Concepts of stability and control

The first part of the paper deals with the role transfer functions play in control problems (closed loop, Nyquist stability criterion, sampled data systems and z-transforms; the ''hog cycle''; spring oscillations; Lyapunov functions; the Zubov method; positive-real functions and the Popov criterion; the circle criterion; linear time-delay systems; equations with periodic coefficients; stability of repeated processes). In the second part the author considers the control of systems which are described by partial differential equations (heat-conduction equation; wave equation; control of the heat and the wave equations; parasitic oscillations; noise in linear systems; discrete noise processes). Many examples are given and briefly discussed. (author)