

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Sergey N. Dashkovskiy

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Björn S. Rüffer

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Fabian R. Wirth

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References
Nonlinear Control of Dynamic Networks | 16 April 2014
Cross Ref
Solving iterative functional equations for a class of piecewise linear K∞ -functions
Journal of Mathematical Analysis and Applications, Vol. 411, No. 2 | 1 Mar 2014
Cross Ref
Stability via Hybrid-Event-Time Lyapunov Function and Impulsive Stabilization for Discrete-Time Delayed Switched Systems
- Bin Liu and
- David J. Hill
SIAM Journal on Control and Optimization, Vol. 52, No. 2 | 29 April 2014
Abstract PDF (669 KB)
Positively Invariant Families of Sets for Interconnected and Time-Delay Discrete-Time Systems
- S. V. Raković and
- R. H. Gielen
SIAM Journal on Control and Optimization, Vol. 52, No. 4 | 17 July 2014
Abstract PDF (577 KB)
Small-gain conditions for stochastic network systems
52nd IEEE Conference on Decision and Control | 1 Dec 2013
Cross Ref
Numerical ISS controller design via a dynamic game approach
52nd IEEE Conference on Decision and Control | 1 Dec 2013
Cross Ref
Separable Lyapunov functions for monotone systems
52nd IEEE Conference on Decision and Control | 1 Dec 2013
Cross Ref
On inter-sampling times for event-triggered large-scale linear systems
52nd IEEE Conference on Decision and Control | 1 Dec 2013
Cross Ref
A small-gain-like theorem for large-scale systems
52nd IEEE Conference on Decision and Control | 1 Dec 2013
Cross Ref
Construction of Lyapunov–Krasovskii functionals for networks of iISS retarded systems in small-gain formulation
Automatica, Vol. 49, No. 11 | 1 Nov 2013
Cross Ref
Global Stabilization of Nonlinear Systems Based on Vector Control Lyapunov Functions
IEEE Transactions on Automatic Control, Vol. 58, No. 10 | 1 Oct 2013
Cross Ref
Non-minimal factorization approach to the -gain of discrete-time linear systems
Automatica, Vol. 49, No. 9 | 1 Sep 2013
Cross Ref
Parsimonious event-triggered distributed control: A Zeno free approach
Automatica, Vol. 49, No. 7 | 1 Jul 2013
Cross Ref
Stability analysis of logistics networks with time-delays
Production Planning & Control, Vol. 24, No. 7 | 20 February 2012
Cross Ref
A two-phase approach to stability of networks given in iISS framework: Utilization of a matrix-like criterion
2013 American Control Conference | 1 Jun 2013
Cross Ref
Dynamic Versus Static Weighting of Lyapunov Functions
IEEE Transactions on Automatic Control, Vol. 58, No. 6 | 1 Jun 2013
Cross Ref
A Contraction Approach to the Hierarchical Analysis and Design of Networked Systems
IEEE Transactions on Automatic Control, Vol. 58, No. 5 | 1 May 2013
Cross Ref
Robust Stability of Networks of iISS Systems: Construction of Sum-Type Lyapunov Functions
IEEE Transactions on Automatic Control, Vol. 58, No. 5 | 1 May 2013
Cross Ref
Input-to-state stability of interconnected hybrid systems
Automatica, Vol. 49, No. 4 | 1 Apr 2013
Cross Ref
Computation of tight integral input-to-state stability bounds for nonlinear systems
Systems & Control Letters, Vol. 62, No. 4 | 1 Apr 2013
Cross Ref
Input‐to‐state‐stability‐type comparison principles and input‐to‐state stability for discrete‐time dynamical networks with time delays
International Journal of Robust and Nonlinear Control, Vol. 23, No. 4 | 9 December 2011
Cross Ref
Input‐to‐state stability for discrete‐time nonlinear impulsive systems with delays
International Journal of Robust and Nonlinear Control, Vol. 23, No. 4 | 9 November 2011
Cross Ref
Input-to-state stability of infinite-dimensional control systems
Mathematics of Control, Signals, and Systems, Vol. 25, No. 1 | 28 August 2012
Cross Ref
A small gain framework for networked cooperative force-reflecting teleoperation
Automatica, Vol. 49, No. 2 | 1 Feb 2013
Cross Ref
Input-to-State Stability of Nonlinear Impulsive Systems
- Sergey Dashkovskiy and
- Andrii Mironchenko
SIAM Journal on Control and Optimization, Vol. 51, No. 3 | 7 May 2013
Abstract PDF (361 KB)
Material balance and closure equations for plasmas in Tokamaks
IFAC Proceedings Volumes, Vol. 46, No. 14 | 1 Jan 2013
Cross Ref
A Non–conservative Small-Gain Theorem for GAS Discrete–Time Systems
IFAC Proceedings Volumes, Vol. 46, No. 23 | 1 Jan 2013
Cross Ref
Utility of iISS in Composing Lyapunov Functions for Interconnections
IFAC Proceedings Volumes, Vol. 46, No. 23 | 1 Jan 2013
Cross Ref
On the Relation between Dwell-Time and Small-Gain Conditions for Interconnected Impulsive Systems
IFAC Proceedings Volumes, Vol. 46, No. 23 | 1 Jan 2013
Cross Ref
Non–conservative and tractable stability tests for general linear interconnected systems with an application to Power Systems
IFAC Proceedings Volumes, Vol. 46, No. 27 | 1 Jan 2013
Cross Ref
A weak version of the small-gain theorem
2012 IEEE 51st IEEE Conference on Decision and Control (CDC) | 1 Dec 2012
Cross Ref
Non-conservative dissipativity and small-gain conditions for stability analysis of interconnected systems
2012 IEEE 51st IEEE Conference on Decision and Control (CDC) | 1 Dec 2012
Cross Ref
Input-to-state stability for model predictive control of single systems and networks with time-delays
2012 IEEE 51st IEEE Conference on Decision and Control (CDC) | 1 Dec 2012
Cross Ref
Reduction of the small gain condition
2012 IEEE 51st IEEE Conference on Decision and Control (CDC) | 1 Dec 2012
Cross Ref
