20th October 2018

wikipedia

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What is a state matrix?

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In control theory, the state-transition matrix is a matrix whose product with the state vector at an initial time gives at a later time . The state-transition matrix can be used to obtain the general solution of linear dynamical systems.

What is state and state variable?

A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system.

What is a state space in artificial intelligence?

State space search is a process used in the field of computer science, including artificial intelligence (AI), in which successive configurations or states of an instance are considered, with the intention of finding a goal state with a desired property.

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What is the zero state response?

In electrical circuit theory, the zero state response (ZSR), also known as the forced response is the behavior or response of a circuit with initial state of zero. The ZSR results only from the external inputs or driving functions of the circuit and not from the initial state.

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What is state trajectory?

Trajectory definition. In dynamical systems, a trajectory is the set of points in state space that are the future states resulting from a given initial state. In a discrete dynamical system, a trajectory is a set of isolated points in state space. In a continuous dynamical system, a trajectory is a curve in state space

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What is the transfer function?

A Transfer Function is the ratio of the output of a system to the input of a system, in the Laplace domain considering its initial conditions and equilibrium point to be zero.

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What is state in control?

A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system.

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What are the characteristics of an equation?

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general matrix , the characteristic equation in variable is defined by. (1)

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What is state variable in control system?

A state variable is one of the set of variables that are used to describe the mathematical "state" of a dynamical system. Intuitively, the state of a system describes enough about the system to determine its future behaviour in the absence of any external forces affecting the system.

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What is the state space?

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. The "state space" is the Euclidean space in which the variables on the axes are the state variables.

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What is the meaning of canonical form?

In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. In this context, a canonical form is a representation such that every object has a unique representation.

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What is the meaning of controllability?

Controllability is an important property of a control system, and the controllability property plays a crucial role in many control problems, such as stabilization of unstable systems by feedback, or optimal control. Controllability and observability are dual aspects of the same problem.

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What is a regular stochastic matrix?

Mathematics. Regular stochastic matrix, a stochastic matrix such that all the entries of some power of the matrix are positive. The opposite of irregular matrix, a matrix with a different number of entries in each row. Regular Hadamard matrix, a Hadamard matrix whose row and column sums are all equal.

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What is a regular transition matrix?

Definition: A transition matrix (stochastic matrix) is said to be regular if some power of T has all positive entries. This means that the Markov chain represented by T is called a regular Markov chain. A Markov process that has a regular transition matrix will have a steady state.

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What does it mean when a matrix is singular?

Singular Matrix. A square matrix that does not have a matrix inverse. A matrix is singular iff its determinant is 0. The following table gives the numbers of singular matrices for certain matrix classes.

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How do you know if a matrix is singular?

We identify the matrix first by the rows and then by the columns. The determinant of a matrix is the product of ad - bc. When this product is zero, then a matrix cannot have an inverse. Also, remember that a singular matrix is one that doesn't have an inverse because the product ab - bc = 0.

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When matrix is singular?

If this is the case, then the matrix B is uniquely determined by A and is called the inverse of A, denoted by A⁻¹. A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0.

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What is singular and non singular matrix?

A square matrix that is not singular, i.e., one that has a matrix inverse. Nonsingular matrices are sometimes also called regular matrices. A square matrix is nonsingular iff its determinant is nonzero (Lipschutz 1991, p. 45).

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What is a singular matrix error?

A singular matrix is a matrix that cannot be inverted, or, equivalently, that has determinant zero. So better make sure your matrix is non-singular (i.e., has non-zero determinant), since numpy.linalg.solve requires non-singular matrices.

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