State feedback ℋ∞ control design of continuous-time switched affine systems

This study deals with state feedback ℋ_∞ control design of continuous-time switched affine systems. The main purpose is to design a set of state feedback gains together with a switching function assuring global asymptotic stability of a desired equilibrium point. The equilibrium point belongs to a set of attainable ones to be determined. Moreover, the control design must take into account a pre-specified upper bound to the ℒ₂ gain from the external input to the controlled output. Two different switching functions are proposed and discussed. The first one depends only on the state and the other depends also on the external input. The results are compared with recent ones available in the literature to date, as for instance, those based on a max-type Lyapunov function and those commonly used to assure practical stability. Numerical examples illustrate the theoretical results and are used for comparisons.