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Constructions of ISS-Lyapunov functions for interconnected impulsive systems
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2012 IEEE 51st IEEE Conference on Decision and Control (CDC) | 1 Dec 2012
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Uniformly asymptotical stability of nonlinear time delay systems
2012 12th International Conference on Control Automation Robotics & Vision (ICARCV) | 1 Dec 2012
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Lyapunov formulation of the ISS cyclic-small-gain theorem for hybrid dynamical networks
Nonlinear Analysis: Hybrid Systems, Vol. 6, No. 4 | 1 Nov 2012
Cross Ref
Decentralized output-feedback control of large-scale nonlinear systems with sensor noise
Automatica, Vol. 48, No. 10 | 1 Oct 2012
Cross Ref
Stability of interconnected impulsive systems with and without time delays, using Lyapunov methods
Nonlinear Analysis: Hybrid Systems, Vol. 6, No. 3 | 1 Aug 2012
Cross Ref
Autonomous control methods in logistics – A mathematical perspective
Applied Mathematical Modelling, Vol. 36, No. 7 | 1 Jul 2012
Cross Ref
Capability and limitation of max- and sum-type construction of Lyapunov functions for networks of iISS systems
Automatica, Vol. 48, No. 6 | 1 Jun 2012
Cross Ref
An iISS formulation for establishing robust stability of dynamical networks with neutral, retarded and communication delay
2012 American Control Conference (ACC) | 1 Jun 2012
Cross Ref
On the application of the small-gain theorem to the stability analysis of large-scale power systems with delay
2012 American Control Conference (ACC) | 1 Jun 2012
Cross Ref
A Lyapunov–Razumikhin approach for stability analysis of logistics networks with time-delays
International Journal of Systems Science, Vol. 43, No. 5 | 1 May 2012
Cross Ref
Small-Gain Based Output-Feedback Controller Design for a Class of Nonlinear Systems With Actuator Dynamic Quantization
IEEE Transactions on Automatic Control, Vol. 57, No. 5 | 1 May 2012
Cross Ref
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Mathematics of Control, Signals, and Systems, Vol. 24, No. 1-2 | 25 February 2012
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Input-to-state stability analysis for interconnected difference equations with delay
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Numerical construction of LISS Lyapunov functions under a small-gain condition
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A sector bound approach to feedback control of nonlinear systems with state quantization
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Lyapunov formulation of the large-scale, ISS cyclic-small-gain theorem: The discrete-time case
Systems & Control Letters, Vol. 61, No. 1 | 1 Jan 2012
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MPC Schemes Guaranteeing ISDS and ISS for Nonlinear (Time-Delay) Systems
Mathematical Problems in Engineering, Vol. 2012 | 1 Jan 2012
Cross Ref
Connecting several stability criteria for iISS networks and their application to a network computing model
IEEE Conference on Decision and Control and European Control Conference | 1 Dec 2011
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Small-gain results for discrete-time networks of systems with delay
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Numerical construction of LISS Lyapunov functions under a small gain condition
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A sensitivity trade-off arising in small-gain design for nonlinear systems: An iISS framework
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Diagonal Stability on Cactus Graphs and Application to Network Stability Analysis
IEEE Transactions on Automatic Control, Vol. 56, No. 12 | 1 Dec 2011
Cross Ref
Pressure Regulation in Nonlinear Hydraulic Networks by Positive and Quantized Controls
IEEE Transactions on Control Systems Technology, Vol. 19, No. 6 | 1 Nov 2011
Cross Ref
Lyapunov formulation of ISS cyclic-small-gain in continuous-time dynamical networks
Automatica, Vol. 47, No. 9 | 1 Sep 2011
Cross Ref
A Sector Bound Approach to Feedback Control of Nonlinear Systems with State Quantization
28 Aug 2011
Cross Ref
Stability analysis of autonomously controlled production networks
International Journal of Production Research, Vol. 49, No. 16 | 15 Aug 2011
Cross Ref
A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems
Proceedings of the 2011 American Control Conference | 1 Jun 2011
Cross Ref
A Small-Gain Condition for Interconnections of ISS Systems With Mixed ISS Characterizations
IEEE Transactions on Automatic Control, Vol. 56, No. 6 | 1 Jun 2011
Cross Ref
Modeling and stability analysis of autonomously controlled production networks
Logistics Research, Vol. 3, No. 2-3 | 20 March 2011
Cross Ref
Advanced Stability Methods and Applications
Stability and Stabilization of Nonlinear Systems | 1 Jan 2011
Cross Ref
Local Input-to-State Stability of Production Networks
Dynamics in Logistics | 20 January 2011
Cross Ref
Autonomous and Central Control of Production Networks
Autonomous Cooperation and Control in Logistics | 15 April 2011
Cross Ref
Discussion on: “On a Small Gain Theorem for ISS Networks in Dissipative Lyapunov Form”
European Journal of Control, Vol. 17, No. 4 | 1 Jan 2011
Cross Ref
On a Small Gain Theorem for ISS Networks in Dissipative Lyapunov Form
European Journal of Control, Vol. 17, No. 4 | 1 Jan 2011
Cross Ref
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