Lyapunov-Based Sliding Mode Control with Multi-Rate Output Feedback

In the preceding chapter a design method for sliding surface is presented for continuous time system using full order Lyapunov matrix. Also this method is extended for to continuous uncertain time system. It is also noted as elaborated in introduction chapter that discrete-time sliding mode control is gaining more necessity since the actual implementation of control is generally carried out with digital signal processors. Recently, efforts have been made to recover the robustness of DSMC such as the discrete approximation approach [102], the sliding sector [45], and the quasisliding modes [92, 12]. Here, it is pointed out that the research on the sliding hyperplane design itself has drawn little attention in the literature relative to the studies on reaching law design. As for the sliding hyperplane design, the eigenvalue assignment methods for the equivalent dynamics matrix have been considered as standard (e.g., see Tang & Misawa [92] and references therein). Apart from those eigenvalue approaches, the parametric approaches utilizing the Lyapunov equation or the Riccati equation have been investigated in some studies. Spurgeon [87] introduced the usage of the Lyapunovmatrix for calculating the sliding hyperplanes. In [45], a Riccati equation is used for the discrete-time sliding mode design for a class of single input systems. Recently, the LQ optimization approach was proposed by Janardhanan & Kariwala [55].