Constrained quadratic state feedback control of discrete-time Markovian jump linear systems

doi:10.1016/S0005-1098(98)00202-7

Automatica

Volume 35, Issue 4, April 1999, Pages 617-626

https://doi.org/10.1016/S0005-1098(98)00202-7 Get rights and content

Abstract

In this paper we consider the quadratic optimal control problem of a discrete-time Markovian jump linear system, subject to constraints on the state and control variables. It is desired to find a state feedback controller, which may also depend on the jump variable, that minimizes a quadratic cost and satisfies some upper bounds on the norms of some random variables, related to the state and control variables of the system. The transition probability of the Markov chain and initial condition of the system may belong to appropriate convex sets. We obtain an approximation for the optimal solution of this problem in terms of linear matrices inequalities, so that convex programming can be used for numerical calculations. Examples are presented to illustrate the usefulness of the developed results.

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^☆: This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor René K. Boel under the direction of Editor Tamer Basa̧r. This work was supported in part by CNPq (Brazilian National Research Council) and FAPESP (Research Council of the State of São Paulo).

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Brief PaperConstrained quadratic state feedback control of discrete-time Markovian jump linear systems☆

Abstract

Brief Paper
Constrained quadratic state feedback control of discrete-time Markovian jump linear systems☆