Quality of stability for linear, time-varying systems using an exact time-varying eigenvalue theory. I

The authors previously (Proc. 1990 IEEE International Symp. on Circuits and Systems, p.1393, 1990) presented an exact eigenvalue theory for the characterization of stability for linear time-varying systems. In this paper they extend these results to include precise characterizations and criteria for the quality of stability for linear, time-varying systems. These results provide analysts and control designers with a variety of mathematical tools and procedures for ensuring that the transient response of a linear, time-varying system is well behaved in the sense of settling-time, overshoot, etc. An example is given to illustrate the results