Dynamic system of relative degree two controlled by discontinuous-hybrid-impulsive feedback in the presence of bounded perturbations is considered. The state feedback impulsive-twisting control exhibits a uniform exact finite time convergence to the second-order sliding mode with zero convergence time. The output feedback discontinuous control augmented by a simplified hybrid-impulsive functions provides uniform exact convergence with zero convergence time of the system's states to a real second-order sliding mode in the presence of bounded perturbations. Only 'snap' knowledge of the output derivative, that is, the knowledge of the output derivative in isolated time instants, is required. The output feedback hybridimpulsive control with practically implemented impulsive actions asymptotically drives the system's states to the origin. The Lyapunov analysis of the considered hybrid-impulsive-discontinuous system proves the system's stability. The efficacy of the proposed control technique is illustrated via computer simulations.2-SM, second-order sliding mode.
1074Y. SHTESSEL ET AL.assume that T δ,i + 1 = T δ,i , then the gain K is to be selected to meet inequality 1090 Y. SHTESSEL ET AL.
The perturbed system with input-output dynamics of arbitrary and well-defined relative degree is considered in a reduced information environment. A novel impulsive second-order sliding mode control in the reduced information environment is proposed. The almost instantaneous convergence to the origin is achieved via impulsive control acting in a concert with second-order sliding mode control, specifically supertwisting and twisting algorithms. The impulsive actions are implemented in a piecewise constant format. Numerical examples illustrate the efficiency of the proposed control algorithms. KEYWORDS impulsive control, reduced information environment, second-order sliding mode control Int J Robust Nonlinear Control. 2018;28:2909-2926.wileyonlinelibrary.com/journal/rnc
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