Robust Adaptive Stabilization of Linear Time‐Invariant Dynamic Systems by Using Fractional‐Order Holds and Multirate Sampling Controls

Abstract

This paper presents a strategy for designing a robust discrete‐time adaptive controller for stabilizing linear time‐invariant (LTI) continuous‐time dynamic systems. Such systems may be unstable and noninversely stable in the worst case. A reduced‐order model is considered to design the adaptive controller. The control design is based on the discretization of the system with the use of a multirate sampling device with fast‐sampled control signal. A suitable on‐line adaptation of the multirate gains guarantees the stability of the inverse of the discretized estimated model, which is used to parameterize the adaptive controller. A dead zone is included in the parameters estimation algorithm for robustness purposes under the presence of unmodeled dynamics in the controlled dynamic system. The adaptive controller guarantees the boundedness of the system measured signal for all time. Some examples illustrate the efficacy of this control strategy.