Stabilization of time-varying linear system using a new time-varying eigenvalue assignment technique

A unified (time-varying) eigenvalue theory was developed for linear time-varying systems of the form y⁽ⁿ⁾+α _n(t)y^(n-1)+...+α₂ (t)y+α₁(t)y= u. The theory is used to develop a new breed of self-tuning adaptive controller based on the assignment of a certain kind of mean value for the unified time-varying eigenvalues in the complex plane. Detailed design procedures for general second-order time-varying linear systems are presented, and some simulation results are shown. Comparisons of the new controller with other control techniques for time-varying linear systems, such as those based on optimal control, adaptive control, and frozen-time eigenvalue techniques, are also discussed. Based on the simulation results presented, the new controller appears to be very powerful, and easy to master