ABSTRACT
A large class of systems, such as linear, nonlinear, time-varying, and nontime-varying, is analyzed using the methodology of the state space, where the system is described by a set of first-order difference equations, describing the state variables. The state differential equation gives the relationship between the system inputs, system state, and rate of change. The controllability of a system refers to whether it is possible to move a system from a given initial state to any final state in finite time. The observability of a system refers to whether each position can be determined by observing the output at a finite time. In the automatic control theory, concepts of controllability and observability are related to the design of the controller, which solves the problem of regulation through the positioning of the hedged system poles at desired positions.
