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This paper studies the distributed interval state estimation problem for cyber–physical systems with bounded disturbance and random stealthy attacks. Since conventional interval observers cannot complete the task of real-time monitoring system under random attacks, an attack-resistant distributed interval observer is designed by using attack frequency and interval attack estimation. Using the designed observer, upper- and lower-bounding estimation error systems are modeled by positive interconnected systems with hybrid deterministic and random bounded inputs. To explicitly attenuate the effect of disturbance and attacks, the resulting deterministic positive error system between upper- and lower-bounding estimates is formulated. By linear programming, the results of interval observer design and l ∞ -gain optimization are proposed. The remote monitoring of vehicle lateral dynamic is given for numerical verification of the results. • A new distributed interval observation method for general linear system is proposed. • The disturbance attenuation problem of stochastic interval error systems is solved. • The method can provide real-time changing ranges of CPS dynamics against attacks. [ABSTRACT FROM AUTHOR]

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 l 1 -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. [ABSTRACT FROM AUTHOR]

This paper proposes some new sufficient conditions and necessary conditions for exponential mean stability with prescribed decay rate, and sufficient conditions for non-fragile controller design of both continuous-time and discrete-time positive Markov jump linear systems with time-delay. First, sufficient stability conditions are derived by constructing novel linear stochastic co-positive Lyapunov-Krasovskii functionals. Second, the corresponding necessary conditions are established by applying a model transformation technique and analyzing the relationship between stochastic stability of the transformed systems and exponential mean stability with given decay rate of the original systems. Compared with the existing conditions, the proposed stability conditions are not only delay-dependent but also decay-rate-dependent, and the sufficient conditions plus the necessary conditions can be used to judge the system stability more precisely. Third, based on the new sufficient conditions, non-fragile controllers are designed by solving linear programming problems such that the closed-loop systems are positive and exponentially mean stable with an expected decay rate. Finally, by numerical examples, the effects of both time-delay and decay rate on exponential mean stability are exploited and the validity of the non-fragile controller design conditions is demonstrated. [ABSTRACT FROM AUTHOR]