PD-eigenstructure assignment control for decoupling and tracking of linear time-varying systems

Concerns the decoupling and tracking control for linear time-varying systems, such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain-scheduling control appears to be a focus of the research efforts. The scheduling of a frozen-time, frozen-state controller for fast time-varying dynamics is known to be mathematically fallacious and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and a novel decoupling and tracking control scheme is proposed by using the PD (parallel differential) eigenstructure assignment scheme via the differential Sylvester equation and a CGT (command generator tracker) for linear time-varying systems. The presented method is illustrated by numerical examples.