Eigenstructure assignment by the differential Sylvester equation for linear time-varying systems

This work is concerned with the assignment of the desired eigenstructure for linear time-varying systems such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain scheduling control continues to be a major focus of research efforts. Scheduling of frozen-time, frozen-state controllers 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 i) introduce a differential algebraic eigenvalue theory for linear time-varying systems, and ii) propose an eigenstructure assignment scheme for linear time-varying systems via the differential Sylvester equation based upon newly developed notions. The whole design procedure of the proposed eigenstructure assignment scheme is very systematic. The scheme can be used to determine the stability of linear time-varying systems easily as well as to provide a new horizon of designing controllers for linear time-varying systems. The presented method is illustrated by a numerical example.