Properties of the Composite Quadratic Lyapunov Functions

Composite quadratic Lyapunov functions for constrained control systems

The composite quadratic function based on a group of quadratic functions was introduced in our recent paper [7]. Some important properties of this Lyapunov function were revealed. We showed that this function is continuously differentiable and its level set is the convex hull of a group of ellipsoids. In this paper, we use these results to study the set invariance properties of linear systems w...

On quadratic Lyapunov functions

Quadratic Control Lyapunov Functions for Bilinear Systems

In this paper the existence of a quadratic control Lyapunov function for bilinear systems is considered. The existence of a control Lyapunov function ensures the existence of a control law which ensures the global asymptotic stability of the closed loop control system. In this paper we will derive conditions for the existence of a control Lyapunov function for bilinear systems. These conditions...

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...

Improving Efficiency in the Computation of Piecewise Quadratic Lyapunov Functions

In a series of papers, the authors have developed a method for analysis of piecewise linear systems. The idea is to use Lyapunov functions that are piecewise quadratic. Such Lyapunov functions can be computed via convex optimization in terms of linear matrix inequalities. This paper presents two approaches for improving the efficiency of these computations. It is shown that by splitting the ana...