Stabilization and \({\mathcal H}_\infty\) control of two-dimensional Markovian jump systems. (English) Zbl 1069.93007

Summary: This paper extends the results obtained for one-dimensional Markovian jump systems to investigate the problems of stochastic stabilization and \({\mathcal H}_\infty\) control of two-dimensional (2D) systems with Markovian jump parameters. The mathematical model of 2D jump systems is established upon the well-known Roesser model, and sufficient conditions are obtained for the existence of desired controllers in terms of linear matrix inequalities, which can be readily solved by available numerical software. These obtained results are further extended to more general cases whose system matrices also contain parameter uncertainties, represented by either polytopic or norm-bounded approaches. A numerical example is provided to show the applicability of the proposed theories.


93B36 \(H^\infty\)-control
93E15 Stochastic stability in control theory
93D15 Stabilization of systems by feedback
60J75 Jump processes (MSC2010)
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