Robust model reference adaptive control for square MIMO LTI systems with uniform vector relative degree of zero

In this paper, we present a systematic procedure for robust model reference adaptive control design for uncertain square multiple-input multiple-output (MIMO) continuous-time linear time-invariant (LTI) systems that admit uniform vector relative degree of zero, under the assumptions of minimum phase and that the upper bounds for the observability indices of all measurement channels are known. We 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 assumptions allow for a successful design of a robust model reference adaptive controller. A numerical example is included to fully illustrate the controller design and the effectiveness of the controller. As compared with the recent paper Pan and Başar (2023), the problem with uniform vector relative degree of zero allows us to relieve the block diagonally identical backbone structure for the measurement channels, choose a general quadratic cost structure that weighs the tracking errors arbitrarily, and achieve optimality for the control design.