Exponential stability of a certain class of hybrid systems and digital feedback stabilizers

Due to the use of digital feedback controllers in the control of continuous-time systems, new methods of analysis must be developed in order to study the behaviour of the resulting closed-loop system. These closed-loop systems are hybrid systems in the sense that some of their states evolve in continuous time while others change only in a discrete time set. In this work we study and characterize the exponential stability of the hybrid systems that result from the use of piecewise constant feedback control laws in the control of general nonlinear systems. We apply these results to the problem of stabilization via digital feedback controllers.