A discretization approach to sampled‐data stabilization of networked systems with successive packet losses

• Published in: International journal of robust and nonlinear control Vol. 31; no. 10; pp. 4589 - 4601
• Main Authors: Hu, Zhipei, Zhang, Jin, Deng, Feiqi, Fan, Zhun, Qiu, Li
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 10.07.2021
• Subjects: Algorithms; Control systems design; discretization approach; Exponential functions; H-infinity control; Mathematical analysis; networked sampled‐data systems; Stability criteria; Stabilization; Stochastic systems; successive packet losses; Upper bounds
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5490

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.