System Theory 1.

Course description:
The subject of system theory. Variables, segment. Closure for segmentation. Abstract object, abstract system. Equivalence of systems. Beam, aggregate, state. Conditions of consistency. Input-output-state relations, state-transition function. Time-invariant linear systems: state variables, solution of the state equation, evaluation of the state transition matrix. Fourier and Laplace transforms, transfer function, causality. Bode plot, Nyquist plot, inverse polar plot. System representations, transformation to canonical form, controllability, observability. Time-variable linear systems: solution of the state equation, fundamental matrix, state transition (Cauchy) matrix, method of variation of constants. Nonlinear systems, state space trajectories, linearization. Stability of time-invariant linear systems, Routh-Hurwitz criterion. Stability in the first (linear) approximation. Ljapunov's second method. Absolute stability. Introduction to control systems.

Recommended Texts:

• Zadeh L. A., Polak  E.: System Theory, McGraw-Hill, New York, 1969
• Zadeh L. A., Desoer C. A.: Linear System Theory, R. E. Krieger Pub. Co., NY, 1979
• Kalman R. E., Falb P. L., Arbib M. A.: Topics in Mathematical System Theory, McGraw-Hill, 1969
•  D'Azzo J. J., Houps C. H.: Linear Control System Analysis and Design: Conventional and Modern, McGraw-Hill,