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

• Published in: Automatica (Oxford) Vol. 45; no. 1; pp. 186 - 193
• Main Authors: Wu, Ligang, Zheng, Wei Xing
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2009; Elsevier
• Subjects: [formula omitted] performance; Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Exact sciences and technology; Exponential stability; Model reduction; Modelling and identification; Switched systems; Time-varying delay; Switched systems; ℋ ∞ performance; Model reduction; Exponential stability; Time-varying delay; Multimodel control; Delay independent system; H infinite control; Minimization; Continuous time; Linear time; Delay system; Delay dependent system; Hybrid system; Time varying system; Time average; H∞ performance; Linear matrix inequality; Reduced order systems; Delay time; Lyapunov function; Linearization
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2008.06.024

This paper is concerned with 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 ∞ 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 ∞ 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.