Question

which functions based on the representation of states.
please answer correctly.

Answer 1

Answer:

In control engineering, a state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations or difference equations. State variables are variables whose values evolve over time in a way that depends on the values they have at any given time and on the externally imposed values of input variables. Output variables’ values depend on the values of the state variables.

The "state space" is the Euclidean space in which the variables on the axes are the state variables. The state of the system can be represented as a vector within that space.

To abstract from the number of inputs, outputs and states, these variables are expressed as vectors. Additionally, if the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.[1][2] The state-space method is characterized by significant algebraization of general system theory, which makes it possible to use Kronecker vector-matrix structures. The capacity of these structures can be efficiently applied to research systems with modulation or without it.[3] The state-space representation (also known as the "time-domain approach") provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. With {\displaystyle p}p inputs and {\displaystyle q}q outputs, we would otherwise have to write down {\displaystyle q\times p}q\times p Laplace transforms to encode all the information about a system. Unlike the frequency domain approach, the use of the state-space representation is not limited to systems with linear components and zero initial conditions.

The state-space model can be applied in subjects such as economics[4], statistics[5], computer science and electrical engineering[6], and neuroscience[7]. In econometrics, for example, state-space models can be used to decompose a time series into trend and cycle, compose individual indicators into a composite index[8], identify turning points of the business cycle, and estimate GDP using latent and unobserved time series[9][10]. Many applications rely on the Kalman Filter to produce estimates of the current unknown state variables using their previous observations.[11][12]

Explanation:

Answer 2

Concept Introduction:

The values on the axis are the key parameters in the Euclidean space known as the "state space." Within that space, the system's state can be represented by a matrix.

Explanation:

We have been given a question about the representation of states.

We have to find out the functions based on it.

A state-space representation is a theoretical representation of a physical system in control engineering that consists of a set of input, output, and state variables connected by first-order differential equations or finite differences. State variables are those variables whose values change over time in a fashion that relies on the quantities they have at any one time and the values that are imposed on input variables from the outside. Values of state variables impact those of output variables.

Final Answer:

A state-space representation is a theoretical representation of a physical system in control engineering.

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