L₂ bumpless transfer control for switched linear systems with stability

ABSTRACT

This paper focuses on the issue of $L_2$ bumpless transfer control for a class of switched linear systems with stability. First, a concept of $L_2$ bumpless transfer performance for a system in this class is introduced. Second, sufficient conditions for the $L_2$ bumpless transfer performance, stabilisation and disturbance rejection are presented by co-design of a switching law and a compensator. The sufficient conditions allow each closed-loop subsystem not to satisfy the $L_2$ bumpless transfer performance, stabilisation and disturbance rejection. Furthermore, a solution to the $L_2$ bumpless transfer control problem for the system with stability is also provided in terms of linear matrix inequalities (LMIs). Finally, an example is given to show the effectiveness of the proposed method.

KEYWORDS:

• Switched linear systems
• $L_2$ bumpless transfer control
• stability
• disturbance attenuation
• multiple lyapunov functions method

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jun Zhao  http://orcid.org/0000-0001-9096-103X

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grant 61233002, the 111 Project (B16009) and IAPI Fundamental Research Funds under Grant 2013ZCX03-01.

Notes on contributors

Ying Zhao

Ying Zhao is a Ph.D. candidate at the College of Information Science and Engineering, Northeastern University, China. Her research interests include constrained problems of switched systems and aero-engine control design.

Jun Zhao

Jun Zhao is a professor at the Northeastern University, Liaoning, China. From 1998 to 1999, he was a senior visiting scholar at the Coordinated Science Laboratory, University of Illinois Urbana-Champaign, IL, USA. From 2003 to 2005, he was a research fellow in the Department of Electronic Engineering, City University of Hong Kong. His main research interests include switched systems, hybrid control, nonlinear systems and robust control.