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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 |

### Keywords:

exponential stability; \(\mathcal H_\infty \) performance; model reduction; switched systems; time-varying delay
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\textit{L. Wu} and \textit{W. X. Zheng}, Automatica 45, No. 1, 186--193 (2009; Zbl 1154.93326)

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