Lyapunov function normalization for controlled switching of hybrid systems

We consider tools for control of switched nonlinear systems using Lyapunov function-based techniques. We focus our efforts on those switched nonlinear systems that admit a single equilibrium point that is common to all subsystems, and have stability properties encoded in Lyapunov functions for each subsystem. We develop techniques by which independent Lyapunov functions can be normalized so that switching surfaces are implicitly generated and switches guarantee some level of system performance, including stability and state convergence.