Regular Papers

International Journal of Control, Automation and Systems 2015; 13(2): 319-326

Published online February 2, 2015

https://doi.org/10.1007/s12555-014-0128-y

© The International Journal of Control, Automation, and Systems

PI Tracking Control for Nonlinear Time-varying Delay Markov Jump Systems

Cong Liu* and Lijuan Xu

Yancheng Institute of Technology

Abstract

This paper considers robust stochastic stability and PI tracking control problem for Markov jump systems with both input delay and an unknown nonlinear function. Based on the traditional PI control strategy, a new controller design scheme is proposed for nonlinear time-delay Markov jump systems which can realize multiple control objectives including robust stochastic stability and tracking performance. By using the Lyapunov stability theory and LMI algorithms, a sufficient condition for the solution to robust stochastic stability and tracking control problem is obtained. Then, the desired controller with PI structure is designed, which ensures the resulting closed-loop system is robust stochastically stable and the system state has favorable tracking performance. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Keywords LMI, Markov, PI tracking control, stochastic stability, time-varying delay, unknown nonlinear function.

Article

Regular Papers

International Journal of Control, Automation and Systems 2015; 13(2): 319-326

Published online April 1, 2015 https://doi.org/10.1007/s12555-014-0128-y

Copyright © The International Journal of Control, Automation, and Systems.

PI Tracking Control for Nonlinear Time-varying Delay Markov Jump Systems

Cong Liu* and Lijuan Xu

Yancheng Institute of Technology

Abstract

This paper considers robust stochastic stability and PI tracking control problem for Markov jump systems with both input delay and an unknown nonlinear function. Based on the traditional PI control strategy, a new controller design scheme is proposed for nonlinear time-delay Markov jump systems which can realize multiple control objectives including robust stochastic stability and tracking performance. By using the Lyapunov stability theory and LMI algorithms, a sufficient condition for the solution to robust stochastic stability and tracking control problem is obtained. Then, the desired controller with PI structure is designed, which ensures the resulting closed-loop system is robust stochastically stable and the system state has favorable tracking performance. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

Keywords: LMI, Markov, PI tracking control, stochastic stability, time-varying delay, unknown nonlinear function.

IJCAS
June 2024

Vol. 22, No. 6, pp. 1761~2054

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