Stability of switched linear differential systems

TL;DR

This paper investigates the stability of switched linear differential systems with complex mode interactions, providing new LMI-based criteria and exploring the role of positive-realness for specific cases.

Contribution

It introduces sufficient LMI conditions for stability of systems with general gluing conditions and analyzes positive-realness in two-mode systems.

Findings

LMI-based stability conditions for general gluing conditions

Positive-realness criteria for two-mode systems

Enhanced understanding of trajectory concatenation at switching points

Abstract

We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching instants is specified by gluing conditions, i.e. algebraic conditions on the trajectories and their derivatives at the switching instant. We provide sufficient conditions for stability based on LMIs for systems with general gluing conditions. We also analyse the role of positive-realness in providing sufficient polynomial-algebraic conditions for stability of two-modes switched systems with special gluing conditions.