| Composite quadratic Lyapunov functions for constrained control systems (2003) | |||||||||||||||||
Abstract | |||||||||||||||||
| The composite quadratic function based on a group of quadratic functions was introduced in our recent pa-per [7]. Some important properties of this Lyapunov function were revealed. We showed that this function is continuously differentiable and its level set is the con-vex hull of a group of ellipsoids. In this paper, we use these results to study the set invariance properties of linear systems with input and state constraints. We show that for a system under a given saturated linear feedback, the convex hull of a group of invariant ellip-soids is also invariant. If each ellipsoid in a group can be made invariant with a bounded control of the satu-rating actuator, then their convex hull can also be made invariant by the same actuator. For a group of ellip-soids, each invariant under a separate saturated linear feedback, we also present a method for constructing a nonlinear continuous feedback law which makes their convex hull invariant. | |||||||||||||||||
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