Forward-integration Riccati-based output-feedback control of linear time-varying systems

In applications involving time-varying systems, the state dynamics matrix is often not known in advance. To address this problem, this paper investigates the effectiveness of a forward-in-time Riccati-based control law. This approach is motivated by the fact that the optimal state estimator is based on a forward-in-time Riccati-based solution that does not require advance knowledge of the system dynamics. In this paper we show that a forward-in-time Riccati-based control law stabilizes the system if the dynamics of the quasi-dual system are asymptotically stable. This property holds if the closed-loop dynamics are symmetric, and, for some plants, is achieved by dynamics with sufficiently fast time variation. In addition, using a separation principal type result, we guarantee closed-loop stability in the case of output feedback.