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

Abstract

In this paper, the problem of linear functional state bounding for linear positive singular system with an interval time‐varying delay is investigated for the first time. First, the authors present new conditions for positivity, regularity, impulse free, and the existence of componentwise bound for the state vector of the singular systems without disturbance. Based on the obtained results, and by using state transformations, we derive the smallest componentwise ultimate bound of the state vector of the linear positive singular system with bounded disturbances. Then, we propose some sufficient criteria for linear functional state bounding problems of the positive singular system with time‐varying delays by using some new mathematical techniques. Since the conditions are given in terms of the linear programming/Hurwit matrix/spectral abscissa, we can check them easily and compute directly the smallest componentwise ultimate bound. Finally, a numerical example is given to demonstrate the correctness and the effectiveness of the proposed methodology.