ℋ ∞ model reduction for continuous-time switched stochastic hybrid systems

• Published in: International journal of systems science Vol. 40; no. 12; pp. 1241 - 1251
• Main Authors: Wu, Ligang, W.C. Ho, Daniel, Lam, James
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Group 01.12.2009; Taylor & Francis
• Subjects: Applied sciences; Approximation; Computer science; control theory; systems; Control theory. Systems; Errors; Exact sciences and technology; Gain; H-infinity control; Lyapunov functions; Mathematical analysis; mean-square exponential stability; Model reduction; Modelling and identification; Scalars; Stochastic systems; switched systems; Multimodel control; performance; switched systems; model reduction; stochastic systems; Stochastic control; Reduced order systems; ℋ; mean-square exponential stability; Hybrid system
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207720902989312

This article deals with the problem of computing an approximation system for a continuous-time switched stochastic system, such that the ℋ ∞ gain of the error system is less than a prescribed scalar. By using the average dwell-time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed, which guarantees the error system to be mean-square exponentially stable with a weighted ℋ ∞ performance. Then, the model reduction is solved by using the projection approach, which casts the model reduction into a sequential minimisation problem subjected to linear matrix inequality constraints by employing the cone complementary linearisation algorithm. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.