Research interests
 Supported projects since  2007
 Supported projects
 (1994 - 2006)
 Biographical Data

  Non-local methods for pendulum-like feedback systems


Leonov, Gennadij A.; Reitmann, Volker; Smirnova, Vera B.

Non-local methods for pendulum-like feedback systems. (English)
[B] Teubner-Texte zur Mathematik. Stuttgart: Teubner. vii, 242 p. (1992).


1.       Systems with Multiple Equilibria
1.1 Global Properties
1.2 Feedback Control Equations
1.3 The Transfer Function
1.4 The Yakubovich-Kalman Theorem
2. Pendulum-Like Systems
2.1 The Two Canonical Forms
2.2 Second-order Pendulum-Like Systems
a) General Properties
b) The Case rS0
c) The Case r=0. Existence of Separatrix-Loops
d) Non-Local Bifurcations in the Case r>0
e) Several Remarks about the Case r i (-1/a,0)
2.3 The Lyapunov Direct Method in the Standard Form
2.4 Monostability and Gradient-Like Behavior of Phase-Controlled Systems with Nonlinearities having Mean Value Zero
3. Invariant Cones
3.1 Extension of the Circle Criterion
3.2 Systems with One Nonlinearity and a Bounded Forcing Term
3.3 Systems with Vector-Valued Nonlinearities
3.4 Bakaev Stability
4. The Bakaev-Guzh Technique
4.1 Basic Tools for Vector Fields on Riemannian Manifolds
4.2 Lyapunov-Type Results for Boundedness and Convergence
4.3 The Bakaev-Guzh Technique for Vector Fields
4.4 Second Order Systems of the Josephson-Type
5. The Method of Non-Local Reduction
5.1 A Lyapunov-Type Theorem
5.2 The Idea of Non-Local Reduction for Autonomous Systems of Indirect Control
5.3 Gradient-Like Behavior of Pendulum-Like Systems
5.4 Gradient-Like Behavior of Equations studied in the Theory of Phase-locked loops
5.5 Non-Local Reduction of Higher dimensional Systems to Autonomous Systems in the Plane
5.6 Non-Local Reduction in Non-Autonomous Pendulum-Like Systems
5.7 A Constructive Approach for Determining Lagrange Stability Criteria in the Non-Autonomous Case
6. Circular Solutions and Cycles
6.1 Pendulum-Like Systems with a Single Sign-Constant Nonlinearity
6.2 Frequency-domain Conditions for Existence of Circular Solutions and Cycles of the Second Kind
6.3 Circular Solutions and Cycles of the Second Kind in Concrete Systems of Phase Synchronization
6.4 Cycles of the First Kind
7. Synchronous Machines Equations
7.1 Special Properties of Synchronous Machines Equations
7.2 Gradient-Like Behavior of Machine Equations with a Zero Load
7.3 Application of Non-Local Reduction Method to some Classes of Synchronous Machines
7.4 Synchronous Machines Equations with a Forcing Term
7.5 The Equation of a Synchronous Machine with a Speed Governor
7.6 The Dynamics of Two Coupled Synchronous Machines
8. Integro-Differential Equations
8.1 General Setting
8.2 A priori Integral Estimates
8.3 Bakaev-Guzh Technique
8.4 Non-Local Reduction Principle
8.5 Phase Synchronization Systems
9. Cycle Slipping in Phase-Controlled Systems
9.1 Frequency-Domain Conditions for Cycle Slipping in ODE´s
9.2 Distributed Parameter Systems
10. Discrete Systems
10.1 Introduction
10.2 Boundedness by Positively Invariant Cones
10.3 Bakaev-Guzh Technique for Discrete Systems
10.4 The Method of Non-Local Reduction

Book reviews