Polytopic control Lyapunov functions for robust stabilization of a class of nonlinear systems

Nonlinear control systems can be stabilized by constructing control Lyapunov functions and computing the regions of state space over which such functions decrease along trajectories of the closed loop system under an appropriate control law. For systems whose dynamics are nonlinear in only a few state variables, we develop a method for computing such a region based on a given polytopic control Lyapunov function. The procedure is computationally tractable, in the sense that computation times vary polynomially with the state dimension for a fixed number of `nonlinear states.' Control constraints and robustness to bounded disturbances are easily incorporated into this framework.