Adaptive Controller Design and Disturbance Attenuation for a Class of MIMO Linear Systems under Noisy Output Measurement

In this paper, we present adaptive controller design for a class of MIMO linear systems subjected to noisy measurement based on worst-case analysis approach. The class of MIMO linear system under studied is composed of two linear subsystems parallelly interconnected with additional feedback. We first formulate the robust adaptive control problem as a nonlinear H-infinity control problem with imperfect state measurement, and derive the estimators and identifiers of the two subsystems using cost-to-come analysis. The integrator backstepping methodology is then applied recursively to obtain the control law. The controller guarantees the boundedness of closed-loop signals with bounded exogenous disturbances, achieves asymptotic tracking and desired disturbance attenuation level with respect to the exogenous disturbance inputs. These strong robustness properties are then illustrated by a numerical example.