# State Space

(redirected from State-space)

## state space

[′stāt ‚spās]
(control systems)
The set of all possible values of the state vector of a system.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## State Space

The state space of a dynamical system is a space such that each point in the space is uniquely associated with a certain state of the system (in some generalized coordinates). The points of the state space are known as representative points. To each process of change of state of the system (that is, to the system’s motion in these coordinates) there corresponds a certain trajectory of the motion of the representative point in the space. The concept of state space is used most often in investigations of the motion of dynamical systems in celestial mechanics, vibration theory, and the theory of automatic control.

In many technological, biological, and economic systems, the generalized coordinates of the system being considered can assume only discrete values. The states of such systems must also be regarded as discrete, and the representative points are viewed as belonging to a discrete state space. To the changes in state of such systems (that is, to the motion of the systems) there correspond successive jumps of the representative point from one position to another.

A different case is presented by systems involving parameters (coordinates) that are distributed in space. A state space with a finite number of dimensions is not sufficient for representing the states of the system in such a way as to provide a one-to-one correspondence between the state of the system (in these coordinates) and the position of the representative point. An example of such a system is a body whose state is characterized by its temperature field. A geometric image of the state of such a system can be obtained only in a space with an infinite number of dimensions.

The state space is a special case of a phase space.

References in periodicals archive ?
The state equation of state-space model is built with the motion characteristic of mobile target.
In Section 2, the FMS estimation for state-space model is reviewed briefly.
These applications use different representations (thermal networks, state-space models, autoregressive models, etc.) for the same physical system.
State-Space Methods for Time Series Analysis: Theory, Applications and Software
We conclude this section by some comments with respect to the extra difficulty to obtain, in addition to the state-space, the unknown input, e.g.
The SG connected to an infinite bus is a multivariable non-linear dynamic system described with a 7th order nonlinear state-space model.
The most influential methods are CVA (Canonical Variate Analysis [5]), MOESP (Multivariable Output Error State Space [6]) and N4SID (Numerical Subspace State-Space System Identification [6]).
This paper, therefore, deals with the problem of stability analysis of a class of discrete-time state-delayed systems in state-space realization employing saturation overflow arithmetic.
Using the three-dimensional theory of elasticity, Alibeigloo and Shakeri [5] combined the state-space and differential quadrature method (DQM) for investigating the free vibration analysis of crossply laminated cylindrical panels.
In this paper, we present a low-order state-space model for the thermal zones in buildings that has low cost sensor requirements.
The method is described in relation to writing differential vectorized equations of the electromechanical process behavior; choice of physical variables to be controlled; writing state-space linear equations in continuous-time, state space equation discretization, and projecting discretized state-space equations into the eigenvector basis of the evolution matrix; discretized state-space equation inversion and calculation of the input equation; and control development, real-time implementation, initial state-space prediction, control under constraints, and examples.

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