Minimal unknown-input functional observers for multi-input multi-output LTI systems. (November 2015) - Mohajerpoor, Reza; Abdi, Hamid; Nahavandi, Saeid
Abstract : Highlights: Disturbance-decoupled functional observer of minimal order for MIMO LTI systems is designed. The observability/detectability requirement of the system is not relaxed. The concept of unknown-input functional detectability is elaborated. An order-increase algorithm for the observer is proposed. A new method to design the observer parameters is proposed. Abstract: Designing minimum possible order ( minimal ) disturbance-decoupled proper functional observers for multi-input multi-output (MIMO) linear time-invariant (LTI) systems is studied. It is not necessary that a minimum-order unknown-input functional observer (UIFO) exists in our proposed design procedure. If the minimum-order observer cannot be attained, the observer's order is increased sequentially through a recursive algorithm, so that the minimal order UIFO can be obtained. To the best of our knowledge, this is the first time that this specific problem is addressed. It is assumed that the system is unknown-input functional detectable, which is the least requirement for the existence of a stable UIFO. This condition also is a certificate for the convergence of our observer's order-increase algorithm. Two methodologies are demonstrated to solve the observer design equations. The second presented scheme, is a new design method that based on our observations has a better numerical performance than the first conventional one. Numerical examples and simulation results in the MATLAB/Simulink environment describe the overall observer design procedure, and highlight the efficacy of our new methodology to solve the observer equations in comparison to the conventional one.