Robust Finite-Time Bounded Controller Design of Time-Delay Conic Nonlinear Systems Using Sliding Mode Control Strategy

The finite-time sliding mode controller design problem of a class of conic-type nonlinear systems with time-delays and mismatched external disturbance is studied. The time-delay conic nonlinearities are considered to lie in a known hypersphere with an uncertain center. A scalar selection criterion dependent sliding mode control (SMC) law is constructed to drive the state trajectories onto the specified sliding surface during any assigned short time interval. By using slack matrix approach, a delay-dependent sufficient condition is derived to ensure the finite-time boundedness of the closed-loop systems over the finite-time interval. Then, the algorithm for designing the finite-time SMC law is established. Finally, two examples related to the time-delayed Chua's circuit is given to demonstrate the effectiveness of the developed methods.