Synthesis of a Minimum Functional State Observer Approach for Unperturbed/Perturbed Dynamical Systems

Abstract

In this paper, we investigate the synthesis of minimum functional state observer for unperturbed and perturbed linear time invariant systems. The principal contribution is the design of a minimum functional state observer, which can estimate directly the state feedback control law. Hence, for the linear time invariant systems, the existence conditions of a minimum functional state observer are obtained by verification of a special dimension condition on system matrices. As a matter of fact, the exact solution of the proposed approach is determined, and the minimum functional state observer that has the same dimension as the control vector is derived by solving a set of linear matrix inequality (LMI) constraints. Whereas, for perturbed linear systems, the proposed minimum functional state observer scheme is developed to ensure the robust quadratic stability of the augmented system. The robustness issue is given via the reconstructed control law designed using an LMI based H∞ method; so that the desired design matrices are derived through the resolution of an optimum LMI system. The effectiveness and usefulness of the proposed approach are validated through a flexible link robot example.