Observer-Based Sampled-Data Stabilisation of Switched Systems with Lipschitz Nonlinearities and Dwell-Time

TL;DR

This paper presents a method for stabilising switched systems with nonlinearities using sampled-data output feedback and Lyapunov-based LMIs, applicable to power systems and other engineering fields.

Contribution

It introduces a novel sampled-data switching law with LMIs that incorporate observer gains and simplifies stability conditions for practical implementation.

Findings

Derived time-dependent LMI conditions for stability and boundedness.

Provided reduced-order LMIs and discretisation techniques for easier feasibility analysis.

Numerical examples demonstrate effectiveness and compare with existing methods.

Abstract

We investigate the stabilisation of nominally linear-affine switched systems with uncertain Lipschitz nonlinearities under dwell-time constraints, using a sampled-data switching law based on a state observer. We design the switching law based on Lyapunov-Metzler inequalities, accounting for the sampled-data output measurements, and we derive time-dependent LMI conditions for global asymptotic stability (or, in the presence of switching affine terms, ultimate boundedness) of the resulting closed-loop system. We obtain an estimate of the average quadratic cost and a bound on its maximum deviation from the actual cost. Moreover, we discuss the feasibility of the derived LMIs. Specifically, we show how the observer gains can be incorporated into the matrix inequalities, provide equivalent reduced-order LMI conditions, and prove that the time dependence of the LMIs can be removed by discretising on a finite grid. Numerical examples, including practical applications to real-world engineering scenarios in power systems, illustrate our theoretical results and compare them with an existing approach for output-feedback stabilisation of switched systems, subject to sampled-data measurements