Resilient model approximation for Markov jump time-delay systems via reduced model with hierarchical Markov chains. (English) Zbl 1346.93012
Summary: In this paper, the resilient model approximation problem for a class of discrete-time Markov jump time-delay systems with input sector-bounded nonlinearities is investigated. A linearised reduced-order model is determined with mode changes subject to domination by a hierarchical Markov chain containing two different nonhomogeneous Markov chains. Hence, the reduced-order model obtained not only reflects the dependence of the original systems but also model external influence that is related to the mode changes of the original system. Sufficient conditions formulated in terms of bilinear matrix inequalities for the existence of such models are established, such that the resulting error system is stochastically stable and has a guaranteed \(l_{2}-l_\infty\) error performance. A linear matrix inequalities optimisation coupled with line search is exploited to solve for the corresponding reduced-order systems. The potential and effectiveness of the developed theoretical results are demonstrated via a numerical example.
MSC:
| 93A13 | Hierarchical systems |
| 60J75 | Jump processes (MSC2010) |
| 60J10 | Markov chains (discrete-time Markov processes on discrete state spaces) |
| 93C10 | Nonlinear systems in control theory |
Keywords:
hierarchical Markov chain; input sector nonlinearities; Markov jump systems; mode-dependent time-varying delays; resilient model approximationReferences:
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