Robust observer-based H∞ control of a Markovian jump system with different delay and system modes

This paper investigates the problem of robust observer-based stabilization for a delayed Markovian jump system. The sources of randomness in the system mode and the delay mode are assumed to be different. To this end, two different Markov processes are considered for modeling the randomness of the system matrices and the state delay. A two mode-dependent Lyapunov-Krasovskii functional is used to design a robust observer based feedback control rule for the stochastic stability of the closed-loop system. The rule4 should also satisfy the condition of disturbance reduction at a prescribed level in the presence of parametric uncertainties. The procedure is implemented by solving linear matrix inequalities (LMIs). The results are tested within a simulation example and the effectiveness of the proposed design method is verified.

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