Comprehensive Approach to Sliding Mode Design and Analysis in Linear Systems

This chapter considers the design of reduced and integral sliding mode (SM) dynamics for state space systems. The prescribed sliding mode dynamics are selected to have either a desired spectrum or optimal behavior in the linear quadratic regulator (LQR) sense. Due to the operator representation of the system equations, separate treatment of the discrete time (DT) and the continuous time (CT) cases is not needed. Fully decentralized design of the control used to satisfy the reachability problem is possible using the obtained sliding subspaces. For the sake of straightforward analysis of the SM dynamics, a new way to obtain the SM equation, based on singular value decomposition (SVD), is also provided. Algorithms are implemented in MATLAB. Simulations illustrating the usefulness of the developed design method conclude the chapter.