Qualitative Theory Of Dynamical Systems: The Role Of Stability Preserving Mappings (monographs And Textbooks In Pure And Applied Mathematics, Vol 18)

"Illuminates the most important results of the Lyapunov and Lagrange stability theory for a general class of dynamical systems by developing topics in a metric space independantly of equations, inequalities, or inclusions. Applies the general theory to specific classes of equations. Presents new and expanded material on the stability analysis of hybrid dynamical systems and dynamical systems with discontinuous dynamics." Booknews By developing topics in a metric space, independently of equations, inequalities, or inclusions, this volume discusses the results of the Lyapunov and Lagrange stability theory for a general class of dynamical systems. In addition, several chapters focus on the stability analysis of hybrid dynamical systems and dynamical systems with discontinuous dynamics, which frequently defy traditional modeling and analysis techniques. Michel (emeritus, engineering, U. of Notre Dame), Wang, Chief Technology Officer at a California corporation, and Hu (postdoc research, electrical engineering, U. of Notre Dame) explain case studies investigating pulse-width-modulated feedback control systems, linear systems under state saturation constraints, switched systems, and systems with impulsive dynamics. Annotation c. Book News, Inc., Portland, OR (booknews.com) "Employing a general definition of dynamical systems applicable to finite and infinite dimensional systems, including systems that cannot be characterized by equations, inequalities, and inclusions, this important reference/text - the only book of its kind available - introduces the concept of stability preserving mappings to establish a qualitative equivalence between two dynamical systems - the comparison system and the system to be studied." "Written by renowned authorities in the field, Qualitative Theory of Dynamical Systems is an incomparable reference for pure and applied mathematicians; electrical and electronics, mechanical, civil, aerospace, and industrial engineers; control theorists; physicists; computer scientists; chemists; biologists; econometricians; and operations researchers; and the text of choice for all upper-level undergraduate and graduate students with a background in linear algebra, real analysis, and differential equations taking courses in stability theory, nonlinear systems, dynamical systems, or control systems."--Jacket Written by renowned authorities in the field, Qualitative Theory of Dynamical Systems is an incomparable reference for pure and applied mathematicians; electrical and electronics, mechanical, civil, aerospace, and industrial engineers; control theorists; physicists; computer scientists; chemists; biologists; econometricians; and operations researchers; and the text of choice for all upper-level undergraduate and graduate students with a background in linear algebra, real analysis, and differential equations taking courses in stability theory, nonlinear systems, dynamical systems, or control systems. Employing a general definition of dynamical systems applicable to finite and infinite dimensional systems, including systems that cannot be characterized by equations, inequalities, and inclusions, this important reference/text - the only book of its kind available - introduces the concept of stability preserving mappings to establish a qualitative equivalence between two dynamical systems - the comparison system and the system to be studied. In this book we present a unified qualitative theory for dynamical systems which is applicable to finite dimensional and infinite dimensional systems determined by various types of classical equations and inequalities (e.g., ordinary differential equations, ordinary difference equations, ordinary differential inequalities, ordinary difference inequalities, functional differential equations, partial differential equations, Volterra integrodifferential equations, and so forth) as well as contemporary technological systems which defy simple and tidy descriptions by such equations and inequalities (e.g., flexible manufacturing systems, temporal logic systems, computer networks, and other types of discrete event and hybrid systems). Introduces the concept of stability preserving mappings to establish a qualitative equivalence between the two dynamical systems - the comparison system and the system to be studied. The book sets out to provide insight into dynamical systems unobtainable by usual treatments of the subject. Content: 1. Introduction -- 2. Dynamical Systems -- 3. Stability Preserving Mappings -- 4. Stability of Motion -- 5. Finite Dimensional Systems -- 6. Infinite Dimensional Systems -- 7. Differential Inclusions. Revised and expanded for the second edition, this text presents material on the stability analysis of hybrid dynamical systems and dynamical systems with discontinuous dynamics