This article proposes a time‐varying nonsingular terminal sliding mode (TSM) control for a class of uncertain second‐order nonlinear system and its application to n‐links rigid robotic manipulators. First, a time‐varying nonsingular terminal sliding manifold is developed by incorporating a piecewise‐defined function of time into a nonsingular TSM manifold. As a result, the singularity problem is avoided and the reaching phase existing in conventional TSM control is totally suppressed which ensures the global robustness of the system against uncertainties and disturbances. Moreover, adaptive tuning laws are developed to omit the requirement of prior knowledge of the upper bound of the lumped uncertainty. In particular, an effective method is provided for the parameters selection to meet a prespecified convergence time. Hence, the convergence time to the origin of the tracking errors can be specified in advance according to the mission requirements. The formulation of the controllers and the stability analysis are verified by Lyapunov theory. Simulation results and comparative studies are presented to demonstrate the effectiveness and the superiority of the proposed algorithms.
Researchers have explored the concept of “practical stability” in the literature, pointing out that stability investigations always guarantee “practical stability” and the inverse is not true. The concept “practical stability” means that the origin is not an equilibrium point and the convergence of the system state is towards a ball centered at the origin. The primary purpose of this work is to investigate the notation of practical stability for a new class of fractional-order systems using the general conformable derivative. As a second objective, the nonlinear condition chosen is novel in that it is not Lipschitz as is customary, which is original in and of itself. In addition, some new analysis related to the LMI techniques was used to prove the main results. To begin, a method of stabilization is provided. Following that, the proposed system’s observer design is presented. Also, the principle of separation is described. Finally, a numerical example is offered to demonstrate the proposed methodology’s validity.
This article investigates the practical exponential stability and design problems of conformable time-delay systems. Sufficient conditions that confirm the practical exponential stability and design of the proposed class of systems are given by utilizing an adequate Lyapunov–Krasovskii functional (L-KF). These conditions are expressed in the form of linear matrix inequalities (LMI) which could be solved by using solvers in LMI Toolbox of MATLAB. Two numerical examples are given to illustrate the applicability of the proposed results.
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