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In this chapter, the applicability of the concept of multirate output feedback based discrete-time sliding mode control, will be analysed for a few practical systems. [ABSTRACT FROM AUTHOR]

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 [55] 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 [30]. 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. [ABSTRACT FROM AUTHOR]

The tracking problem of systems is one that has come under a lot of investigation. The initial studies were on the transfer function models of the system, based on internal model control [23], which used the inverse dynamics of the system to design a tracking controller. The problem with this simple logic arouse in cases wherein the system was nonminimum phase, i.e., had unstable zeros. In such a case, the inverse dynamics were unstable, which generated a closed loop system that may be stable , but was not internally stable [1]. Further study on the topic brought into light numerous techniques that handled the tracking problem, for both linear [5, 43] and nonlinear systems [16, 17, 32]. The research on unstable zero dynamics was also extended to discrete-system representations [26, 59]. [ABSTRACT FROM AUTHOR]

In recent years, the study of sliding mode control for systems with time delay in its state dynamics has received consideration. The delays present in a system can be broadly categorized into three categories. The input delay, state delay and output delay. Input delay is caused by the transmission of a control signal over a long distance. State delay is due to transmission or transport delay among interacting elements in a dynamic system. The output delay is to delay due to sensors. A lumped function based approach is adopted in [50] to design a sliding mode control law for systems with state delay. An added uncertainty is handled in [13]. In [78], a control law has been proposed for systems where delay is present in both state and input. A state feedback discrete-time sliding mode controller for time-delay system has also been investigated in [54]. In [58], an observer based sliding mode algorithm has been proposed. The algorithm handles systems with computational delay. [ABSTRACT FROM AUTHOR]

This chapter introduces various techniques of multirate output feedback based discrete-time sliding mode control of LTI systems with uncertainty. Systems satisfying the so-called matching condition [19] would be studied first. Linear systems that do not satisfy this condition would be handled next in the chapter. Finally the chapter would present a discrete-time version of the integral sliding-mode [76] control technique. This technique can be used to impart robustness to a controller structure. [ABSTRACT FROM AUTHOR]

In [27], a reaching law approach was proposed for the quasi-sliding mode control of discrete-time LTI systems of form (1.20). The reaching law approach aims at satisfying the condition s(k+1)–s(k)=–qτs(k)–ετsgn (s(k)), where, s(k)=cTx(k) is the sliding function, q and ε are controller parameters satisfying the relationship 1–qτ > 0,ε > o. [ABSTRACT FROM AUTHOR]

In this chapter, a brief introduction to the concepts of sliding mode control and multirate output feedback would be given. The chapter would describe and distinguish the concepts of variable structure control and sliding mode control and would clarify the concept of discrete-time sliding mode and discrete-time sliding mode control. The chapter would also explain the concept of multirate output sampling and the relationship between the system states and the output samples for linear time invariant systems. [ABSTRACT FROM AUTHOR]

The use of digital Computers and samplers in control circuitry in recent years, has made the use of discrete-time system representations of the system more justifiable for controller design than continuous-time representations. A few researchers have worked on discrete-time sliding mode controller design [3, 7, 8] during the last decade. In discrete-time sliding mode control, the control input is calculated once in every sampling interval and is held constant during this period. Due to the finite sampling frequency, it may happen in discrete-time sliding mode, that the system state trajectory is unable to move along the sliding surface. It may move about the surface, thus giving a sliding-like mode or Quasi-sliding motion (QSM). [ABSTRACT FROM AUTHOR]