We analyze the connection between turnpike behaviors and strict dissipativity properties for discrete time finite dimensional linear quadratic optimal control problems. We first use strict dissipativity as a sufficient condition for the turnpike property. Next, we characterize strict dissipativity and the newly introduced property of strict pre-dissipativity in terms of the system matrices related to the linear quadratic problem. These characterizations then lead to new necessary conditions for the turnpike properties under consideration, and thus eventually to necessary and sufficient conditions in terms of spectral criteria and matrix inequalities. One of the key novelties which distinguishes the results in the present paper from earlier ones on linear quadratic optimal control problems is the consideration of state and input constraints.


  1. turnpike property
  2. linear quadratic optimal control
  3. dissipativity
  4. detectability
  5. Lyapunov matrix inequality
  6. long time behavior

MSC codes

  1. 49K15
  2. 49N10
  3. 49J15
  4. 93D20
  5. 93C15

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Published In

cover image SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Pages: 1282 - 1302
ISSN (online): 1095-7138


Submitted: 30 March 2017
Accepted: 24 January 2018
Published online: 3 April 2018


  1. turnpike property
  2. linear quadratic optimal control
  3. dissipativity
  4. detectability
  5. Lyapunov matrix inequality
  6. long time behavior

MSC codes

  1. 49K15
  2. 49N10
  3. 49J15
  4. 93D20
  5. 93C15



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