Decoupling and tracking control for linear time-varying systems using eigenstructure assignment and CGT

This work is concerned with the decoupling and tracking control for linear time-varying systems such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain-scheduling control appeared to be focus of the research efforts. Scheduling of 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, i) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and ii) a novel decoupling and tracking control scheme is proposed by using the PD-eigenstructure assignment scheme via differential Sylvester equation and CGT (command generator tracker) for linear time-varying systems. The presented method is illustrated by numerical examples.