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 la w. 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 Lya punov function is exponential in the number of ''nonlinear states'' bu t otherwise polynomial in the dimension of the full state space. Contr ol constraints and robustness to bounded disturbances are easily incor porated. (C) 1998 Elsevier Science B.V. All rights reserved.