1 PERFORMANCE GUARANTEE CONTROL OF NONLINEAR SYSTEMS: SEMI-GLOBAL CASE

In this paper, we consider nonlinear systems which satisfy the generalized sector conditions in a given region X. We adopt Piecewise Linear Lyapunov Functions (PLLFs), and consider ζ1 control problem. We use PLLFs to get an estimate of the state space region with guaranteed ζ1 performance, that is, if the initial state belongs to the region and the disturbance is bounded in ζ1 sense, then the state stays in X and ζ1 performance is guaranteed. We formalize the design issue as bilinear programming problem and propose a scheme to solve it. We show examples to demonstrate the usefulness of the results.