Martynyuk A.A. Qualitative Analysis of Set-Valued Differential Equations

Springer, 2019. — 203 p. — ISBN: 978-3-030-07643-6.The book discusses set-valued differential equations defined in terms of the Hukuhara derivative. Focusing on equations with uncertainty, i.e., including an unknown parameter, it introduces a regularlization method to handle them. The main tools for qualitative analysis are the principle of comparison of Chaplygin – Wazhewsky, developed for the scalar, vector and matrix-valued Lyapunov functions and the method of nonlinear integral inequalities, which are used to establish existence, stability or boundedness.
Driven by the question of how to model real processes using a set-valued of differential equations, the book lays the theoretical foundations for further study in this area. It is intended for experts working in the field of qualitative analysis of differential and other types of equations.General Properties of Set-Valued Equations
Analysis of Continuous Equations
Discrete-Time Systems with Switching
Qualitative Analysis of Impulsive Equations
Stability of Systems with Aftereffect
Impulsive Systems with Aftereffect
Dynamics of Systems with Causal Operator
Finite-Time Stability of Standard Systems Sets