Differential Equations with Impulse Effects Multivalued Right hand Sides with Discontinuities 1st Edition by Nikolai Perestyuk, Peter Malyshev, Natalia Skripnik, Viktor Plotnikov ISBN 978-3110218169 3110218169

Differential Equations with Impulse Effects Multivalued Right hand Sides with Discontinuities 1st Edition by Nikolai A. Perestyuk, Peter V. Malyshev, Natalia V. Skripnik, Viktor A. Plotnikov – Ebook PDF Instant Download/Delivery: 978-3110218169, 3110218169
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Product details: 

ISBN 10: 3110218169

ISBN 13: 978-3110218169

Author: Nikolai A. Perestyuk, Peter V. Malyshev, Natalia V. Skripnik, Viktor A. Plotnikov

Significant interest in the investigation of systems with discontinuous trajectories is explained by the development of equipment in which significant role is played by impulsive control systems and impulsive computing systems. Impulsive systems are also encountered in numerous problems of natural sciences described by mathematical models with conditions reflecting the impulsive action of external forces with pulses whose duration can be neglected.

Differential equations with set-valued right-hand side arise in the investigation of evolution processes in the case of measurement errors, inaccuracy or incompleteness of information, action of bounded perturbations, violation of unique solvability conditions, etc. Differential inclusions also allow one to describe the dynamics of controlled processes and are widely used in the theory of optimal control.

This monograph is devoted to the investigation of impulsive differential equations with set-valued and discontinuous right-hand sides. It is intended for researchers, lecturers, postgraduate students, and students of higher schools specialized in the field of the theory of differential equations, the theory of optimal control, and their applications.

Table of contents: 

1 Impulsive Differential Equations

1.1 General Characterization of Systems of Impulsive Differential Equa-

tions

1.2 Linear Systems

2 Impulsive Differential Inclusions

2.1 Differential Inclusions with Fixed Times of Pulse Action

2.2 Differential Inclusions with Nonfixed Times of Pulse Action

2.3 Examples

3 Linear Impulsive Differential Inclusions

3.1 Statement of the Problem. Theorem on Existence and Uniqueness

3.2 Stability of Solutions of Linear Impulsive Differential Inclusions

3.3 Periodic Solutions of Linear Impulsive Differential Inclusions

3.4 Linear Differential Equations with Pulse Action at Indefinite Times.

4 Linear Systems with Multivalued Trajectories

4.1 Differential Equations with Hukuhara Derivative

4.2 Approximation of the Integral Funnel of a Linear Differential Inclusion with the Help of Systems of Differential Equations with Hukuhara Derivative

4.3 Linear Differential Equations with n – Derivative

4.4 Extension of the Space conv (R”) for n = 1

4.5 Approximation of the Integral Funnel of a Linear Differential Inclusion with the Help of Systems of Differential Equations with π-Derivative

5 Method of Averaging in Systems with Pulse Action

5.1 Oscillating System with One Degree of Freedom

5.2 Systems with Fixed Times of the Pulse Action

5.3 Systems with Nonfixed Times of the Pulse Action

6 Averaging of Differential Inclusions

6.1 Averaging of Inclusions with Pulses at Fixed Times

6.2 Krasnosel’skii-Krein Theorem for Differential Inclusions

6.3 Averaging of Inclusions with Pulses at Nonfixed Times

6.4 Averaging of Impulsive Differential Equations with Hukuhara Derivative

7 Differential Equations with Discontinuous Right-Hand Side

7.1 Motions and Quasimotions

7.2 Impulsive Motions and Quasimotions

7.3 Euler Quasibroken Lines

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Tags: Nikolai Perestyuk, Peter Malyshev, Natalia Skripnik, Viktor Plotnikov, Differential Equations, Impulse Effects, Right hand Sides