invariantSet

Purpose

Computation of invariant sets for linear systems

Syntax

S = system.invariantSet()
S = system.invariantSet('X', X, 'U', U)

Description

For an autonomous LTI system ../../../../../fig/mpt/modules/ui/@LTISystem/invariantset1.png this function computes the set of states for which recursive satisfaction of state constraints can be shown.

The set is computed by running the set recursion

../../../../../fig/mpt/modules/ui/@LTISystem/invariantset9.png

initialized by ../../../../../fig/mpt/modules/ui/@LTISystem/invariantset2.png and terminating once ../../../../../fig/mpt/modules/ui/@LTISystem/invariantset3.png. If ../../../../../fig/mpt/modules/ui/@LTISystem/invariantset4.png is not provided, ../../../../../fig/mpt/modules/ui/@LTISystem/invariantset5.png is assumed.

For an LTI system ../../../../../fig/mpt/modules/ui/@LTISystem/invariantset6.png, which is subject to polyhedral state constraints ../../../../../fig/mpt/modules/ui/@LTISystem/invariantset7.png and input constraints ../../../../../fig/mpt/modules/ui/@LTISystem/invariantset8.png this function calculates the maximal control-invariant set

../../../../../fig/mpt/modules/ui/@LTISystem/invariantset10.png

Note that this function requires that state constraints defined in system.x.min and system.x.max (see "help SystemSignal").

Input Arguments

X

Polyhedron defining state constraints (optional)

Class: polyhedron

U

Polyhedron defining input constraints (optional)

Class: polyhedron

maxIterations

Maximal number of iterations (optional)

Class: double

Output Arguments

S

Invariant set

Class: Polyhedron


© 2003-2013 Michal Kvasnica: STU Bratislava, michal.kvasnica@stuba.sk