Lifted polytope methods for stability analysis of switching systems

TL;DR

This paper introduces innovative lifted polytope methods that enhance the stability analysis of switching systems by combining existing ideas and reducing computational complexity through a pruning algorithm.

Contribution

It presents a novel combination of polytope norm iteration and lifting procedures, along with a pruning algorithm, to improve stability analysis efficiency.

Findings

The methods extend finiteness results for unlifted matrix sets.

Numerical examples demonstrate good performance and computational benefits.

The approach offers a new theoretical framework for stability analysis.

Abstract

We describe new methods for deciding the stability of switching systems. The methods build on two ideas previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of these two ideas allows us to introduce a pruning algorithm which can importantly reduce the computational burden. We prove several appealing theoretical properties of our methods like a finiteness computational result which extends a known result for unlifted sets of matrices, and provide numerical examples of their good behaviour.