Weighted ℋ∞ℋ∞ model reduction for linear switched systems with time-varying delay

This paper is concerned with ℋ∞ℋ∞ 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 ℋ∞ℋ∞ performance. By applying the average dwell time approach and the piecewise Lyapunov function technique, delay-dependent/deley-independent sufficient conditions are proposed in terms of linear matrix inequality (LMI) to guarantee the exponential stability and the weighted ℋ∞ℋ∞ 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.