Controllability, Observability, Realizability, and Stability of Dynamic Linear Systems

Abstract

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from our recent work \cite{DaGrJaMaRa}. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's) in both the time invariant and time varying settings and compare the results. We also explore observability in terms of both Gramian and rank conditions as well as realizability results. We conclude by applying this systems theory to connect exponential and BIBO stability problems in this general setting. Numerous examples are included to show the utility of these results.

typos corrected; current form is as accepted in EJDE

Cited by in corpus (5)

• Linear State Feedback Stabilization on Time Scales
• Algebraic and Dynamic Lyapunov Equations on Time Scales
• High order concentrated non-negative matrix-exponential functions
• Spectral Theory for Second-Order Vector Equations on Finite Time-Varying Domains
• Stability and stabilization of linear positive systems on time scales