High Performance Super-twisting Control for State Delay Systems

Robust stabilisation of linear time‐invariant time‐delay systems via first order and super‐twisting sliding mode controllers

“…As stated above, the super-twisting SMC scheme for time-delay systems has scarcely been investigated. The lack of information regarding the design steps for the super-twisting SMC proposed in [5] precludes the development of a comparative analysis with the SMC proposed in this study.…”

“…Lemma 1: Consider the transformed system (2) and the sliding surface s(t) defined in (5). If there exist a Lyapunov function V(t) and real numbers β > 0 and 0 < γ < 1 such that…”

“…In recent years, many research works have been published concerning the stability analysis of time delay systems based for example on the characteristic equation method or on Lyapunov theory techniques. To facilitate the analysis, some of them consider partitions or approximations of the time-delay [4][5][6][7]. Nevertheless, the presence of uncertainties and external disturbances affects analysis performance.…”

“…To the best knowledge of the authors, the only research works that address the super-twisting SMC design for time-delay systems are presented by Khimani and Patil [5] and Caballero-Barragan et al [17,18]. Khimani and Patil [5] present a conventional first-order and a second-order SMC that give rise to improved transient responses for a class of uncertain time-delay systems.…”

Exoskeleton Hand Control by Fractional Order Models

“…The exponential stability of nonlinear FOM using the Lyapunov method was analyzed in [24,25]. Other control problems for a class of FOMs with delay were rigorously investigated in [26,27]. Reference [28] proposed an observer for a class of linear and nonlinear FOM using Lyapunov methods.…”