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

This work is concerned with the assignment of the desired eigenstructure fo r linear time-varying systems such as missiles, rockets, fighters, etc. Des pite its well-known limitations, gain scheduling control continues to be a major focus of research efforts. Scheduling of frozen-time, frozen-state co ntrollers for fast time-varying dynamics is known to be mathematically fall acious and practically hazardous. Therefore, recent research efforts are be ing directed towards applying time-varying controllers. In this paper, we i ) introduce a differential algebraic eigenvalue theory for linear time-vary ing systems, and ii) propose an eigenstructure assignment scheme for linear time-varying systems via the differential Sylvester equation based upon ne wly developed notions. The whole design procedure of the proposed eigenstru cture assignment scheme is very systematic. The scheme can be used to deter mine the stability of linear time-varying systems easily as well as to prov ide a new horizon of designing controllers for linear time-varying systems. The presented method is illustrated by a numerical example.