This book focuses on some problems of stability theory of nonlinear large-scale systems. The purpose of this book is to describe some new applications of Lyapunov matrix-valued functions method to the stability of evolution problems governed by nonlinear continuous systems, discrete-time systems, impulsive systems and singularly perturbed systems under structural perturbations. The authors take a challenging and original approach based on concept of structural perturbations combined with direct Lyapunov's method. This new approach will lead to results that cannot be obtained by standard theories of stability in the field.

The Stability Theory of Large Scale Dynamical Systems addresses to specialists in dynamical systems, applied differential equations, and the stability theory. It may be useful for graduated students in mathematics, control theory, and mechanical engineering.

1. Generalities
   1. Introduction
   2. Some Types of Large-Scale Dynamical Systems
   3. Structural Perturbations of Dynamical Systems
   4. Stability under Nonclassical Structural Perturbations
   5. Method of Stability Analysis of Motion
   6. Notes and References
2. Continuous Large-Scale Systems
   1. Introduction
   2. Nonclassical Structural Perturbations in Time-Continuous Systems
   3. Estimates of Matrix-Valued Functions
   4. Tests for Stability Analysis
   5. Linear Systems Analysis
   6. Certain Trends of Generalizations and Applications
   7. Notes and References
3. Discrete-Time Large-Scale Systems
   1. Introduction
   2. Nonclassical Structural Perturbations in Discrete-Time Systems
   3. Liapunov’s Matrix-Valued Functions
   4. Tests for Stability Analysis
   5. Certain Trends of Generalizations and Applications
   6. Notes and References
4. Impulsive Large-Scale Systems
   1. Introduction
   2. Nonclassical Structural Perturbations in the Impulsive Systems
   3. Definitions of Stability
   4. Tests for Stability and Instability Analysis
   5. Linear Systems Analysis
   6. Certain Trends of Generalizations and Applications
   7. Notes and References
5. Singularly Perturbed Large-Scale Systems
   1. Introduction
   2. Nonclassical Structural Perturbations in Singularly Perturbed Systems
   3. Tests for Stability Analysis
   4. Tests for Instability Analysis
   5. Linear Systems
   6. Certain Trends of Generalizations and Applications
   7. Notes and References