Solutions to general \(H_{\infty}\) almost disturbance decoupling problem with measurement feedback and internal stability for discrete-time systems
The authors propose a general technique for measurement feedback design which ensures attenuation of disturbances up to any prespecified degree and internal stability for a closed loop discrete-time linear system. The problem is solved using the \(H_\infty\) machinery in three steps. First necessary and sufficient conditions for solvability of the considered problem with perfect measurements (i.e., all state variables and disturbances are measured) are presented. Then similar conditions for output feedback controllers and strictly proper output feedback controllers are given. In the full information case the controller may be static while in the general measurement case it should be dynamic. The authors allow for invariant zeros on the unit circle that makes the considered problem general. Moreover, a method for reduction of the order of the controller is also presented. The results are illustrated by a simple numerical example.
scientific article; zbMATH DE number 1491305
scientific article