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ROBUST STABILIZATION FOR MULTI-INPUT POLYTOPIC NONLINEARSYSTEMS

Lipo MO   

  1. College of Computer and Information Engineering, Beijing Technology and Business University
  • Received:2008-06-26 Revised:1900-01-01 Online:2011-02-25 Published:2011-02-25

Lipo MO. ROBUST STABILIZATION FOR MULTI-INPUT POLYTOPIC NONLINEARSYSTEMS[J]. Journal of Systems Science and Complexity, 2011, 24(1): 93-104.

This paper deals with the problem of the stabilization for multi-input polytopic nonlinear systems. Based on the robust control Lyapunov function, a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controller is derived. It is shown that the obtained sufficient condition is also necessary if there exists a state feedback controller such that the closed-loop system has a robust Lyapunov function for all possible uncertainties. Moreover, a universal formula for constructing stabilizing controller is proposed and the existence of the corresponding Lyapunov function is proven. Particularly, a
Lyapunov function is constructed for the polytopic nonlinear system in canonical form. Finally, the feasibility of the proposed control law is verified by a numerical example.
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