# Shared Flashcard Set

## Details

ASYS 525 FA15
theory and foundation for analysis of linear systems
15
Engineering
11/08/2015

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
 continuous-time system
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
 convolution
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
 discrete-time system
Definition
 The input-output relationship is defined wherever t is a natural number.
Term
 gain
Definition
 Property of systems that map their input to an output that is a scalar multiple of the input.
Term
 homogeneous response
Definition
 An output corresponding to the zero input.
Term
 impulse response
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
 initial condition
Definition
 The specific way the state of the system affects the output.
Term
 input-output model
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
 zero-state response
Definition
 A forced response that satisfies y = 0 when u = 0.
Term
 transfer function
Definition
 The Laplace transform of the impulse response signal H(t - t0) of a causal LTI system.
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