A tutorial account of variable structure control with sliding mode is presented in this paper. The purpose is to introduce in a concise manner the fundamental theory, main results, and practical applications of this powerful control system design approach. This approach is particularly attractive for the control of nonlinear systems. Prominent characteristics such as invariance, robustness, order reduction, and control chattering are discussed in detail. Methods for coping with chattering are presented. Both linear and nonlinear systems are considered. Future research areas are suggested and an extensive list of references is included. CONVENTIONS FOR SYMBOLS Capital, italic letters represent matrices, e.g., A and K. Boldface, roman lowercase letters represent vectors, brief discussions about its historical development are presented. A. The Basic Notion of VSC second-order system [431, [ 1541 similar to the following The basic idea of VSC was originally illustrated by a X = y y = 2 y-x + U U =-*x (l a) where (1b) * = 4 when s (x , y) > 0 =-4 when s (x , y) < 0 e.g., a and k. and k. respectively. s (x , y) = X U , u = 0. 5 x + y. (IC) Lowercase , italic letters represent scalars, e.g., a and dim-x and d i m 4 stand for dimensions of x and B, A block diagram of the system is shown in Fig. l(a). The variable s(x, y) in (1.14 is the product of two functions

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