Relations between Common Quadratic Lyapunov Functions and Common Infinity-Norm Lyapunov Functions

A result on common quadratic Lyapunov functions

In this paper we define strong and weak common quadratic Lyapunov functions (CQLF’s) for sets of linear time-invariant (LTI) systems. We show that the simultaneous existence of a weak CQLF of a special form, and the non-existence of a strong CQLF, for a pair of LTI systems, is characterised by easily verifiable algebraic conditions. These conditions are found to play an important role in provin...

Preservation of common quadratic Lyapunov functions and Padé approximations

It is well known that the bilinear transform, or first order diagonal Padé approximation to the matrix exponential, preserves quadratic Lyapunov functions between continuous-time and corresponding discrete-time linear time invariant (LTI) systems, regardless of the sampling time. It is also well known that this mapping preserves common quadratic Lyapunov functions between continuous-time and di...

The Computation of Common Infinity-norm Lyapunov Functions for Linear Switched Systems

Abstract. This paper studies the problem of the computation of common infinity-norm Lyapunov functions. For a set of continuous-time LTI systems or discrete-time LTI systems whose system matrices are upper triangular form or lower triangular form, it is proved that there exist common infinity-norm Lyapunov functions for them. Then four algorithms of computing common infinity-norm Lyapunov funct...

On common linear/quadratic Lyapunov functions for switched linear systems

Using duality and complementarity ideas, and Z-transformations, in this article, we discuss equivalent ways of describing the existence of common linear/quadratic Lyapunov functions for switched linear systems. In particular, we extend a recent result of Mason-Shorten on positive switched system with two constituent linear time-invariant systems to an arbitrary finite system.

On quadratic Lyapunov functions