A robust distributed secure interval observation approach for uncertain discrete-time positive systems under deception attacks

This paper deals with the network-based robust distributed state estimation problem of a class of discrete-time positive systems with bounded parameter perturbation and bounded disturbance. The system outputs are measured by multiple groups of sensors and transmitted to observers through communication networks suffering from deception attacks. To attain real-time monitoring and interval estimation of the system state and achieve a satisfactory estimation accuracy, a distributed secure interval observation approach is presented, where the interval observer is composed of an upper-bounding observer and a lower-bounding observer. The construction of each interval observer is based on the system positivity and the bounds of parameter perturbation, disturbance input and attack signals. Using the stochastic finite-time boundedness and l1-gain analysis method together with the linear programming technique, some sufficient conditions on analysis, design and optimization of the distributed interval observers for the uncertain positive system against deception attacks are established. The practicability and advantage of the proposed approach is checked by a numerical example, which comes from the remote monitoring of power distribution in smart grid.