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Stabilization of infinite-dimensional linear system using finite- dimensional state controllers. (English. Russian original) Zbl 0742.93080
Autom. Remote Control 51, No. 9, 1176-1181 (1990); translation from Avtom. Telemekh. 1990, No. 9, 27-34 (1990).
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 $$F_ m$$.

##### MSC:
 9.3e+21 Optimal stochastic control