| Summary: | The purpose of this monograph is to give a different dimension to sliding surface design to achieve high performance of the system. Design of the switching surface is vital because the closed loop dynamics is governed by the parameters of the sliding surface. Therefore sliding surface should be designed to meet the closed loop specifications. Many systems demand high performance with robustness. To address this issue of achieving high performance with robustness, we propose nonlinear surfaces for different classes of systems. The nonlinear surface is designed such that it changes the systems closed-loop damping ratio from its initial low value to a final high value. Initially, the system is lightly damped resulting in a quick response and as the system output approaches the setpoint, the system is made overdamped to avoid overshoot. The technique of using a nonlinear surface to improve performance is discussed in four chapters after introducing basic notions in the introductory chapter. To address performance objectives in sliding mode, a generalized framework for sliding surface design is presented in last two chapters for continuous and discrete time systems, based on the full order Lyapunov matrices which constitute Lyapunov- or Riccati-type inequalities. The same method ensures performance in the face of parametric uncertainty which does not satisfy the matching condition. It also enables to optimize the sliding motion by applying the guaranteed cost control idea.
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