Eigenstructure-based robust stability analysis for linear time-varying systems

Stability robustness of a linear time-varying system with time-varying structured state space uncertainties is considered by using extended-mean theorem and Bellman´s lemma. The extended-mean theorem is a necessary and sufficient exponential stability criterion based on the recently developed PD-eigenvalue and PD-eigenvector for a linear time-varying system. Our new result required that the extended-mean of each nominal PD-eigenvalue should be negative real, which is determined by a norm involving the structures of the uncertainty and the nominal left/right PD-eigenvectors. It is believed that this result is well suited for a design of control systems using PD-eigenvalue assignment or PD-eigenstructure assignment. The usefulness and correctness will be validated by a numerical example.