Discrete-Time Sliding Mode Control Using Output Feedback and Nonlinear Surface

In this chapter, a nonlinear sliding surface is discussed to improve the transient response for general discrete-time multiple input multiple output linear systems with matched perturbations. The nonlinear surface modulates the closed loop damping ratio from an initial low to final high value to achieve better transient performance. The control law is based on the discrete-time sliding mode equivalent control and thus eliminates chattering. The control law is proposed based on two approaches: (1) reaching law based approach which needs only disturbance bounds and (2) disturbance observer based approach. Multirate output feedback is used to relax the need of the entire state vector for implementation of the control law. A possible extension of the nonlinear surface to input-delay systems is also presented.