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Dynamic output-feedback control of linear semi-Markov jump systems with incomplete semi-Markov kernel. (English) Zbl 1442.93045

Summary: This paper is devoted to the dynamic output-feedback control problem for a class of linear semi-Markov jump systems (SMJSs) in discrete-time domain. A mode-dependent control scheme is employed with an adaptation sense under incomplete semi-Markov kernel, which has been shown to be more practical. By introducing the upper bound of sojourn time for each system mode, numerically testable stabilization criteria are established for discrete-time linear SMJSs via a novel form of Lyapunov function. The adopted Lyapunov matrix depends on the modes and their elapsed time simultaneously. Based on above-mentioned Lyapunov function combined with projection lemma, a desired mode-dependent stabilizing controller is designed such that the closed-loop system is mean-square stable. Finally, the theoretical results are applied to a practical example of F-404 aircraft engine system to demonstrate the effectiveness and applicability of the proposed control strategy.

MSC:

93E15 Stochastic stability in control theory
93D15 Stabilization of systems by feedback
93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory
60K15 Markov renewal processes, semi-Markov processes
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