PWASystem
Purpose
Represents discrete-time piecewise affine systems
Syntax
sys = PWASystem([lti1, lti2, ..., ltiM])
Description
This class represents PWA systems, which are composed of a finite
number of local affine dynamics, each valid in a corresponding
polyhedral region of the state-input space:

where
is the state vector,
is the vector of inputs,
is the vector of outputs,
represents the sampling time, and
are the polyhedral
regions of validity of the
-th local dynamics.
Each PWA system defines following properties:
-
A, B, f: matrices of the
state-update equation, stored as cell arrays (read-only)
-
C, D, g: matrices of the
output equation, stored as cell arrays (read-only)
-
Ts: sampling time (read-only)
-
domain: array of polyhedra denoting domain of the
-th local model (read-only)
-
nx, nu, ny: number of states,
inputs and outputs (automatically determined, read-only)
-
ndyn: number of local models (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)
-
d: specifications of the binary dynamics selector
signal (see help SystemSignal)
The preferred way to define a PWA system consisting of a finite
number of local affine models is to provide the list of LTI models
to the PWASystem constructor:
pwasys = PWASystem([ltisys1, ltisys2, ..., ltisysM])
Here, each LTI model must have its domain defined by the
ltisys.setDomain() method (see "help
LTISystem/setDomain").
Example(s)
Example
1
We create a PWA system, consisting of two local affine
models.The first model is given by
, and is
valid for
.sys1 = LTISystem('A', 1, 'B', 1);
sys1.setDomain('x', Polyhedron('lb', 0));
The second model has dynamics
, and
is valid if
.sys2 = LTISystem('A', -2, 'B', 0.5);
sys2.setDomain('x', Polyhedron('ub', 0));
Create the PWA system using sys1 and
sys2:pwa = PWASystem([sys1, sys2])
State/input/output constraints not imported, set them manually afterwards.
PWASystem with 1 state, 1 input, 0 outputs, 2 modes
See Also
ltisystem
© 2003-2013 Michal Kvasnica: STU Bratislava, michal.kvasnica@stuba.sk