Time-Varying Vector Norm and Lower and Upper Bounds on the Solutions of Uniformly Asymptotically Stable Linear Systems

• Main Author: Robert Vrabel
• Format: Article
• Language: English
• Published: MDPI AG 2020-06-01
• Series: Mathematics
• Subjects: linear time-varying system; uniformly asymptotically stable system; lower and upper bound on the solutions; time-varying vector norm; simulation
• Online Access: https://www.mdpi.com/2227-7390/8/6/915
• ISSN: 2227-7390

Based on the eigenvalue idea and the time-varying weighted vector norm in the state space <inline-formula> <math display="inline"> <semantics> <msup> <mi mathvariant="double-struck">R</mi> <mi>n</mi> </msup> </semantics> </math> </inline-formula> we construct here the lower and upper bounds of 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.