Simple LP-type criteria for positively invariant polyhedral sets

Let S be a convex polyhedral set in the state space of a linear dynamical system. A new proof of an algebraic condition for the set S to be positively invariant is given by the dual set of S. The condition obtained in this correspondence can be examined by solving a set of standard LP-type formulas....

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Bibliographic Details
Published in:IEEE transactions on automatic control 2000-01, Vol.45 (1), p.98-101
Main Authors: Yoshida, K., Kawabe, H., Nishimura, Y.
Format: Article
Language:English
Subjects:
Algebra
Automatic control
Criteria
Differential equations
Dynamical systems
Feedback
Filtering theory
Genetics
Invariants
Mathematics
Nonlinear equations
Nonlinear systems
Proving
Redundancy
Stability
Stochastic processes
Stochastic systems
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Summary:Let S be a convex polyhedral set in the state space of a linear dynamical system. A new proof of an algebraic condition for the set S to be positively invariant is given by the dual set of S. The condition obtained in this correspondence can be examined by solving a set of standard LP-type formulas. It is also shown that the conventional algebraic conditions have redundancies in the LP-type formulas. Discrete-time systems as well as continuous-time systems are considered.
ISSN:0018-9286
1558-2523
DOI:10.1109/9.827362