Robust control for nonlinear systems with uncertain time-varying parameters coupled with non-triangular terms

ABSTRACT

In this paper, a robust control scheme is proposed for a class of nonlinear systems which consist of uncertain time-varying parameters that are coupled with non-triangular terms, perturbed nonlinearity, and external disturbance. In order to deal with time-varying parameters, we provide determination process of allowed time-varying parameters utilising a Lyapunov equation. With system analysis associated with perturbed nonlinearity, we show that all states of the controlled system remain bounded by a gain-scaling feedback controller in the presence of external disturbance. Moreover, the ultimate bounds of some system states can be made (arbitrarily) small by adjusting a gain-scaling factor depending on the system nonlinearity. The effectiveness of our control scheme is shown via an application example, with comparison of the existing result.

KEYWORDS:

• Nonlinear systems
• non-triangular terms
• uncertain time-varying parameters
• perturbed nonlinearity
• ultimate bounds

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ho-Lim Choi  http://orcid.org/0000-0001-6471-0333

Additional information

Funding

This work was supported by the Dong-A University research fund.

Notes on contributors

Sang-Young Oh

Sang-Young Oh received the B.S.E. degree from the Department of Electrical Engineering, Dona-A University, Busan, Korea in 2013 and M.S. degree in 2015, respectively. He is currently working toward a Ph.D. degree. His research interests include nonlinear system control problems including optimal controls, feedback linearization problems, time-delay issues. He is a member of IEEE, ICROS, and KIEE.

Ho-Lim Choi

Ho-Lim Choi received the B.S.E. degree from the department of electrical engineering, The Univ. of Iowa, USA in 1996, and M.S. degree in 1999 and Ph.D degree in 2004, from KAIST, respectively. Currently, he is a professor at department of electrical engineering, Dong-A University, Busan. His research interests are in the nonlinear control problems with emphasis on feedback linearization, gain scheduling, singular perturbation, output feedback, time-delay systems, time-optimal control. He is a senior member of IEEE.