ABSTRACT
Dynamic systems are often described in terms of differential equations (in continuous time) or in terms of difference equations (in discrete time). The state of the system (or the state vector) is a set of numbers x1(t0), x2(t0), . . . , xm(t0), characterized by the fact that, together with possible input-signals and noise disturbances at time t ≥ t0, they uniquely determine the system at times t ≥ t0. For deterministic systems (i.e., systems without noise), the state contains the initial values necessary to determine the particular solution to the differential or difference equation. The complete solution and the set of initial conditions will determine the future evolution of the system without uncertainty. For stochastic systems, the state vector at a given time contains all information available for the future evaluation of the system. The state (or the state vector) is thus a (first order) Markov process. A system having m states is called an m’th order system.
