Stability analysis and uniform ultimate boundedness control synthesis for a class of nonlinear switched difference systems

Abstract

In this paper, we deal with stability analysis of a class of nonlinear switched discrete-time systems. Systems of the class appear in numerical simulation of continuous-time switched systems. Some linear matrix inequality type stability conditions, based on the common Lyapunov function approach, are obtained. It is shown that under these conditions the system remains stable for any switching law. The obtained results are applied to the analysis of dynamics of a discrete-time switched population model. Finally, a continuous state feedback control is proposed that guarantees the uniform ultimate boundedness of switched systems with uncertain nonlinearity and parameters.

Keywords:

• switched difference systems
• asymptotic stability
• Lyapunov functions
• population dynamics
• uniform ultimate boundedness
• robust control

Keywords:

• 34A38
• 93D20

Acknowledgements

This work was supported by the Russian Foundation of Basic Researches under grant nos. 08-08-92208-GFEN_a, National Science Foundation of China under grant nos. 60774037, 60911120067, 60904069, 10926048 and the Doctoral Fund of Ministry of Education of China under grant no. 20091103120008.