6 Discrete-time Terminal Sliding Mod: Concept
The behavior of the system in sliding mode is determined by the sliding manifold upon which the system states are constrained. Sliding hyperplanes, being the most generally used manifolds guarantee asymptotic stability of the system in the sliding mode. This would mean that the system states converge to the origin, but generally at an infinite time. Terminal sliding mode (TSM) control  aims at designing a sliding mode control strategy that would guarantee a finite time convergence to the origin. This is accomplished by using a nonlinear sliding line which results in finite time convergence . The concept of terminal sliding mode in continuous time systems has been studied in detail [56, 79–81]. The discrete-time equivalent of the continuous time terminal sliding mode control would be investigated in this chapter.
KeywordsControl Input Slide Mode Control Sliding Mode Time Convergence Continuous Time System
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