ABSTRACT

Every entry of the n-dimensional vector variables a(.), g(.), p(.), r(.), v(.), ϑ(.), w(.), x(.), can be, in principle, measured relative to a time axis associated with that entry. This characterizes complex processes and systems (automatic control systems of aircrafts, of power stations, of ships, and of robots; biological control systems of beings, and control systems of economic processes). The dimension of the state vector x of such systems can be (much) greater than three. This holds also for the vector physical variable g(.) and for the vector variable p(.) composed of different physical variables. We will use r(.) in the broad sense so that it can represent, and can be replaced by g(.) or p(.) or x(.). This means that what follows is valid for complex processes and systems whatever is their nature.