Linear functional state bounding for positive singular systems with unbounded delay and disturbances varying within a bounded set

Abstract In this paper, the linear functional state bounding problem, which is considered in [25], is extended to the singular system with unbounded delay. Firstly, some conditions are presented to guaranteed positivity, regularity, impulse‐free, and the component‐wise bound for the state vector of the singular system without disturbance. Then, based on the results obtained and by using state transformations, the smallest component‐wise ultimate bound of the state vector of the singular system with bounded disturbances is derived. By using the new technique, some sufficient conditions were proposed given in terms of the linear programming/Hurwit matrix/spectral abscissa for linear functional state bounding problems of the singular system with unbounded delay. Finally, a numerical example is given to illustrate the obtained results