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Worst case control of uncertain jumping systems with multi-state and input delay information. (English) Zbl 1121.93022

Summary: The problem of worst case (also called \(\mathcal H_{\infty}\)) control for a class of uncertain systems with Markovian jump parameters and multiple delays in the state and input is investigated. The jumping parameters are modelled as a continuous-time, discrete-state Markov process and the parametric uncertainties are assumed to be real, time-varying and norm-bounded that appear in the state, input and delayed-state matrices. The time-delay factors are unknowns and time-varying with known bounds. Complete results for instantaneous and delayed state feedback control designs are developed which guarantee the weak-delay dependent stochastic stability with a prescribed \(\mathcal H_{\infty}\)-performance. The solutions are provided in terms of a finite set of coupled linear matrix inequalities (LMIs). Application of the developed theory to a typical example has been presented.

MSC:

93B36 \(H^\infty\)-control
93C23 Control/observation systems governed by functional-differential equations

Software:

LMI toolbox
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Full Text: DOI

References:

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