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

• Published in: Journal of optimization theory and applications Vol. 157; no. 1; pp. 96 - 107
• Main Authors: That, Nguyen D., Nam, Phan T., Ha, Q. P.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.04.2013; Springer Nature B.V
• Subjects: Analysis; Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Convergence; Delay; Discrete systems; Disturbances; Ellipsoids; Engineering; Inequalities; Interval arithmetic; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Projection; Robust control; Set theory; Studies; Theory of Computation; Interval time-varying delay; Reachable set bounding; Projection distance; Lyapunov–Krasovskii functional
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-012-0179-2

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.