Page 63 - Electrical Engineering Dictionary

i, j ∈ Z + (the set of nonnegative integers) is that start “sufficiently close,” approach this
called a full-order asymptotic observer of the point in time. See also stable equilibrium.
second generalized Fornasini–Marchesini 2-
D model asymptotically stable in the large the
equilibrium state of a stable dynamic system
Ex i+1,j+1 = A 1 x i+1,j + A 2 x i,j+1 described by a first-order vector differential
+ B 1 u i+1,j + B 2 u i,j+1 equation is said to be asymptotically stable in
the large if its region of attraction is the entire
y i,j = Cx i,j + Du i,j
n
space < . See also region of attraction.
i, j ∈ Z + if
asymptotically stable state the equilib-

lim x i,j −ˆx i,j = 0 riumstate of adynamicsystem described by a
i,j→∞
first-order vector differential equation is said
for any u i,j , y i,j and boundary conditions to be asymptotically stable if it is both con-
x i0 for i ∈ Z + and x 0j for j ∈ Z + where vergent and stable. See also stable state and
n
z i,j ∈ R is the local state vector of the ob- convergent state.
server at the point (i, j), u ij ∈ R m is the
p
input, y i,j ∈ R is the output, and x i,j ∈ R n
asynchronous not synchronous.
is the local semistate vector of the model, F 1 ,
F 2 , G 1 , G 2 , H 1 , H 2 , L, K, E, A 1 , A 2 , B 1 , B 2 ,
C, D are real matrices of appropriate dimen- asynchronous AC systems AC systems
sions with E possibly singular or rectangular. either with different operating frequencies or
In a similar way a full-order asymptotic ob- that are not in synchronism.
server can be defined for other types of the
2-D generalized models. asynchronous bus a bus in which the
timing of bus transactions is achieved with
asymptotic stability (1) an equilibrium two basic “handshaking” signals, a request
state of a system of ordinary differential signal from the source to the destination and
equations or of a system of difference equa- an acknowledge signal from the destination
tions is asymptotically stable (in the sense of to the source. The transaction begins with
Lyapunov) if it is stable and the system tra- the request to the destination. The acknowl-
jectories converge to the equilibrium state as edge signal is generated when the destination
time goes to infinity, that is, the equilibrium is ready to accept the transaction. Avoids
x eq is asymptotically stable if it is stable and the necessity to know system delays in ad-
vance and allows different timing for differ-
x(t) → x eq as t →∞ . ent transactions. See also synchronous bus.

(2) a measure of system damping with re-
asynchronous circuit (1) a sequential
gard to a power system’s ability to reach its
logic circuit without a system clock.
original steady state after a disturbance.
(2) a circuit implementing an asyn-
chronous system.
asymptotic tracking refers to the abil-
ity of a unity feedback control to follow its
setpoint exactly with zero error once all tran- asynchronous demodulation a tech-
sientshavedecayedaway. Clearlythisisonly nique for extracting the information-carrying
achieved by stable systems. waveform from a modulated signal with-
out requiring a phase-synchronized carrier
asymptotically stable equilibrium a sta- for demodulation. See also synchronous
ble equilibrium point such that all solutions demodulation.

c
2000 by CRC Press LLC