Decay rate estimations for linear quadratic optimal regulators

Details Decay rate estimations for linear quadratic optimal regulators Decay rate estimations for linear quadratic optimal regulators

2012-01-09

arxiv.org/abs/1201.1786v1

Mathematics

Optimization and Control

18 pages, 1 figure

Scientific paper

Let $u(t)=-Fx(t)$ be the optimal control of the open loop system $x'(t)=Ax(t)+Bu(t)$ in a linear quadratic optimization problem. By using different complex variable arguments, we give several lower and upper estimates of the exponential decay rate of the closed loop system $x'(t)=(A-BF)x(t)$. Main attention is given to the case of a skew-Hermitian matrix $A$. Given an operator $A$, for a class of cases, we find a matrix $B$ that provides an almost optimal decay rate. Some open questions are listed.

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