Title: Linear state feedback stabilisation on time scales

Authors: Billy J. Jackson, John M. Davis, Ian A. Gravagne, Robert J. Marks II

Addresses: Department of Mathematics, Saint Xavier University, Chicago, IL 60655, USA. ' Department of Mathematics, Baylor University, Waco, TX 76798, USA. ' Department of Electrical and Computer Engineering, Baylor University, Waco, TX 76798, USA. ' Department of Electrical and Computer Engineering, Baylor University, Waco, TX 76798, USA

Abstract: For a general class of dynamical systems (of which the canonical continuous and uniform discrete versions are but special cases), we prove that there is a state feedback gain such that the resulting closed-loop system is uniformly exponentially stable with a prescribed rate. The methods here generalise and extend Gramian-based linear state feedback control to much more general time domains, e.g., nonuniform discrete or a combination of continuous and discrete time. In conclusion, we discuss an experimental implementation of this theory.

Keywords: time scales; feedback control; Gramian; exponential stability; systems theory; linear state feedback stabilisation.

DOI: 10.1504/IJDSDE.2011.038500

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.1/2, pp.163 - 177

Published online: 09 Feb 2011 *

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