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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]

This article is concerned with the stabilization problem for a class of networked systems subject to successive packet losses. Different from the input delay approach used in some existing literature, the continuous‐time system under consideration is first converted into a discrete‐time stochastic system with system matrices subject to stochastic characteristic. In order to deal with the difficulties in the calculations of mathematical expectations of both matrix exponential and integral of matrix exponential function, the upper bound of successive packet losses and packet drop rate are assumed to be known and then the probabilities of the number of successive packet losses taking each value in a bounded set are calculated. Based on this, stability criteria are derived by recurring to the law of total expectation, which guarantee the exponential mean‐square stability of resulting closed‐loop discrete‐time stochastic system with a prescribed H∞ performance. Moreover, a controller design procedure is then proposed. Finally, to verify the analysis results and testify the effectiveness and applicability of the designed algorithm, a numerical simulation example is given. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration. [ABSTRACT FROM AUTHOR]