State Space Models Flashcards

1
Q

What is a state?

A

A set of variables used to describe the behaviour of a dynamic system at any particular time.

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2
Q

What is a state variable?

A

A state variable is a parameter in which models a system, allows us to find all other parameters of a system and describes the current and future state of the overall system.

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3
Q

What two primary kinds of equations used in state space models?

A

Differential Equations, Difference Equations

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4
Q

What is a difference equation?

A

A mathematical equation describing the relationship of a value to its previous value/values. It is the equivalent of a differential equation in discrete time.

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5
Q

What is the order of a system?

A

The dimension of the system’s state vector.

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6
Q

What is a state vector?

A

A set of data describing exactly where an object is located in space and how an object in space is moving.

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7
Q

What is an eigenvector?

A
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8
Q

What is an eigenvalue?

A
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9
Q

What is the transpose of a matrix?

A
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10
Q

How do you find the transpose of a matrix?

A
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11
Q

What is the state space?

A

The nth dimensional space where state variables change as a function of time.

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12
Q

What is the benefit of using state-space methods vs frequency domain methods in terms of types of systems that can be described?

A

State space methods can describe multiple-input-multiple-output (MIMO), non-linear, time-variant systems while frequency domain methods can only describe single-input, single-output (SISO), linear, time-invariant systems.

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13
Q

What is the general state equation for a linear state space system?

A

dx/dt = Ax + Bu ,
where matrix A is called the dynamics matrix, and matrix B is called the control matrix.

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14
Q

What is the general output equation for a linear state space system?

A

y = Cx + Du ,
where the matrix C is called the sensor matrix, and matrix D is called the direct term.

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