Analysis of Positive Systems Using Copositive Programming

Teruki Kato, Yoshio Ebihara, Tomomichi Hagiwara

Research output: Contribution to journalArticle

Abstract

In the field of control, a wide range of analysis and synthesis problems of linear time-invariant (LTI) systems are reduced to semidefinite programming problems (SDPs). On the other hand, in the field of mathematical programming, a class of conic programming problems, so called the copositive programming problem (COP), is actively studied. COP is a convex optimization problem on the copositive cone, and the completely positive cone, the doubly nonnegative cone, and the Minkowski sum of the positive semidefinite cone and the nonnegative cone are also closely related to COP. These four cones naturally appear when we deal with optimization problems described by nonnegative vectors. In this letter, we show that the stability, the H2 and the H∞ performances of LTI positive systems are basically characterized by the feasibility/optimization problems over these four cones. These results can be regarded as the generalization of well-known LMI/SDP-based results on the positive semidefinite cone. We also clarify that in some performances such direct generalization is not possible due to inherent properties of the copositive or the completely positive cone. We thus capture almost entire picture about how far we can generalize the SDP-based results for positive systems to those on the four cones related to COP.

Original languageEnglish
Article number8864008
Pages (from-to)444-449
Number of pages6
JournalIEEE Control Systems Letters
Volume4
Issue number2
DOIs
Publication statusAccepted/In press - Jan 1 2019

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Positive Systems
Cones
Programming
Cone
Semidefinite Programming
Positive Cone
Non-negative
Positive semidefinite
Optimization Problem
Linear Time
Conic Programming
Minkowski Sum
Invariant
Convex optimization
Mathematical programming
Convex Optimization
Mathematical Programming
Entire
Synthesis
Generalise

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Control and Optimization

Cite this

Analysis of Positive Systems Using Copositive Programming. / Kato, Teruki; Ebihara, Yoshio; Hagiwara, Tomomichi.

In: IEEE Control Systems Letters, Vol. 4, No. 2, 8864008, 04.2020, p. 444-449.

Research output: Contribution to journalArticle

Kato, Teruki ; Ebihara, Yoshio ; Hagiwara, Tomomichi. / Analysis of Positive Systems Using Copositive Programming. In: IEEE Control Systems Letters. 2020 ; Vol. 4, No. 2. pp. 444-449.
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