2020/01/16 by Mark A. Pinsky, Pinsky, Mark A., Steve Koblik +1
Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2001.06482
openalex publication_date 2020/01/16 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Estimation of solution norms and stability for time-dependent nonlinear\nsystems is ubiquitous in numerous engineering, natural science and control\nproblems. Yet, practically valuable results are rare in this area. This paper\ndevelops a novel approach, which bounds the solution norms, derives the\ncorresponding stability criteria, and estimates the trapping/stability regions\nfor some nonautonomous and nonlinear systems, which arise in various\napplication domains. Our inferences rest on deriving a scalar differential\ninequality for the norms of solutions to the initial systems. Utility of the\nLipschitz inequality linearizes the associated auxiliary differential equation\nand yields both the upper bounds for the norms of solutions and the relevant\nstability criteria. To refine these inferences, we introduce a nonlinear\nextension of the Lipschitz inequality, which improves the developed bounds and\nallows estimation of the stability basins and trapping regions for the\ncorresponding systems. Finally, we confirm the theoretical results in\nrepresentative simulations.\n