earticle

영어

This paper deals with the determination of the optimal state observer gain matrix for discrete-time linear systems. In this way, it has been shown that an improved optimal gain is reached by minimizing a quadratic criterion formulated as a quadratic output feedback control of the observation error system.
The gradient matrix operation is applied to the Lagrangian function in order to obtain necessary conditions, for minimizing the proposed criterion, to perform the optimal gain matrix. It has been shown, by Lyapunov stability theory, that this optimal gain ensures the asymptotic convergence of the observation error towards zero.
The necessary and sufficient conditions are presented by coupled discrete Lyapunov equations which resolution, by a proposed numerical algorithm, allows the calculus of the optimal observation gain.
The importance of the proposed criterion for the synthesis of the state observer has been illustrated through numerical simulation study of the state observation of a robot with flexible link which has highlighted the effectiveness of the developed method in relation to that optimizing the dual system.