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Minimization of state bounding for perturbed positive systems with delays
journal contribution
posted on 2018-01-01, 00:00 authored by P T Nam, Hieu TrinhHieu Trinh, Pubudu PathiranaPubudu PathiranaThis paper studies the minimum state bounding problem of linear positive differential systems with discrete and distributed delays and unknown-but-bounded disturbances. Specifically, two problems are addressed: (i) The first problem is to derive the smallest componentwise bound of the state vector when the time tends to infinity, and (ii) the second problem is to derive the smallest possible componentwise bound of the state vector when the time tends to a prespecified finite time. A new method which is based on state transformations, the Lyapunov method, and optimization techniques is presented for deriving the smallest bounds of the state vector which solves the two stated problems. The obtained results are extended to a class of nonlinear systems which are upper bounded by linear positive systems. An application of the results to the L8-gain problem for positive time-delay systems is also presented. The feasibility and effectiveness of our derived results are illustrated through two numerical examples.
History
Journal
SIAM journal on control and optimizationVolume
56Issue
3Pagination
1739 - 1755Publisher
Society for Industrial and Applied MathematicsLocation
Philadelphia, Pa.Publisher DOI
ISSN
0363-0129Language
engPublication classification
C1 Refereed article in a scholarly journal; C Journal articleCopyright notice
2018, Society for Industrial and Applied MathematicsUsage metrics
Keywords
ultimate boundsprespecified time boundspositive systemsbounded disturbancestime delaysScience & TechnologyTechnologyPhysical SciencesAutomation & Control SystemsMathematics, AppliedMathematicsREACHABLE SET ESTIMATIONDISCRETE-TIME-SYSTEMSSLIDING-MODE CONTROLSTABILITY ANALYSISEXPONENTIAL STABILITYINTERVAL OBSERVERSSWITCHING SYSTEMSUNCERTAIN SYSTEMSINVARIANT-SETSMechanical Engineering
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