Output feedback variable structure control design for a class of uncertain linear systems

A dynamic output feedback variable structure controller for linear systems with mismatched uncertainties is studied. The proposed controller consists of nonlinear and linear parts. The linear part with full dynamics completely handles mismatched uncertainties and on the other hand, the nonlinear part is simplified as possible. By using the Lyapunov theory and linear matrix inequality method, the condition of existence of dynamic output feedback variable structure control law is derived and transformed as the feasibility problem described by linear matrix inequality, which can be solved by Matlab LMI toolbox to obtain the variable structure control for a class of system. A simulation example is given to illustrate that the analysis method and the result are valid and feasible.