LTISystem
Purpose
Represents linear time-invariant systems
Syntax
sys = LTISystem('A', A, 'B', B, 'C', C, 'D', D, 'T_s', Ts)
Description
This class represents linear time-invariant systems of the form

where
is the state vector,
is the vector of inputs,
is the vector of outputs, and
represents the sampling time.
Each LTI system defines following properties:
-
A, B: matrices of the
state-update equation (read-only)
-
C, D: matrices of the
output equation (read-only)
-
Ts: sampling time (read-only)
-
nx, nu, ny: number of states,
inputs and outputs (automatically determined, read-only)
-
x: specifications of system's states (see help
SystemSignal)
-
u: specifications of system's inputs (see help
SystemSignal)
-
y: specifications of system's outputs (see help
SystemSignal)
To define an LTI system, provide the list of system's matrices to
the constructor:
sys = LTISystem('A', A, 'B', B, 'C', C, 'D', D, 'Ts', Ts)
All inputs, except of the A matrix, can be omitted. In
such a case they are set to empty matrices of corresponding
dimension. As a consequence, one can easily define autonomous
systems
by calling sys =
LTISystem('A', A, 'f', f, 'Ts', Ts). Similarly, to define an
LTI system without outputs, call sys = LTISystem('A', A, 'B',
B, 'Ts', Ts). If the sampling time is omitted, it is set to
Ts=1.
Another option to define an LTI system is to import the dynamics
from Control toolbox' discre-time state-space objects:
sys = LTISystem(ss(A, B, C, D, Ts))
Important to remember is that LTI systems carry with them the
value of the state vector. The initial value can be set by the
sys.initialize(x0) method (see "help
LTISystem/initialize"). Value of the internal state can be
retrieved by the sys.getStates() method (see "help
LTISystem/getStates"). To update the internal state using the
system's state-update equation, use the sys.update(u)
function (see "help LTISystem/update").
Example(s)
Example
1
Create a 1D LTI system
,
sys = LTISystem('A', 2, 'B', 1, 'C', 3)
LTISystem with 1 state, 1 input, 1 output
See Also
pwasystem
© 2003-2013 Michal Kvasnica: STU Bratislava, michal.kvasnica@stuba.sk