Mathematical Theory of Control

Solutions of uncontrolled systems, spectral form, exponential matrix, repeated roots, solutions of controlled systems, time varying systems, discrete time varying systems, relation between state space and classical forms; Controllability, observability, controllability and polynomials, linear feedback, state observer realization of constant systems; Algebraic criteria for linear systems, Nyqist criteria Liapunov theory, applications to linear systems, construction of liapunov functions, input-output stability, optimal control.