Induced ℒ_∞ control for continuous-time nonlinear systems

Abstract

In this paper, the problem of induced ${\mathcal{L}}_{\mathrm{\infty }}$ control in the presence of disturbance signals in the control output of continuous-time nonlinear systems is considered. Under the condition that the system control output has a disturbance signal, the expected design conditions of the controller that satisfy the asymptotic stability and the specified performance are given. The sufficient conditions for such an induced ${\mathcal{L}}_{\mathrm{\infty }}$ controller are expressed in terms of linear matrix inequalities (LMIs). Finally, the effectiveness and feasibility of the proposed induced ${\mathcal{L}}_{\mathrm{\infty }}$ control design strategy is illustrated by a tunnelling diode circuit.

Keywords:

• Nonlinear systems
• fuzzy systems
• induced ${\mathcal{L}}_{\mathrm{\infty }}$ performance
• dynamic output feedback control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Li-Wei Hou

Li-Wei Hou received the B.E. degree in automation from Heilongjiang University of Science and Technology, Harbin, China, in 2020. He is currently pursuing the M.S. degree in the College of Control Science and Engineering, Bohai University, Jinzhou, China.His research interests include fuzzy control systems, networked control systems.

Xiao-Heng Chang

Xiao-Heng Chang (M-11) received the B.E. and M.S. degrees from Liaoning Technical University, Fuxin, China, in 1998 and 2004, respectively, and the Ph.D. degree from Northeastern University, Shenyang, China, in 2007.He is currently a professor with the College of Engineering, Bohai University, Jinzhou, China, and is also a professor with the Institute of Automation, Bohai University, Jinzhou, China. His research interests include fuzzy control systems, networked control systems and robust control.Prof. Chang is an associate editor of Applied Mathematics and Computation, International Journal of Control, Automation and Systems, Transactions of the Institute of Measurement and Control and Frontiers in Control Engineering, and an academic editor/guest editor of Mathematical Problems in Engineering. He is also an editorial board member of International Journal of Modelling, Identification and Control and Journal of Computational and Cognitive Engineering.