Home > mpt > @polytope > le.m

# le

## PURPOSE

LE Checks if polytope P is a subset of polytope Q

## SYNOPSIS

function status = le(P,Q,Options)

## DESCRIPTION

```LE Checks if polytope P is a subset of polytope Q

status = le(P,Q,Options)

---------------------------------------------------------------------------
DESCRIPTION
---------------------------------------------------------------------------
STATUS = LE(P,Q) returns TRUE (1) if P<=Q (i.e. P is a subset of Q)

USAGE:
P<=Q
le(P,Q)
le(P,Q,Options)

NOTE:
If P is an empty polytope, the statement is always TRUE
If Q is an empty polytope, the statement is always FALSE

---------------------------------------------------------------------------
INPUT
---------------------------------------------------------------------------
P,Q              - Polytopes
Options.rel_tol  - relative tolerance
Options.abs_tol  - absolute tolerance
Options.lpsolver - LP solver to use (see help mpt_solveLP)

Note: If Options is missing or some of the fields are not defined, the default
values from mptOptions will be used

---------------------------------------------------------------------------
OUTPUT
---------------------------------------------------------------------------
status           - Logical statement (true if P<=Q, false otherwise)

## CROSS-REFERENCE INFORMATION

This function calls:
• length LENGTH Returns number of regions over which the explicit control law is defined
• bounding_box BOUNDING_BOX Compute a bounding box for a given polytope
• dimension DIMENSION Returns dimension of the given polytope
• end END Returns the last element in a given polytope array
• isfulldim ISFULLDIM Checks if a polytope is full dimensional
• le LE Checks if polytope P is a subset of polytope Q
• length LENGTH Returns number of elements in a polytope array
• mldivide MLDIVIDE Set difference
• chebyball_f CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope
• size SIZE Returns size of the given polytope object
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
This function is called by:
• display DISPLAY Displays details about the given polytope
• ge GE Checks if polytope P is a superset of polytope Q
• le LE Checks if polytope P is a subset of polytope Q
• mpt_maxCtrlSet MPT_MAXCTRLSET Computes the maximal robust control invariant set C_inf
• mpt_boolMinTime MPT_BOOLMINTIME Computes minimum time controller for systems with discrete inputs
• mpt_iterative MPT_ITERATIVE Computes a time-optimal or low-complexity explicit controller for LTI systems
• mpt_iterativePWA MPT_ITERATIVEPWA Computes a time-optimal or low-complexity explicit controller for PWA systems
• mpt_mixedMinTime MPT_MIXEDMINTIME Computes minimum time controller for systems with discrete and continuous inputs

Generated on Thu 30-Mar-2006 10:26:47 by m2html © 2003