Adaptive controller design and disturbance attenuation for minimum phase multiple‐input multiple‐output linear systems with noisy output measurements and with measured disturbances

Abstract

SummaryIn this paper, we present a systematic procedure for robust adaptive control design for minimum phase uncertain multiple‐input multiple‐output linear systems that are right invertible and can be dynamically extended to a linear system with vector relative degree using a dynamic compensator that is known. For this class of systems, it is always possible to dynamically extend them, and/or integrate a select set of output channels, and/or padding dummy state variables to arrive at a system model that admits uniform vector relative degree and uniform observability indices that is further minimum phase according to Reference 13. We assume that the uniform vector relative degree is known and an upper bound for the uniform observability indices is known. We also assume that the unknown parameter vector lies in a convex compact set such that the high frequency gain matrix remains invertible for any parameter vector value in the set. These are the assumptions that allow for a successful design of a robust adaptive controller. A numerical example is included to fully illustrate the controller design and the effectiveness of the controller.