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lt

PURPOSE

LT Checks if polytope P is a strict subset of polytope Q

SYNOPSIS

function status = lt(P,Q,Options)

DESCRIPTION

```LT Checks if polytope P is a strict subset of polytope Q

status = lt(P,Q,Options)

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

USAGE:
P<Q
lt(P,Q)
lt(P,Q,Options)

NOTE:
comparing two polyarrays involves making a minkowski sum of one of them
with an epsilon-box. This operation is computationally very expensive, so
try to use no-strict operator (<=) if possible.

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

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INPUT
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P,Q                 - Polytopes
Options.rel_tol     - relative tolerance
Options.abs_tol     - absolute tolerance
Options.lpsolver    - LP solver to use (see help mpt_solveLP)
Options.verbose     - level of verbosity
Options.elementwise - compares two polyarrays elementwise

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

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OUTPUT
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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
• length LENGTH Returns number of elements in a polytope array
• lt LT Checks if polytope P is a strict subset of polytope Q
• mldivide MLDIVIDE Set difference
• plus PLUS Minkowski sum of two polytopes
• chebyball_f CHEBYBALL_F Computes center and radius of the largest ball inscribed in a polytope
• reduce REDUCE Reduces the polytope by removing redundant inequalities
• size SIZE Returns size of the given polytope object
• mpt_error MPT_ERROR Function called if MPT toolbox is not initialized
• unitbox UNITBOX Creates a unit box centered at origin
This function is called by:
• gt GT Checks if polytope P is a strict superset of polytope Q
• lt LT Checks if polytope P is a strict subset of polytope Q

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