On the control of uncertain impulsive systems: approximate stabilization and controlled invariance

Abstract

The problems of stabilization and controlled invariance of a fairly wide class of uncertain hybrid systems is considered. Uncertainty enters in the form of a disturbance input that can affect both the continuous and the discrete dynamics. A method for designing piecewise constant, feedback controllers for this class of systems is developed. In the case of controlled invariance, the controller ensures that the state of the system remains arbitrarily close to a desired set over an arbitrarily long time horizon. In the case of stabilization, the controller ensures approximate exponential convergence of the runs of the closed loop system to the zero level set of a Lyapunov function.

Acknowledgement

The work was supported by the EPSRC under grant GR/R51575/01 and by the European Commission under the project COLUMBUS, IST-2001-38314.

Notes

 Conditions under which the sampling period can be chosen independently of the state are discussed in subsequent sections.