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. |