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\(H_{\infty }\) model reduction of Markovian jump linear systems. (English) Zbl 1157.93519

Summary: The \(H_{\infty }\) model reduction problem for linear systems that possess randomly jumping parameters is studied. The development includes both the continuous and discrete cases. It is shown that the reduced order models exist if a set of matrix inequalities is feasible. An effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the model reduction solutions. Using the numerical solutions of the matrix inequalities, the reduced order models can be obtained. An example is given to illustrate the proposed model reduction method.

MSC:

93E03 Stochastic systems in control theory (general)
93B36 \(H^\infty\)-control
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