## Robust stabilization of discrete-time nonlinear Lur’e systems with sector and slope restricted nonlinearities.(English)Zbl 1146.93017

Summary: We present a novel method for the robust control problem of uncertain nonlinear discrete-time linear systems with sector and slope restrictions. The nonlinear function considered in this paper is expressed as convex combinations of sector and slope bounds. Then the equality constraint is derived by using convex properties of the nonlinear function. A stabilization criterion for the existence of the state feedback controller is derived in terms of linear matrix inequalities (LMIs) by using Finsler’s lemma. The proposed method is demonstrated by a system with saturation nonlinearity.

### MSC:

 93B35 Sensitivity (robustness) 93C41 Control/observation systems with incomplete information 93C10 Nonlinear systems in control theory 93C55 Discrete-time control/observation systems

### Keywords:

Lur’e systems; sector and slope bound; LMIs
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### References:

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