Adaptive control of linear Markov jump systems

Abstract

Stabilization of linear Markov jump systems via adaptive control is considered in this paper. The switching law is assumed to be unobservable Markov process. A sufficient condition is obtained for the stochastic stabilizability based on common quadratic Lyapunov functions (QLFs). The constructive proof provides a method to construct a sampling adaptive stabilizer. An example is used to describe the design of adaptive control, which stabilizes the system.

Keywords:

• Switched system
• Common quadratic Lyapunov function
• Linear Markov jump system
• Adaptive control

Acknowledgments

The authors would like to thank nominal referees for their very constructive comments. Some of their comments have been cited in the paper. This study is supported partly by NNSF 60274010, 60221301, 60334040, 60228003 of China.