Term
characteristic polynomial 

Definition
The denominator (s  Abar) of the transfer function that is realized from the LTI system; an ndegree polynomial whose roots are the eigenvals of the n x n matrix A. 


Term

Definition
The inputoutput 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 blackbox system. The operation is a rewritten function with a timeshift, a flip, and a multiplication. Convolution computes the zerostate response in the time domain. 


Term
convolution Laplace transform 

Definition
L{ (x * y) (t)} = xbar(s) • ybar(s). 


Term
degree of a transfer function 

Definition
The degree of the pole/characteristic polynomial. 


Term

Definition
The inputoutput 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
xdot = A•x + B•u, y = C•x + D•u. A firstorder diffeq state equation and a linear output equation. 


Term
Laplace transform derivative operator 

Definition
Xdotbar = s • xbar(s)  x0. 


Term
linear timeinvariant (LTI) system 

Definition
A timeshift in input [u(tt0)] results in a timeshift in output [y(tt0) 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. 

