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Weighted $$H_\infty$$ model reduction for linear switched systems with time-varying delay. (English) Zbl 1154.93326
Summary: This paper is concerned with $$\mathcal H_\infty$$ 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 $$\mathcal H_\infty$$ 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 $$\mathcal H_\infty$$ 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:
 93B11 System structure simplification 93C15 Control/observation systems governed by ordinary differential equations 93B18 Linearizations
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