Interval estimation for asynchronously switched positive systems

In this paper, the zonotopic state estimation is investigated for discrete-time switched positive systems under asynchronism. Taking into account the particularity of the positive system, new radius definition called positive generator matrix based radius (PGR) is proposed to characterize the size of state zonotope and derive linear programming conditions. First, using the merging signal technique, the estimation error system is modeled as a switched positive system with augmented switching signal. Then, we propose an iterative estimation procedure to construct the state bounding zonotope. To be more realistic, the mode-dependent weighted PGR of the resulting zonotope is allowed to increase within asynchronous intervals, and the PGR is proven to be bounded with an L∞ disturbance attenuation performance by establishing a suitable radius function. Furthermore, the asynchronous positive observer is designed for the considered system, based on which the interval estimation is determined for the switched positive system. Finally, a simulation example is provided to verify the advantages and effectiveness of the proposed approach.