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Zbl 0928.93047
Costa, O.L.V.; Marques, R.P.
Maximal and stabilizing hermitian solutions for discrete-time coupled algebraic Riccati equations.
(English)
[J] Math. Control Signals Syst. 12, No.2, 167-195 (1999). ISSN 0932-4194; ISSN 1435-568X/e

Discrete-time coupled algebraic Riccati equations (CARE) that arise in quadratic optimal control and $H_\infty$-control of Markovian jump linear systems are considered in this paper. In Section 3, the CARE that arise from the quadratic optimal control problem are considered. The matrix cost is only assumed to be Hermitian. A sufficient condition for the existence of a maximal solution is presented (Theorem 1). Theorem 2 establishes a link between the LMI optimization problem and a maximal solution. Section 4 deals with necessary and sufficient conditions for the existence of a stabilizing solution (Theorem 3 and 4). Section 5 presents a recursive procedure for obtaining a stabilizing solution of the CARE that arise in the $H_\infty$-problem, whenever it exists (Theorem 6).
[Kunihiko Ichikawa (Tokyo)]
MSC 2000:
*93D15 Stabilization of systems by feedback
93E15 Stochastic stability
15A24 Matrix equations
93C55 Discrete-time control systems
93B36 $H^\infty$-control

Keywords: discrete-time coupled algebraic Riccati equations; quadratic optimal control; $H_\infty$-control; Markovian jump linear systems; maximal solution; LMI optimization

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