Lyapunov Differential Equation Hierarchy and Polynomial Lyapunov Functions for Switched Implicit Systems

摘要

This paper investigates stability analysis for implicit, switched linear systems using homogeneous Lyapunov functions (HLF). HLFs of increasing degree are constructed through an outer-product, lifting transformation of the state vector to higher dimensions. This paper presents linear matrix inequalities sufficient conditions for asymptotic stability of these systems based on HLFs. A method is provided to search for Lyapunov functions by incrementally increasing the degree of the homogeneous Lyapunov functions. To address the dimensional growth of the problem space incurred by the lifting transform, a method for dimensional reduction is derived.