Matrix diagonal stability in systems and computati

Matrix diagonal stability and the related diagonal type Liapunov functions possess properties that make them attractive and very useful for applications. This new book addresses the matrix-stability concept and its applications to the analysis and design of several types of dynamical systems, both discrete-time and continuous-time. The comprehensive presentation begins with an introductory chapter surveying applied examples from diverse fields, i.e., robust stability analysis, asynchronous iterative computation, neural networks and variable structure dynamical systems. The next few chapters develop the theory and includes a unified presentation of results in the area of matrix-diagonal stability and D-stability. The remaining chapters examine the various applications in greater detail. Both classical and new results are discussed, and the overall treatment is self-contained, only requiring linear algebra, difference equations and differential equations. Topics and Features: Diverse applications presented with minimum of technical prerequisites Unified presentation of results on discrete-time and continuous-time diagonal and D-stability Extensive guide to current literature and discussion of open problems Asynchronous iterative methods Stability and stabilization Neural networks, circuits and systems Matrix Diagonal Stability in Systems and Computation provides an essential reference for new methods and analysis related to dynamical systems described by linear and nonlinear ordinary differential equations and difference equations. Researchers, professionals and graduates in applied math, control engineering, stability of dynamical systems, scientific computation and computer science will find the book a successful guide to current results and developments. Contents: Preface 1. Diagonally Stable Structures in Systems and Computation 1.1 Introduction 1.2 Robust Stability of a Mechanical System 1.3 Lotka-Volterra Equations of Population Biology 1.4 Convergence of Asynchronous Computation 1.5 Global Stability of Neural Networks 1.6 Variable Structure Systems 1.7 Existence of Diagonal Type Liapunov Functions 1.8 Notes and References 2. Matrix Diagonal and D-Stability 2.1 Matrix stability concepts 2.1.1 Basic notation and terminology 2.1.2 Basic results on Hurwitz diagonal and D-stability 2.2 Special classes of Hurwitz diagonally stable matrices 2.3 Similarity for Hurwitz diagonally stable matrices 2.4 Persistence of diagonal stability under perturbations 2.5 Basic results on Schur diagonal and D-stability 2.6 A matrix polytopic view of Schur diagonal and D-stability 2.7 Special classes of Schur diagonally stable matrices 2.7.1 Schur diagonal and D-stability for 2 by 2 matrices 2.7.2 Nonegative matrices 2.7.3 Qualitatively Schur stable matrices 2.8 Testing for diagonal and D-stability 2.9 Notes and References 3. Mathematical Models Admitting Diagonal Type Liapunov Functions 3.1 Classes of nonlinearities and diagonal type Liapunov functions 3.2 Continuous-time models and stability results 3.3 Discrete-time models and stability results 3.3.1 Discrete-time interval systems 3.4 Models for asynchronous systems 3.5 Discrete-time systems with delays 3.6 Seeking diagonal stability: state space realization procedures 3.7 Notes and References 4. Convergence of Asynchronous Iterative Methods 4.1 What are asynchronous iterative methods? 4.2 A mathematical model for asynchronous block-iterations 4.2.1 Convergence conditions for the asynchronous case 4.2.2 Convergence conditions for the synchronous case 4.3 Asynchronous iterations to solve almost linear equations 4.4 Parallel asynchronous team algorithms 4.5 Notes and References 5. Neural Networks, Circuits and Systems 5.1 Continuous-time neural networks 5.1.1 A global stability result 5.1.2 Refinements of the global stability result 5.1.3 Persistence of global asymptotic stability 5.2 Discrete-time neural networks 5.3 Passive RLC circuits 5.4 Digital filters in state-space description 5.5 Two-dimensional dynamical systems 5.6 Trophic chains and communities with vertical structure 5.7 Notes and References 6. Interconnected Systems: Stability and Stabilization 6.1 Diagonal stability in the large scale systems approach 6.2 Absolute stability of interconnected systems 6.3 Linearly interconnected Lur'e systems 6.4 Linear feedback stabilization 6.5 Power systems with decentralized power-frequency control 6.6 Notes and References 6.7 Appendix: Summary of the large scale system approach Epilogue References Index