This paper addresses the problem of designing of positive interval observers for linear functions of the state vector of linear positive systems with time-varying unknown delays. We provide upper bound and lower bound of linear functions of the state vector. | Vo Van Dinh/ Positive interval observers for linear functions of the state vector of linear. POSITIVE INTERVAL OBSERVERS FOR LINEAR FUNCTIONS OF THE STATE VECTOR OF LINEAR POSITIVE SYSTEMS WITH TIME-VARYING UNKNOWN DELAYS Vo Van Dinh Department of Fundamental Science, Long An University of Economics and Industry Received on 18/8/2017, accepted for publication on 15/11/2017 Abstract: This paper addresses the problem of designing of positive interval observers for linear functions of the state vector of linear positive systems with time-varying unknown delays. We provide upper bound and lower bound of linear functions of the state vector. Conditions for the existence of a pair of reducedorder positive linear functional observers which constructs a positive interval observer for linear functions of the state vector of considered system and the asymptotic convergence of the interval error are presented and they are translated into a linear programming (LP) problem. Finally, the effectiveness of the proposed design method is supported by two numerical examples and simulation results. 1 Introduction In recent years, time-delay systems have attracted a lot of research attentions due to the increase in their practical applications (see, for example, [1], [2], [3], [10], [11], [14], [16], [24], [25] and the references therein). As we known, the existence of time delays in systems may cause instability and performance degradation of systems. Therefore, many results have been published to deal with this kind of systems such as stability, control and state estimation (see, for example, [12], [13], [21] and the references therein). In particular, the problem of designing state observers has many important applications in the realization of state feedback control, system supervision, fault diagnosis of dynamic processes, and general control and diagnosis issues from available information (see, for example, [4], [5], [7], [8], [23]). Most of the design methods available in
