Theory of Stability for Important Classes of Dynamical Systems

This work explores dynamical systems and pertinent mathematics. One of its main objectives is to demonstrate that by using functional-analytic methods, it is possible to obtain a unified treatment of the Theory of Dynamical Systems. The important classes of Dynamical Systems that are treated in this book are Linear Autonomous Systems, Linear Periodic Systems, and Nonlinear Systems, such as Quasi-Linear Systems with Autonomous or Periodic Linear Part. It also contains two-sided bounds on the solution of stability problems leading to new results and significant improvements compared to results obtained by the Lyapunov method. The Lyapunov method shortcomings in predicting the stability of certain dynamical systems are overcome in this book by the state-space description of the associated differential equations, the special weighted norm left | cdot right |?R derived by the author in previous work, and the equivalence of norms in finite-dimensional spaces. This study serves both as a monograph and a textbook. It is intended for Mathematicians as well as for Physicists and Engineers. The numerous exercises and their complete solutions included in this book could be used for study by students and experts in the industry. ``With its rigorous theoretical foundation and practical problem-solving approach, this book provides useful tools for stability analysis of dynamical systems, control systems theory, and applied mathematics.'' (Yan Wu, Georgia Southern University)