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In this paper, the H∞$$ {H}_{\infty } $$ saturated control problems of networked systems with random sampling periods and stochastic transmission delays are investigated. The main issue is to design an H∞$$ {H}_{\infty } $$ saturated controller such that the controlled close‐loop system is exponentially mean‐square stable with a desired H∞$$ {H}_{\infty } $$ performance. A matrix exponential which is different from some existing literature is used to reconstruct the discrete‐time stochastic system to an equivalent yet tractable augmented model without any additional conditional constraint. In virtue of reduced‐order confluent Vandermonde matrix approach and Kronecker product operation, the stability condition in terms of linear matrix inequality is derived and then the desired H∞$$ {H}_{\infty } $$ saturated controller is designed. It should be emphasized that the improved method can also be used for the stability analysis and controller design when the system matrix contains complex roots. Finally, two numerical examples and a three‐axis milling machine system are utilized to manifest the reliability and practicality of the designed strategy. [ABSTRACT FROM AUTHOR]

In this paper, the stabilization problem of networked systems with communication constraints is studied, where the random sampling periods, deception attacks and packet losses are considered simultaneously. Different from the existing literature, the actual sampling periods are subject to undesirable physical constraints and fluctuate around an ideal sampling period with certain probability distribution. First, a closed-loop discrete-time stochastic system is constructed by considering the random sampling periods, deception attacks and packet losses in a unified framework. Second, an equivalent yet tractable stochastic model is established with the aid of matrix exponential computation. By reduced-order confluent Vandermonde matrix approach, law of total expectation, convolution formula and Kronecker product operation, a controller is designed such that the exponential stability in the mean-square sense of closed-loop stochastic system is guaranteed. Subsequently, a special model is discussed where no deception attack occurs and then the corresponding controller is designed. Finally, an illustrative example is given to show the effectiveness of the designed approach. [ABSTRACT FROM AUTHOR]