Linear functional state bounding for positive systems with disturbances varying within a bounded set

In most of the existing works on state bounding for perturbed dynamical systems, the disturbance vector is only considered under the assumption that its norms/components are bounded by known constant bounds. This paper considers a more general case where the disturbance vector is assumed to vary within a known bounded set. Furthermore, instead of finding bounds of the full system state vector, this paper focuses on finding the smallest componentwise bound of a given linear function of the system state vector. A class of perturbed positive systems is considered and a new method for deriving the smallest bound is presented. Our presented method is also extended to positive systems with time delays and to nonlinear systems which are bounded by positive systems. A numerical example is given to illustrate the effectiveness of the obtained results.