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Zbl 1154.93326
Wu, Ligang; Zheng, Wei Xing
Weighted $H_\infty $ model reduction for linear switched systems with time-varying delay. (English)
[J] Automatica 45, No. 1, 186-193 (2009). ISSN 0005-1098

Summary: This paper is concerned with $\cal H_\infty $ model reduction for continuous-time linear switched systems with time-varying delay. For a given stable switched system, our attention is focused on construction of a reduced-order model such that the error system is exponentially stable with a prescribed weighted $\cal H_\infty $ performance. By applying the average dwell time approach and the piecewise Lyapunov function technique, delay-dependent/delay-independent sufficient conditions are proposed in terms of Linear Matrix Inequality (LMI) to guarantee the exponential stability and the weighted $\cal H_\infty $ performance for the error system. The model reduction problem is solved by using the projection approach, which casts the model reduction problem into a sequential minimization problem subject to LMI constraints by employing the cone complementary linearization algorithm. A numerical example is provided to illustrate the effectiveness of the proposed theory.

MSC 2000:: *93B11 System structure simplification
93C15 Control systems governed by ODE
93B18 Linearizability of systems

Keywords: exponential stability; $\cal H_\infty $ performance; model reduction; switched systems; time-varying delay

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Zentralblatt MATH Berlin [Germany]