Preliminary Concepts

Abstract

Over the past several decades, a substantial amount of research work has been done in the field of SMC design and discrete-time SMC design (Veselić and Draženović in J. Frankl. Inst. 351(4):1920, 2014, Furuta in Syst. Control Lett. 14(2):145, 1990, Edwards and Spurgeon in Sliding Mode Control: Theory and Applications. Taylor & Francis, Milton Park, 1998, Janardhanan and Bandyopadhyay in IEEE Trans. Autom. Control 51(6):1030, 2006) [1–4]. In this book, we propose the design of functional observer-based SMC for discrete-time stochastic systems having deterministic, unmatched uncertain, parametric uncertain, time-delay, and parametric uncertain time delayed in nature. Therefore, a concise introduction to the idea of functional observer design for estimating the state vector and its linear function and stochastic SMC for deterministic systems is provided in this chapter.