TY - GEN
T1 - L 1 gain analysis of linear positive systems and its application
AU - Ebihara, Yoshio
AU - Peaucelle, Dimitri
AU - Arzelier, Denis
PY - 2011
Y1 - 2011
N2 - In this paper, we focus on L 1 gain analysis problems of linear time-invariant continuous-time positive systems. A positive system is characterized by the strong property that its output is always nonnegative for any nonnegative input. Because of this peculiar property, it is natural to evaluate the magnitude of positive systems by the L 1 gain (i.e. the L 1 induced norm) in terms of the input and output signals. In contrast with the standard L 1 gain, in this paper, we are interested in L 1 gains with weightings on the input and output signals. It turns out that the L 1 gain with weightings plays an essential role in the stability analysis of interconnected positive systems. More precisely, as a main result of this paper, we show that an interconnected positive system is stable if and only if there exists a set of weighting vectors that renders the L 1 gain of each positive subsystem less than unity. As such, using a terminology in the literature, the weighting vectors work as 'separators,' and thus we establish solid separator-based conditions for the stability of interconnected positive systems. We finally illustrate that these separator-based conditions are effective particularly when we deal with robust stability analysis of positive systems against both L 1 gain bounded and parametric uncertainties.
AB - In this paper, we focus on L 1 gain analysis problems of linear time-invariant continuous-time positive systems. A positive system is characterized by the strong property that its output is always nonnegative for any nonnegative input. Because of this peculiar property, it is natural to evaluate the magnitude of positive systems by the L 1 gain (i.e. the L 1 induced norm) in terms of the input and output signals. In contrast with the standard L 1 gain, in this paper, we are interested in L 1 gains with weightings on the input and output signals. It turns out that the L 1 gain with weightings plays an essential role in the stability analysis of interconnected positive systems. More precisely, as a main result of this paper, we show that an interconnected positive system is stable if and only if there exists a set of weighting vectors that renders the L 1 gain of each positive subsystem less than unity. As such, using a terminology in the literature, the weighting vectors work as 'separators,' and thus we establish solid separator-based conditions for the stability of interconnected positive systems. We finally illustrate that these separator-based conditions are effective particularly when we deal with robust stability analysis of positive systems against both L 1 gain bounded and parametric uncertainties.
UR - http://www.scopus.com/inward/record.url?scp=84860660547&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84860660547&partnerID=8YFLogxK
U2 - 10.1109/CDC.2011.6160692
DO - 10.1109/CDC.2011.6160692
M3 - Conference contribution
AN - SCOPUS:84860660547
SN - 9781612848006
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 4029
EP - 4034
BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
T2 - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Y2 - 12 December 2011 through 15 December 2011
ER -