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Solution Bounds, Stability, and Estimation of TrappingStability Regions of Some Nonlinear Time-Varying Systems
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-16, 16 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-04-24
Country of Publication
Egypt
No. of Pages
16
Main Subjects
Abstract EN
Estimation of solution norms and stability for time-dependent nonlinear systems is ubiquitous in numerous engineering, natural science, and control problems.
Yet, practically valuable results are rare in this area.
This paper develops a novel approach, which bounds the solution norms, derives the corresponding stability criteria, and estimates the trapping/stability regions for some nonautonomous and nonlinear systems, which arise in various application domains.
Our inferences rest on deriving a scalar differential inequality for the norms of solutions to the initial systems.
Utility of the Lipschitz inequality linearizes the associated auxiliary differential equation and yields both the upper bounds for the norms of solutions and the relevant stability criteria.
To refine these inferences, we introduce a nonlinear extension of the Lipschitz inequality, which improves the developed bounds and allows estimation of the stability/trapping regions for the corresponding systems.
Finally, we confirm the theoretical results in representative simulations.
American Psychological Association (APA)
Pinsky, Mark A.& Koblik, Steve. 2020. Solution Bounds, Stability, and Estimation of TrappingStability Regions of Some Nonlinear Time-Varying Systems. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1195681
Modern Language Association (MLA)
Pinsky, Mark A.& Koblik, Steve. Solution Bounds, Stability, and Estimation of TrappingStability Regions of Some Nonlinear Time-Varying Systems. Mathematical Problems in Engineering No. 2020 (2020), pp.1-16.
https://search.emarefa.net/detail/BIM-1195681
American Medical Association (AMA)
Pinsky, Mark A.& Koblik, Steve. Solution Bounds, Stability, and Estimation of TrappingStability Regions of Some Nonlinear Time-Varying Systems. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-16.
https://search.emarefa.net/detail/BIM-1195681
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1195681