A control Lyapunov function approach to robust stabilization of nonlinear systems

We propose an alternative to gain scheduling for stabilizing a class of nonlinear systems. The computation times required to find stability regions for a given control Lyapunov function vary polynomially with the state dimension for a fixed number of scheduling variables. Control Lyapunov functions to various trim points are used to expand the stability region, and a Lyapunov based synthesis formula yields a control law guaranteeing stability over this region. Robustness to bounded disturbances is easily handled, and the optimal stability margin, defined as a Lyapunov derivative, is recovered asymptotically. We apply the procedure to an example.