Minimum Functional State Observer Based Guaranteed Cost Performance for Uncertain Dynamical Systems

The focus of this paper is on the design of an optimal and robust minimum functional state observer scheme for uncertain dynamical systems composed of linear model and uncertain parameters. Its aim is to study a minimum functional observer which can estimate, directly, the state feedback control law. Moreover, the minimum functional state observer which has the same dimension as the control vector is derived by solving a Linear Matrix Inequality (LMI) constraint. The proposed approach is formulated as an optimization problem in terms of LMI constraint to compute the robust gain matrices characterizing the proposed minimum functional observer. Indeed, a design method is developed to ensure the stability of the closed-loop system with the Lyapunov technique and to minimize the upper bound of a cost function leading to optimal performances. Through an example, characterized by a flexible link robot, it will be illustrated the proposed approach provide the effectiveness and the availability of the developed method.

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