Stabilization of infinite-dimensional linear system using finite- dimensional state controllers (Q1175874)

Defining an infinite-dimensional plant via an input-output model, it is possible to solve a linear-quadratic optimum control problem using a sequence of linear finite-dimensional models of increasing dimension. The complementary sensitivity function \(G_ m\) of a finite-dimensional closed-loop system is firstly investigated. The closed-loop system consists of an \(m\)-dimensional model \(P_ m\) of the plant and the optimum dynamic controller \(F_ m\) designed for the model \(P_ m\). The robustness of the controller is determined by investigating the behaviour of \(| G_ m(j\omega)|\) depending on the order \(m\) of the model \(P_ m\). Then some results are presented about the dependence between two functionals and the order \(m\) of the model \(P_ m\). The functionals are defined on the impulse responses of two closed-loop systems: the plant \(P\) and the plant model \(P_ m\) both feedback by the controller \(F_ m\).