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

We develop a method for computing a region in state space over which a nonlinear system is guaranteed by a given polytopic control Lyapunov function to be stable in closed loop under some appropriate control law. For systems which are nonlinear in only a few state variables, the procedure is computationally tractable; the computation time required to evaluate stability over each cone comprising a level set of the Lyapunov function is exponential in the number of "nonlinear states" but otherwise polynomial in the dimension of the full state space. Control constraints and robustness to bounded disturbances are easily incorporated. © 1998 Elsevier Science B.V. All rights reserved.