Qualitative Analysis of Set-Valued Differential Equations [electronic resource] /
Martynyuk, Anatoly A.author.
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 Equations -- Analysis of the Set of Continuous Equations -- Stability of the Set of Discrete-Time Systems -- Qualitative Analysis of Set Impulsive Equations -- Stability of Set Systems with Aftereﬀect -- Analysis of Set Impulsive Systems with Aftereﬀect -- Stability of Set Equations with Causal Operator -- Finite-Time Stability of Standard Systems Sets.
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.
Differential equations.
System theory.
Ordinary Differential Equations.
Systems Theory, Control.