On the continuous time-varying JLQ problem

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.