Abstract
This paper is concerned with the optimal control of time-varying, continuous-time linear systems both with parameters depending on time and the process being a finite-state Markovian one. The performance index to be minimized is the infinite-time quadratic cost functional. The solution of this time-varying jump linear quadratic control problem consists of the study of nonnegative definite global and bounded solution of coupled differential Riccati equation. Necessary and sufficient conditions for existence of such a solution are obtained in terms of optimizability and detectability. Moreover, the conditions for stability of the optimal closed-loop system are established.
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