Abstract
In this paper, we introduce various definitions of practical stability and integral stability for nonlinear singular differential systems with maxima and give criteria of stability for such systems via the Lyapunov method and comparison principle.
Highlights
Differential equations with maxima are a special type of differential equations that contain the maximum of the unknown function over a previous interval, of which many examples are found in the fields of application such as automatic control, population dynamics, disease control, and so on
Some stability results for such equations can be found in the monographs [1, 2], the papers [3,4,5,6,7,8,9], and references cited therein
Many problems can be described by singular system models, such as optimal control problems and constrained control problems, which can be found in the monographs of Campbell [10] and Dai [11]
Summary
Introduction and PreliminariesDifferential equations with maxima are a special type of differential equations that contain the maximum of the unknown function over a previous interval, of which many examples are found in the fields of application such as automatic control, population dynamics, disease control, and so on.
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