Algebraic and Dynamic Lyapunov Equations on Time Scales

2009/10/10 by John M. Davis, Ian Gravagne, Davis, John M. +7
Engineering · Mathematics · #15A24 #37B25 #39B42 #93D05 #93D30 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #math.DS #math.OC #msc:15A24 #msc:37B25 #msc:39B42 #msc:93D05 #msc:93D30

paper · pdf · doi:10.48550/arxiv.0910.1895

arxiv created 2009/10/10 · openalex publication_date 2009/10/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We revisit the canonical continuous-time and discrete-time matrix algebraic and matrix differential equations that play a central role in Lyapunov based stability arguments. The goal is to generalize and extend these types of equations and subsequent analysis to dynamical systems on domains other than \R or \Z, e.g. nonuniform discrete domains or domains consisting of a mixture of discrete and continuous components. We compare and contrast the standard theory with the theory in this general case.

Citations

• The general problem of the stability of motion

Related

• Lyapunov Theory for Discrete Time Systems
• Stability by linear approximation for time scale dynamical systems
• Discrete conditions of Lyapunov stability
• The Fundamental Theorem of Dynamical Systems: all at once and all in the same place
• Optimal Dichotomy of Temporal Scales and Boundedness and Stability of Time-Varying Multidimensional Nonlinear Systems