On event‐triggered guaranteed cost control for discrete‐time semi‐Markovian neural networks having communication delays and dual‐terminal probabilistic faults

Abstract This article aims to address the guaranteed cost control synthesis problem for discrete‐time semi‐Markovian neural networks (D‐SMNNs) considering communication delays along with probabilistic faulty sensors and actuators (dual‐terminal probabilistic faults) by adopting a modified event‐triggered mechanism. Our primary target of this research is to implement a suitable feedback controller such that the resulting D‐SMNNs achieve stochastically stable. To be more concrete, the structural and coefficient switchings of the NNs are characterized by a semi‐Markovian process (SMP) along with the lower and upper bounds of the transition probabilities (TPs), which can reflect the reality more accurately and has a wider application scope. For optimize the resource utilization of the band‐limited communication networks, a modified event‐triggered transmission strategy is put forward to lessen the unnecessary data transmission over network. Additionally, according to different failure rates and the measurement distributions of intelligent modules, a more practical probabilistic sensors and actuators faulty model for networked D‐SMNNs is synthesized, which including additivity and multiplicity. The anamorphic probability of sensors and actuators are governed by a battery of mutually independent stochastic variables that obeys certain probabilistic distribution over the preknown interval . Therein, the distortion degree and failure rate for each sensor and actuator can be separately quantized and characterized with the aid of mathematical variance and expectation. Briefly, in comparison to the existing faulty models, the novelty of this extended fault model lies in it can characterize more features in practical industrial applications. Afterwards, by resorting to the Lyapunov functional method and combining with both the stochastic analysis technique and matrix inequality decoupling manipulation, several sufficient conditions on ensuring stabilization for solving both the guaranteed cost controller gains and event‐triggered coefficients are formulated in the shape of a group of linear matrix inequalities (LMIs), which can be verified by exploiting standard compute software. After that, the controller design is reformulated as an optimization problem with LMI constraints immediately. Eventually, three simulation examples are carried out to substantiate the potency and accuracy of the proposed control synthesis methodology.