Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 47, Issue 12, Pages 2089-2094Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2002.805670
Keywords
H-infinity control; linear matrix inequality; robust stochastic stabilization; stochastic systems; time-delay systems; uncertain systems
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This note deals with the problems of robust stochastic stabilization and robust H-infinity control for uncertain stochastic systems with a time-varying delay in the state. The parameter uncertainties are assumed to be time-varying norm-bounded appearing in both the state and input matrices. The purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H-infinity control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H-infinity performance is required to be achieved. In terms of a linear matrix inequality, sufficient conditions for the solvability of these problems are proposed respectively; the expressions of desired state feedback controllers are given. An example illustrating the proposed approach is provided.
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