Analysis and control for a new chaotic system via piecewise linear feedback

Abstract This paper presents a new three-dimensional chaotic system containing two system parameters and a nonlinear term in the form of arc-hyperbolic sine function. The complicated dynamics are studied by virtue of theoretical analysis, numerical simulation and Lyapunov exponents spectrum. The system proposed is converted to an uncertain piecewise linear system. Then, based on piecewise quadratic Lyapunov function technique, the global control of the new chaotic system with α -stability constraint via piecewise linear state feedback is studied, where the optimal controller maximizing the decay rate α can be obtained by solving an optimization problem under bilinear matrix inequalities (BMIs) constraints.

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