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The state diagram from Figure 2 is an example of an extended state machine, in which the complete condition of the system (called the extended state) is the combination of a qualitative aspect—the state variable—and the quantitative aspects—the extended state variables.
A state diagram for a door that can only be opened and closed. A state diagram is used in computer science and related fields to describe the behavior of systems. State diagrams require that the system is composed of a finite number of states. Sometimes, this is indeed the case, while at other times this is a reasonable abstraction.
The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector, the state vector. If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
It is possible to draw a state diagram from a state-transition table. A sequence of easy to follow steps is given below: Draw the circles to represent the states given. For each of the states, scan across the corresponding row and draw an arrow to the destination state(s).
A sample UML class and sequence diagram for the State design pattern. [2] The state design pattern is one of twenty-three design patterns documented by the Gang of Four that describe how to solve recurring design problems. Such problems cover the design of flexible and reusable object-oriented software, such as objects that are easy to ...
The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form ˙ = () + (), =, where () are the states of the system, () is the input signal, () and () are matrix functions, and is the initial condition at .
An invariant point is defined as a representation of an invariant system (0 degrees of freedom by Gibbs' phase rule) by a point on a phase diagram. A univariant line thus represents a univariant system with 1 degree of freedom. Two univariant lines can then define a divariant area with 2 degrees of freedom.
Example of a measure that is invariant under the action of the (unrotated) baker's map: an invariant measure. Applying the baker's map to this image always results in exactly the same image. In dynamical systems theory, the baker's map is a chaotic map from the unit square into itself.