Positive state-bounding observer for positive interval continuous-time systems with time delay.

*(English)*Zbl 1274.93039Summary: This paper is concerned with the problem of positive observer synthesis for positive systems with both interval parameter uncertainties and time delay. Conventional observers may no longer be applicable for such kind of systems due to the positivity constraint on the observers, and they only provide an estimate of the system state in an asymptotic way. A pair of positive observers with state-bounding feature is proposed to estimate the state of positive systems at all times in this paper. A necessary and sufficient condition for the existence of desired observers is first established, and the observer matrices can be obtained easily through the solutions of a set of linear matrix inequalities (LMIs). Then, to reduce the error signal between the system state and its estimates, an iterative LMI algorithm is developed to compute the optimized state-bounding observer matrices. Finally, a numerical example is presented to show the effectiveness and applicability of the theoretical results.

##### MSC:

93B07 | Observability |

93C15 | Control/observation systems governed by ordinary differential equations |

93C05 | Linear systems in control theory |

##### Keywords:

interval systems; linear matrix inequality; positive systems; positive observer; state-bounding observer; time delay
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\textit{P. Li} and \textit{J. Lam}, Int. J. Robust Nonlinear Control 22, No. 11, 1244--1257 (2012; Zbl 1274.93039)

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