Robust Stabilization and Disturbance Rejection for a Class of Hybrid Linear Systems Subject to Exponential Uncertainty

In this paper, we address the problem of robust stabilization and disturbance rejection for a class of hybrid linear systems subject to exponential uncertainties. By using Taylor series approximation and convex polytope technique, the exponentially uncertain hybrid linear system is transformed into an equivalent hybrid polytopic model subject to norm bounded uncertainty. For such equivalent hybrid linear model, we design its switching strategy and associated state feedback controllers so that such model is asymptotically stable with $H∞$ disturbance attenuation based on multiple Lyapunov function technology and linear matrix inequality (LMI) approach.