Initial-Excitation-Based Robust Adaptive Observer for MIMO LTI Systems

This article addresses the problem of adaptive observer design for multi-input multioutput linear time-invariant plants, under the effects of bounded disturbances in the system dynamics and the output, without requiring the persistence of excitation (PE) condition for parameter convergence. A switched robust adaptive observer is proposed, based on initial excitation, a milder condition as compared to PE in terms of excitation requirement and online verifiability. The unknown initial condition of the state is strategically included as an additional unknown parameter in the estimation framework, which, as far as the authors are aware, is a first of its kind technique in the context of adaptive observer design. The extended estimation error dynamics ensures the global uniformly ultimately bounded stability of the estimation error dynamics. Furthermore, estimation errors in a disturbance-free case result in uniform global exponential stability in a delayed sense. Simulation results are presented, and the estimation performance of the proposed adaptive observer is compared with that of the existing algorithms to illustrate the effectiveness.