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Finite time chaos control for a class of chaotic systems with input nonlinearities via TSM scheme. (English) Zbl 1263.93108
Summary: This paper investigates nonsingular terminal sliding mode control for a class of uncertain systems with nonlinear inputs and its application in chaos control. When some of the system states are finite-time stable, the nonlinear items that coupled with these states may come into zeros in other subsystems. This will simplify the stability analysis of the whole system greatly. Compared with the traditional finite-time stabilization design method, the introduction of the terminal sliding mode can reduce the input dimensions. Only one control input is requested to realize chaos control of the Liu system when unmatched uncertainties and input nonlinearity coexist. The parameter matrices in the TSM can be determined through the solution of LMIS. Simulation results are given to demonstrate the effectiveness of the proposed method.

##### MSC:
 93C15 Control/observation systems governed by ordinary differential equations 34H10 Chaos control for problems involving ordinary differential equations 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 34C28 Complex behavior and chaotic systems of ordinary differential equations
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