Bounds for quadratic Lyapunov functions

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...

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 optimal quadratic Lyapunov functions for polynomial systems

Abstract The problem of estimating the Domain of Attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem, a semi-convex approach based on Linear Matrix Inequalities (LMIs) is proposed. Moreover, for the...