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:

../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem12.png

where ../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem1.png is the state vector, ../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem2.png is the vector of inputs, ../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem3.png is the vector of outputs, ../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem4.png represents the sampling time, and ../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem5.png are the polyhedral regions of validity of the ../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem6.png-th local dynamics.

Each PWA system defines following properties: 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 ../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem8.png, and is valid for ../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem9.png.
sys1 = LTISystem('A', 1, 'B', 1);

sys1.setDomain('x', Polyhedron('lb', 0));
The second model has dynamics ../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem10.png, and
    is valid if ../../../../../fig/mpt/modules/ui/@PWASystem/pwasystem11.png.
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