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SIAM J. on Control and Optimization

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1965

Volume 3, Issue 3, pp. 357-508


On Stability in Control Systems

Emilio Roxin

J. Soc. Indus. and Appl. Math. Ser. A 3, pp. 357-372 (16 pages) | Cited 6 times

Online Publication Date: July 18, 2006

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Abstract Unavailable

On the Existence of Lyapunov Function for the Problem of Lur’e

K. R. Meyer

J. Soc. Indus. and Appl. Math. Ser. A 3, pp. 373-383 (11 pages) | Cited 9 times

Online Publication Date: July 18, 2006

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Abstract Unavailable

A Method for Computing Least Squares Estimators that Keep Up with the Data

Arthur Albert and Robert W. Sittler

J. Soc. Indus. and Appl. Math. Ser. A 3, pp. 384-417 (34 pages)

Online Publication Date: July 18, 2006

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Abstract Unavailable

Weakened Hypotheses for the Variational Problem Considered by Hestenes

T. Guinn

J. Soc. Indus. and Appl. Math. Ser. A 3, pp. 418-423 (6 pages)

Online Publication Date: July 18, 2006

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Abstract Unavailable

Variational Problems with Unbounded Controls

J. Warga

J. Soc. Indus. and Appl. Math. Ser. A 3, pp. 424-438 (15 pages)

Online Publication Date: July 18, 2006

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Abstract Unavailable

A Remark on Complete Controllability

Hsin Chu

J. Soc. Indus. and Appl. Math. Ser. A 3, pp. 439-442 (4 pages)

Online Publication Date: July 18, 2006

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Abstract Unavailable

The Application of Lyapunov’s Second Method to Interconnected Systems

F. N. Bailey

J. Soc. Indus. and Appl. Math. Ser. A 3, pp. 443-462 (20 pages) | Cited 8 times

Online Publication Date: July 18, 2006

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Show Abstract
As many engineering systems are made up of an interconnection of simple subsystems, it is natural to attempt to utilize this interconnection structure in developing system analysis techniques. In this paper interconnection information is used in conjunction with properties of the individual subsystems to obtain sufficient conditions for asymptotic stability-in-the-large. This method may be applied to a broad class of linear, nonlinear and time-varying interconnected systems as indicated in the following three steps.
First, the Lyapun-ov functions and comparison equations are found for the individual subsystems. Second, the comparison equations are interconnected, following the interconnections in the original system, into a system of comparison equations. This system is linear, with constant coefficients and of order equal to the number of subsystems in the original interconnected system. Finally, the stability of the null solution of this auxiliary system is examined. If it is asymptotically stable, then the null solution of the interconnected system is asympotically stable-in-the-large. An example illustrates the use of interconnection information in determining the sufficient conditions for asymptotic stability-in-the-large for a ninth-order interconnected system.

On the Existence of Optimal Stochastic Controls

Harold J. Kushner

J. Soc. Indus. and Appl. Math. Ser. A 3, pp. 463-474 (12 pages) | Cited 1 time

Online Publication Date: July 18, 2006

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Abstract Unavailable

Existence Theorems for Optimal Solutions in Pontryagin and Lagrange Problems

Lamberto Cesari

J. Soc. Indus. and Appl. Math. Ser. A 3, pp. 475-498 (24 pages)

Online Publication Date: July 18, 2006

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Abstract Unavailable

Sufficient Conditions for the Optimality of a Stochastic Control

Harold J. Kushner

J. Soc. Indus. and Appl. Math. Ser. A 3, pp. 499-508 (10 pages) | Cited 1 time

Online Publication Date: July 18, 2006

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Abstract Unavailable
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