Derandomisation-based multiple frequency control for stochastic Markov jump systems

ABSTRACT

Under the framework of derandomisation approach, the state feedback control issues for both continuous-time and discrete-time Markov jump linear systems (MJLSs) are investigated to meet multiple performance objectives over multiple frequency ranges. Because of the stochastic jumping among different modes, the generalised Kalman–Yakubovic–Popov lemma-based finite-frequency controller design approach cannot be directly applied to MJLSs. To overcome this limitation, a derandomisation approach is established by transforming the original stochastic multiple modes systems to deterministic ones. Then the multiple frequency controllers for both discrete-time and continuous-time MJLSs are designed to guarantee the multiple performances of the closed-loop systems. To verify the effectiveness of the developed algorithms, examples are presented, where the performance requirements include specifications in low-frequency and high-frequency ranges, respectively.

KEYWORDS:

• Hybrid systems
• stability
• Markov jump linear systems
• finite-frequency control
• derandomisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61722306, 61473137], and the National First-Class Discipline Program of Light Industry Technology and Engineering [grant number LITE2018-25].

Notes on contributors

Xiaoli Luan

Xiaoli Luan received the B.Sc. degree in industrial automation from Jiangnan University, China, in 2002; the M.Sc. degree in control theory and control engineering from Jiangnan University, China, in 2006; and the Ph.D. degree in control theory and control engineering from Jiangnan University, China, in 2010. Now she is a professor of the Institute of Automation, Jiangnan University. In 2016, she was a Visiting Professor with the University of Alberta, Canada. Her research interests include robust control and optimisation of complex nonlinear systems.

Haiying Wan

Haiying Wan is a Ph.D. candidate of the Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Institute of Automation, Jiangnan University. Her current research interests include robust control and finite frequency control of multimode systems.

Fei Liu

Fei Liu received the B.Sc. degree in electrical technology from Wuxi Institute of Light Industry, China, in 1987; the M.Sc. degree in industrial automation from Wuxi Institute of Light Industry, China, in 1990; and the Ph.D. degree in control science and control engineering from Zhejiang University, China, in 2002. From 1990 to 1999, he was an Assistant, Lecturer, and Associate Professor in Wuxi Institute of Light Industry. Since 2003, he has been a Professor of the Institute of Automation, Jiangnan University. In 2006, he was a Visiting Professor with the University of Manchester, UK. His research interests include advanced control theory and applications, batch process control engineering, statistical monitoring and diagnosis in industrial process, and intelligent technique with emphasis on fuzzy and neural systems.