Sufficient conditions for the genericity of feedback stabilisability of switching systems via Lie-algebraic solvability

TL;DR

This paper establishes sufficient conditions ensuring that the feedback stabilizability of switching systems is generically achievable through Lie-algebraic solvability, providing a practical approach for control design.

Contribution

It introduces new sufficient conditions for generic Lie-algebraic solvability in switching systems, enhancing control design methods based on this property.

Findings

Conditions for generic Lie-algebraic solvability derived

Applicable to almost all system parameters

Efficient numerical implementation proposed

Abstract

This paper addresses the stabilisation of discrete-time switching linear systems (DTSSs) with control inputs under arbitrary switching, based on the existence of a common quadratic Lyapunov function (CQLF). The authors have begun a line of work dealing with control design based on the Lie-algebraic solvability property. The present paper expands on earlier work by deriving sufficient conditions under which the closed-loop system can be caused to satisfy the Lie-algebraic solvability property generically, i.e. for almost every set of system parameters, furthermore admitting straightforward and efficient numerical implementation.