Textbook in PDF format

This book presents a projector analysis of dynamic systems on time scales. The dynamic systems are classified as first, second, third and fourth kinds. For each classes of dynamic systems the basic matrix chains are constructed. The proposed theory is applied for decoupling of dynamic equations on time scales. Properly involved derivatives, constraints and consistent initial values for the considered equations are defined. A linearization for nonlinear dynamic systems is introduced and the total derivative for regular linearized equations with tractability index one is investigated. Preface Introduction Linear dynamic-algebraic equations with constant coefficients P-projectors. Matrix chains First kind linear time-varying dynamic-algebraic equations Second kind linear time-varying dynamic-algebraic equations Third kind linear time-varying dynamic-algebraic equations Fourth kind linear time-varying dynamic-algebraic equations Jets and jet spaces Nonlinear dynamic-algebraic equations Elements of theory of matrices Fréchet derivatives and Gâteaux derivatives Pötzsche’s chain rule Bibliography Index