Quadratic Optimal Control through Spectral and Coprime Factorisation

摘要

We study the infinite horizon quadratic cost minimis- ation problem for a linear time-invariant distributed parameter system with finitely many inputs and out- puts. We work in an input/output framework, and reduce the unstable case to the stable case by the use of a right coprime factorisation of the impulse response and a preliminary stabilising feedback. The stable case is then solved through speciral factorisation. The theory is illustrated with two examples involving pure time delays.