Adaptive control with asymptotical sliding mode of uncertain plants with input and state delays

Asymptotical sliding mode design of direct model reference adaptive control (MRAC) for a class of systems with input and state delays based only on the lumped-delays is developed. To overcome the difficulty to directly predict the plant state, a control design is proposed based on a new approach. The approach relies on a decomposition of the adaptive control design procedure where a "generalized error" in conjunction with auxiliary linear filters with adjustable gains are introduced and the sliding variable is formed on the basis of this error. The effect of such a decomposition is to pull the input delay out of first step of the design procedure.