State Space Models Flashcards
What is a state?
A set of variables used to describe the behaviour of a dynamic system at any particular time.
What is a state variable?
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.
What two primary kinds of equations used in state space models?
Differential Equations, Difference Equations
What is a difference equation?
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.
What is the order of a system?
The dimension of the system’s state vector.
What is a state vector?
A set of data describing exactly where an object is located in space and how an object in space is moving.
What is an eigenvector?
What is an eigenvalue?
What is the transpose of a matrix?
How do you find the transpose of a matrix?
What is the state space?
The nth dimensional space where state variables change as a function of time.
What is the benefit of using state-space methods vs frequency domain methods in terms of types of systems that can be described?
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.
What is the general state equation for a linear state space system?
dx/dt = Ax + Bu ,
where matrix A is called the dynamics matrix, and matrix B is called the control matrix.
What is the general output equation for a linear state space system?
y = Cx + Du ,
where the matrix C is called the sensor matrix, and matrix D is called the direct term.
