Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances
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 syst...
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| Published in | Journal of optimization theory and applications Vol. 157; no. 1; pp. 96 - 107 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.04.2013
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| 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. |
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| AbstractList | 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. 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.[PUBLICATION ABSTRACT] |
| Author | Ha, Q. P. Nam, Phan T. That, Nguyen D. |
| Author_xml | – sequence: 1 givenname: Nguyen D. surname: That fullname: That, Nguyen D. email: That.NguyenDinh@uts.edu.au organization: Faculty of Engineering and Information Technology, University of Technology – sequence: 2 givenname: Phan T. surname: Nam fullname: Nam, Phan T. organization: Department of Mathematics, Quynhon University – sequence: 3 givenname: Q. P. surname: Ha fullname: Ha, Q. P. organization: Faculty of Engineering and Information Technology, University of Technology |
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| Keywords | Interval time-varying delay Reachable set bounding Projection distance Lyapunov–Krasovskii functional |
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| SubjectTerms | 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 |
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| Title | Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances |
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