Hybrid control of switched LFT uncertain systems with time-varying input delays

Abstract

This paper addresses the problem of hybrid control for a class of switched uncertain systems. The switched system under consideration is subject to structured uncertain dynamics in a linear fractional transformation (LFT) form and time-varying input delays. A novel hybrid controller is proposed, which consists of three major components: the integral quadratic constraint (IQC) dynamics, the continuous dynamics, and the jump dynamics. The IQC dynamics are developed by leveraging methodologies from robust control theory and are utilised to address the effects of time-varying input delays. The continuous dynamics are structured by feeding back not only measurement outputs but also some system's internal signals. The jump dynamics enforce a jump (update/reset) at every switching time instant for the states of both IQC dynamics and continuous dynamics. Based on this, robust stability of the overall hybrid closed-loop system is established under the average dwell time framework with multiple Lyapunov functions. Moreover, the associated control synthesis conditions are fully characterised as linear matrix inequalities, which can be solved efficiently. An application example on regulation of a nonlinear switched electronic circuit system has been used to demonstrate effectiveness and usefulness of the proposed approach.

Keywords:

• Switched systems
• hybrid switching and impulsive control
• time-varying input delay
• linear fractional transformation
• linear matrix inequality

Disclosure statement

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

Additional information

Funding

This work was partially supported by the National Science Foundation (NSF) [grant number CMMI-1952862].