This paper focuses on the fault detection of a class of discrete-time systems with random faults and proposes a fault-dependent approach. Firstly, a mathematical model is constructed to describe the above problems, and the characteristics of fault signals are transformed into matrices containing uncertainties. By constructing a fault detection filter as a residual generator, the fault detection and isolation (FDI) problem is transformed into a H∞filtering problem. Based on the established model, the H∞ performance is analyzed by adopting a fault-dependent method. The parameter-dependent Lyapunov function is selected for processing. On this basis, the existence condition of the fault detection filter is given in the form of linear matrix inequalities. Finally, an example is used to verify the effectiveness and practicability of the theoretical results.
It was focused on the pinning control problem for a class of complex dynamic networks with linearly continuoustime coupled nodes. A new method for designing pinning controllers with stochastic pinning viewpoint is firstly proposed, which is referred to be stochastic pinning control. By adding such a controller to a fraction of nodes the stochastic stability of the entire complex networks can be guaranteed. It is claimed that the stochastic pinning control method without adding the selected nodes always could also stabilize the complex networks. By exploiting the robust method, sufficient condition is given for a kind of generally complex networks with coupling matrix changing to be another one, where the designed stochastic pinning controller is still available. Based on the established results, some results with the expectation of Bernouli variable uncertain and unknown are presented too. Finally, the correctness and effectiveness of the proposed methods is verified by a numerical example.