Time-varying vector norm and lower and upper bounds on the solutions of uniformly asymptotically stable linear systems

TL;DR

This paper develops bounds on solutions of linear systems that are uniformly asymptotically stable, extending existing results from time-invariant to time-varying systems using a novel time-varying vector norm approach.

Contribution

It introduces a new method based on time-varying vector norms to establish bounds for solutions of linear systems, generalizing known results to time-varying cases.

Findings

Derived lower and upper bounds for solutions

Extended stability bounds from time-invariant to time-varying systems

Utilized eigenvalue-based approach with time-varying norms

Abstract

Based on the eigenvalue idea and the time-varying weighted vector norm in state space we construct here the lower and upper bounds on the solutions of uniformly asymptotically stable linear systems. We generalize the known results for the linear time-invariant systems to the linear time-varying ones.