Journal
NONLINEAR ANALYSIS-HYBRID SYSTEMS
Volume 3, Issue 4, Pages 738-748Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.nahs.2009.06.011
Keywords
Discrete event systems; Continuous Petri net; Positive invariance; Contractivity; Polyhedral sets; Linear Matrix Inequalities (LMI)
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Funding
- ministry of higher education and scientific research
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This paper deals with constrained regulation of continuous Petri nets under the so-called infinite servers semantics. Our aim is to design feedback gains that permit us to reach both desired stationary marking vector and desired asymptotic firing rate vector. The proposed approach takes into account constraints on the control, the marking of the Petri net, and the stability of the closed-loop system. The existence of a solution is first expressed geometrically, in terms of the inclusion of two polyhedral sets. They are reformulated algebraically as linear matrix inequalities, which provides an effective way to calculate feedback gains answering the problem. Finally, an application to an assembly production system is given. (C) 2009 Elsevier Ltd. All rights reserved.
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