mpt_infset

MPT_INFSET Calculates the maximal positively invariant set for an LTI system

 [Oinf,tstar,fd,isemptypoly] = mpt_infset(A,X,tmax,Pnoise,Options)

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 DESCRIPTION
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 Calculates the maximal positively invariant set for an autonomous discrete-time
 LTI system
 Takes into account polytopic and additive system uncertainty, if defined
 in "sysStruct" / "Pnoise", respectively.

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 INPUT
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 A                - The A matrix of the discrete-time LTI system x{k+1} = Ax{k}.
 X                - State constraints given as a polytope (x \in X)_
 tmax             - Maximum number of iterations allowed.
 Options.lpsolver - Solver for LPs (see help mpt_solveLP for details)
 Options.verbose  - level of verbosity (see help mpt_init for details)
 Options.abs_tol  - absolute tolerance

 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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 Oinf         - Maximal positively invariant set contained in X, i.e.
                  Oinf = {x_k \in X: x_{k+1} = Ax_k \in X}.
 tstar        - Determinedness index.
 fd           - 1 if Oinf is finitely determined (tstar <= tmax).
                0 if Oinf tstar > tmax.
 isemptypoly  - 1 if resulting polyhedron is empty; 0 otherwise

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   Literature:
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 "Theory and Computation of Disturbance Invariant Sets for Discrete-Time Linear Systems"
 I. Kolmanovsky and E. G. Gilbert, Mathematical Problems in Egineering, vol (4), 1998, 
 pages 317-367

 AND

 "Linear systems with state and control constraints: the theory and
 applications of maximal output admissible sets", E. G. Gilbert and K. Tin Tan,
 IEEE Transcations on Automatic Control, 1991, vol 36, number 9, pages 1008--1020


 see also MPT_INFSETPWA