CONTROLLABILITY, OBSERVABILITY, REALIZABILITY, AND STABILITY OF DYNAMIC LINEAR SYSTEMS

By John M. Davis, I. Gravagne, Billy Jackson, R. Marks. 2009

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We develop a linear systems theory that coincides with the ex- isting theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time scales. The approach here is based on generalized Laplace transform methods (e.g. shifts and con- volution) from the recent work (13). 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 explore observability in terms of both Gramian and rank conditions and establish related 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.

Subfields: Control and Systems Engineering, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cc64226daca378a93680bbd4fbb0a1f9ac26148d