Quadratic Lyapunov functions for systems with state-dependent switching

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...

Switching Lyapunov Functions for Periodic TS Systems

This paper considers the stability analysis of periodic Takagi-Sugeno fuzzy models. For this we use a switching Lyapunov function defined at the time instants when the subsystems switch. Using the developed conditions we are able to prove the stability of periodic TS systems where the local models or even the subsystems are unstable. The application of the conditions is illustrated on numerical...

Piecewise-quadratic Lyapunov functions for systems with deadzones or saturations

A piecewise quadratic Lyapunov function is developed for the analysis of the global and regional performances for systems with saturation/deadzone in a general feedback configuration with an algebraic loop. This piecewise quadratic Lyapunov function effectively incorporates the structure of the saturation/deadzone nonlinearity. Several sector-like conditions are derived to describe the complex ...

On 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...