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

Abstract

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.

Keywords:

• mean-square exponential stability
• ℋ_∞ performance
• model reduction
• stochastic systems
• switched systems

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 60804002 and 60834003, and in part by research grants from CityU 7002208 and RGC HKU 7029/05P.