Parameter-dependent conditions for H_∞ stabilisation of polynomial parameter-varying system with delay

Abstract

This paper considers the problems of achieving exponential stability and $H_{\mathrm{\infty }}$ stabilisation for polynomial parameter-varying system with time-varying delay. Unlike some existing linear parameter-varying results that treat system parameters as time invariant factors, this paper makes full use of the nonlinearity and time-varying characteristics of system through introducing a novel delay-and-parameter-dependent Lyapunov function. The main conclusions are discussed in three cases (system without input, system with disturbance input, system with disturbance input and control input). And the $H_{\mathrm{\infty }}$ stabilisation problem is solved by constructing a controller which is inserted with system parameters and their derivatives. The structures of Lyapunov function and controller lead to that the derived criteria for exponential stabilisation are expressed by state-and-parameter-dependent linear matrix inequalities, which are efficiently solved by sum-of-squares program. The effectiveness and superiority are verified through two numerical examples.

Keywords:

• Polynomial parameter-varying system
• delay-and-parameter-dependent Lyapunov function
• $H_{\mathrm{\infty }}$ stabilisation
• time-varying delay
• sum-of-squares

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Science and Technology Major Project (2017-V-0004-0054) and Research Project (PZ2020016).