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Model reduction for discrete-time Markov jump Lur’e systems with time-varying delays in a unified framework. (English) Zbl 1395.93138
Summary: This paper addresses the model reduction problem for a class of Markov jump Lur’e systems with piecewise homogeneous transition probabilities and time-varying delays in discrete-time domain. The purpose of this paper is to solve the $$H_\infty$$, $$l_2$$-$$l_\infty$$, passivity and dissipativity model reduction problems in discrete-time domain in a unified framework by using an extended dissipativity performance index. By constructing a mode-dependent Lyapunov-Krasovskii functional with the sector condition assumption for the nonlinearities, the sufficient conditions on the existence of desired reduced-order models are derived in terms of linear matrix inequalities, which ensures that the resulting error system is stochastically stable and has a prescribed performance index. A numerical example is presented to show the effectiveness of the proposed theories.

##### MSC:
 93B11 System structure simplification 93C55 Discrete-time control/observation systems 93B36 $$H^\infty$$-control 93C10 Nonlinear systems in control theory 60J75 Jump processes (MSC2010) 93E15 Stochastic stability in control theory
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