This paper presents a systematic approach for nonlinear control design by using the gain scheduling technique to insure the transition of a nonlinear dynamical process from an actual operating condition to a desired one. The nonlinear system is represented in neighborhoods of equilibrium points by a family of polytopic uncertain linear systems. The nonlinear equations of the system are imbedded in the interior of an inclusion polyhedron. A robust control law is built so as to insure asymptotic stability to a given equilibrium within a maximal ellipsoidal region contained in the interior of the polyhedron. Given a pre-specified equilibrium curve connecting the initial and final points, it is shown how to fix a sequence of equilibrium points together with the local associated ellipsoids covering the curve and enabling a convergent control sequence. State feedback and output feedback for the local robust control synthesis are considered, together with local performance criteria. A simple numerical experiment is provided to illustrate both the effectiveness of the synthesis and the performance achieved.
Gain Scheduling, Transition Control, Polytopic Uncertainty, Quadratic Stability, Linear Matrix Inequalities (LMI).
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