Article

# Controllability, Observability, Reachability, and Stability of Dynamic Linear Systems

02/2009;

Source: arXiv

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**ABSTRACT:**This paper considers connections between bounded-input, bounded-output smbility and asymptotic shb)lity in the sense of Lyapunov for linear ttme-varying systems. By modifying slightly the definition of bounded-input, bounded-output stability, an equivalence between the two types of stability is found for systems which are uniformly completely controllable and observable. The various matrices describing the system need not be bounded. Other results relate to the characterization of uniform complete controllability and the derivation of Lyapunov functions for linear time-varying {ystems. 1. Introduction. Connections between various types of stabilit y are examined in this paper. More precisely, we study linear, finite-dimensional, dynamical systems which in general are time-varying, and consider descriptions of such systems of the formSiam Journal on Control. 01/1969; 7(3). - [Show abstract] [Hide abstract]

**ABSTRACT:**The notions of transfer matrix, transfer equivalence, and i nput-output equivalence for linear control systems on time scales are introduced. These concepts generalize the cor- responding continuous- and discrete-time versions. Necessary and sufficient conditions for transfer and input-output equivalence are presented. As the main tool, an extension of the Laplace transform for functions defined on a time scale is use d.01/2006; - 01/2006;

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