Technical communique: Further result on reachable set bounding for linear uncertain polytopic systems with interval time-varying delays

Authors:
Phan T. Nam;Pubudu N. Pathirana
Affiliations:
Department of Mathematics, Quynhon University, Binhdinh, Viet Nam;School of Engineering, Deakin University, Geelong, VIC 3217, Australia
Venue:
Automatica (Journal of IFAC)
Year:
2011

Citing 6
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Abstract

The problem of reachable set estimation of linear uncertain polytopic time-varying delay systems subject to bounded peak inputs is studied in this paper. The delays considered in this paper are assumed to be non-differentiable and vary within an interval where the lower and upper bounds are known. Based on the Lyapunov-Krasovskii method and delay decomposition technique, a sufficient condition for the existence of a ball that bounds the reachable set of the system is proposed in terms of matrix inequalities containing only one scalar which can be solved by using an one-dimensional search method and Matlab's LMI Toolbox and allow us to find the smallest radius. A numerical example is given to illustrate the effectiveness of the proposed result.