Robust H∞ Control for Nonlinear Uncertain Switched Descriptor Systems with Time Delay and Nonlinear Input: A Sliding Mode Approach

Abstract

This paper addresses the problem of sliding mode control (SMC) design for a class of uncertain switched descriptor systems with state delay and nonlinear input. An integral sliding function is designed and an adaptive sliding mode controller for the reaching motion is then synthesised such that the trajectories of the resulting closed-loop system can be driven onto a prescribed sliding surface and maintained there for all subsequent times. Moreover, based on a new Lyapunov-Krasovskii functional, a delaydependent sufficient condition is established such that the admissibility as well as the ∞ performance requirement of the sliding mode dynamics can be guaranteed in the presence of time delay, external disturbances, and nonlinear input which comprises dead-zones and/or sector nonlinearities. The major contributions of this paper of this approach include (i) the closed-loop system exhibiting strong robustness against nonlinear dynamics and (ii) the control scheme enjoying the chattering-free characteristic. Finally, two representative examples are given to illustrate the theoretical developments.

Robust Asynchronous H∞ Observer-Based Control Design for Discrete-Time Switched Singular Systems with Time-Varying Delay and Sensor Saturation: An Average Dwell Time Approach

“…It should be noted that time-delay occurrence represents, usually, a source of instability and poor performance of dynamic systems. As a result, the study of switched singular delayed systems has aroused considerable attention [8][9][10][11][12].…”

Robust sliding model control-based adaptive tracker for a class of nonlinear systems with input nonlinearities and uncertainties

“…However, Li et al (2012) and Pai (2019) only developed the control strategy to solve the stabilization problems with known bounds of input nonlinearity and uncertainties; therefore, these papers cannot apply to the systems with unknown bounds of input nonlinearities. Kchaou and Ahmadi (2017) proposed an adaptive law with high order. Moreover, the paper (Mondal and Mahanta, 2013) mentioned that the adaptive law should avoid overestimation.…”

“…As for the input nonlinearity issue, the work (Li et al, 2012) indicates that the input nonlinearity phenomenon does exist in the real physical applications due to the actuator with limitations. For example, in Pai (2019), the author utilizes SMC to process a class of uncertain time-delay nonlinear systems with input nonlinearity; in Kchaou and Ahmadi (2017), the authors indicate that input nonlinearity consist of dead-zones and/or sector nonlinearities. However, Li et al (2012) and Pai (2019) only developed the control strategy to solve the stabilization problems with known bounds of input nonlinearity and uncertainties; therefore, these papers cannot apply to the systems with unknown bounds of input nonlinearities.…”

Robust Control for Switched Systems With Unmatched Uncertainties Based on Switched Robust Integral Sliding Mode

“…Recently, the ISM method has been successfully applied to the uncertain SS to compensate exactly the matched uncertainties or perturbations. For example, Kchaou and Ahmadi extended an adaptive SMC design based on the switched integral sliding mode (SISM) for a class of uncertain switched descriptor systems with state delay and nonlinear input [26]. Ferrara et al proposed a switching structure scheme for the motion control of industrial robot manipulators [27].…”