Sliding Mode Control for Linear Systems with Time-Varying Input and State Delays

Abstract

This paper deals with a sliding mode control for linear systems with input and state time-varying delays. Two different time delays are considered for the sliding mode control of a continuous linear system. Delay-dependent sufficient conditions are given for the existence of sliding manifolds in terms of linear matrix inequalities. A reaching motion controller is also proposed for such systems by means of both reaching law and inequality approach. An inverted pendulum system is utilized to illustrate the effectiveness of the developed techniques.

Systematic approach of extracting sliding manifold in robust stabilizing of stochastic multi-input systems

“…The significant advantages of SMC are: i) fast response and good transient performance; ii) its robustness against a large class of perturbations or model uncertainties; and iii) the possibility of stabilizing some complex nonlinear systems which are difficult to stabilize by continuous state feedback laws. Hence, during the past decades, SMC has received a lot of attention by the control community for different type of systems such as uncertain stochastic delay systems [1], uncertain linear discrete systems independent of time-delay [2], singular stochastic hybrid systems [3], linear systems with time-varying input and state delays [4], systems with mismatched uncertainties [5], distributed networked control systems [6], uncertain stochastic nonlinear systems with unknown dead zone [7], MIMO nonlinear systems [8,9], stochastic nonlinear strictfeedback systems [10], and uncertain linear systems with quantization [11].…”

A variational characterization of the sliding mode control processes

“…Moreover, the developed analytic tool and results related to the variable structures systems (VSSs) constitute a valuable part of the modern systems theory. We refer to [9], [12], [13], [20], [25], [29], [30], [33], [35], [36], [37], [38], [39], [40] for the basic facts and also for some interesting real world uses of the sliding mode techniques.…”

Integral sliding mode control for uncertain systems with input delay based on singular perturbation approach

“…X. Li discussed the stability of dynamical systems with input-delay [13]. Yuanqing Xia dealt with a SMC design for LTI systems with both input and state time-varying delays [14]. J. Chen studied the combination of loop transfer recovery (LTR) observer and sliding mode control (SMC) to deal with input time delay by utilizing non-singular linear transformation [15].…”