Term
| characteristic polynomial |
|
Definition
| The denominator (s - A-bar) of the transfer function that is realized from the LTI system; an n-degree polynomial whose roots are the eigenvals of the n x n matrix A. |
|
|
Term
|
Definition
| The input-output relationship between u and y is defined from 0 to ∞. One input generally corresponds to several possible outputs, due to different initial conditions. u and y are signals. |
|
|
Term
|
Definition
| The, possibly infinite, sum of point responses that represent u acting on a black-box system. The operation is a rewritten function with a time-shift, a flip, and a multiplication. Convolution computes the zero-state response in the time domain. |
|
|
Term
| convolution Laplace transform |
|
Definition
| L{ (x * y) (t)} = x-bar(s) • y-bar(s). |
|
|
Term
| degree of a transfer function |
|
Definition
| The degree of the pole/characteristic polynomial. |
|
|
Term
|
Definition
| The input-output relationship is defined wherever t is a natural number. |
|
|
Term
|
Definition
| Property of systems that map their input to an output that is a scalar multiple of the input. |
|
|
Term
|
Definition
| An output corresponding to the zero input. |
|
|
Term
|
Definition
| An array of individual outputs at time t, corresponding to a pulse of zero length but unit area applied at time tau. y(t) = int[ H(t,tau)•u(tau)dtau] from 0 to ∞, t>0. The impulse response satisfies H = 0 for tau > t, and y is the convolution of H and u. |
|
|
Term
|
Definition
| The specific way the state of the system affects the output. |
|
|
Term
|
Definition
| x-dot = A•x + B•u, y = C•x + D•u. A first-order diffeq state equation and a linear output equation. |
|
|
Term
| Laplace transform derivative operator |
|
Definition
| X-dot-bar = s • x-bar(s) - x0. |
|
|
Term
| linear time-invariant (LTI) system |
|
Definition
| A time-shift in input [u(t-t0)] results in a time-shift in output [y(t-t0) is in R]. The matrices A, B, C, D are all constant wrt time for t>0. The transfer function concept is meaningful only for LTI systems. |
|
|
Term
|
Definition
| A forced response that satisfies y = 0 when u = 0. |
|
|
Term
|
Definition
| The Laplace transform of the impulse response signal H(t - t0) of a causal LTI system. |
|
|
