UC Santa Cruz

We propose tools for the study of robust stabilizability and the design of robustly stabilizing feedback laws for a wide class of hybrid systems given in terms of hybrid inclusions with inputs and disturbances. We introduce notions of ro-bust uniform global stabilizability and stabilization that cap-ture the case when disturbances can be fully rejected, prac-tically rejected, and when they induce a residual set that can be stabilized. Robust control Lyapunov functions are em-ployed to determine when stabilizing static state-feedback laws are available and also to synthesize robustly stabiliz-ing feedback laws with minimum pointwise norm. Sufficient conditions on the data of the hybrid system as well as on the control Lyapunov function are proposed for the said proper-ties to hold. An example illustrates the results throughout the paper.