This note introduces a small-gain result for interconnected MIMO orthant-monotone systems for which no matching condition is required between the partial orders in input and output spaces of the considered subsystems. Previous results assumed that the partial orders adopted would be induced by positivity cones in input and output spaces and that such positivity cones should fulfill a compatibility rule: namely either be coincident or be opposite. Those two configurations corresponded to positive-feedback or negative feedback cases. We relax those results by allowing arbitrary orthant orders.
A small-gain result for orthant-monotone systems in feedback: the non sign-definite case / Angeli, David; Sontag, Eduardo D.. - ELETTRONICO. - (2011), pp. 6049-6053. (Intervento presentato al convegno IEEE Conference on Decision and Control).
A small-gain result for orthant-monotone systems in feedback: the non sign-definite case
Angeli, David;
2011
Abstract
This note introduces a small-gain result for interconnected MIMO orthant-monotone systems for which no matching condition is required between the partial orders in input and output spaces of the considered subsystems. Previous results assumed that the partial orders adopted would be induced by positivity cones in input and output spaces and that such positivity cones should fulfill a compatibility rule: namely either be coincident or be opposite. Those two configurations corresponded to positive-feedback or negative feedback cases. We relax those results by allowing arbitrary orthant orders.
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