Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances

Nguyen D. That (), Phan T. Nam () and Q. P. Ha ()
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Nguyen D. That: University of Technology
Phan T. Nam: Quynhon University
Q. P. Ha: University of Technology

Journal of Optimization Theory and Applications, 2013, vol. 157, issue 1, No 6, 96-107

Abstract: Abstract This paper addresses the problem of reachable set bounding for linear discrete-time systems that are subject to state delay and bounded disturbances. Based on the Lyapunov method, a sufficient condition for the existence of ellipsoid-based bounds of reachable sets of a linear uncertain discrete system is derived in terms of matrix inequalities. Here, a new idea is to minimize the projection distances of the ellipsoids on each axis with different exponential convergence rates, instead of minimization of their radius with a single exponential rate. A smaller bound can thus be obtained from the intersection of these ellipsoids. A numerical example is given to illustrate the effectiveness of the proposed approach.

Keywords: Reachable set bounding; Interval time-varying delay; Lyapunov–Krasovskii functional; Projection distance (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-012-0179-2

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