Non-fragile H ∞ control with randomly occurring gain variations, distributed delays and channel fadings

Zhen’na Li; Zidong Wang; Derui Ding; Huisheng Shu

Non-fragile H _∞ control with randomly occurring gain variations, distributed delays and channel fadings

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Author(s): Zhen’na Li ¹ ; Zidong Wang ^{2, 3} ; Derui Ding ¹ ; Huisheng Shu ¹
- Affiliations: 1: School of Information Science and Technology, Donghua University, Shanghai 200051, People's Republic of China;
  2: Department of Computer Science, Brunel University, Uxbridge, Middlesex, UB8 3PH, UK;
  3: Communication Systems and Networks (CSN) Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Source: Volume 9, Issue 2, 19 January 2015, p. 222 – 231
DOI: 10.1049/iet-cta.2014.0426 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 24/04/2014, Accepted 24/08/2014, Revised 21/07/2014, Published 15/10/2014

This study is concerned with the non-fragile H _∞ control problem for a class of discrete-time systems subject to randomly occurring gain variations (ROGVs), channel fadings and infinite-distributed delays. A new stochastic phenomenon (ROGVs), which is governed by a sequence of random variables with a certain probabilistic distribution, is put forward to better reflect the reality of the randomly occurring fluctuation of controller gains implemented in networked environments. A modified stochastic Rice fading model is then exploited to account for both channel fadings and random time-delays in a unified representation. The channel coefficients are a set of mutually independent random variables which abide by any (not necessarily Gaussian) probability density function on [0, 1]. Attention is focused on the analysis and design of a non-fragile H _∞ output-feedback controller such that the closed-loop control system is stochastically stable with a prescribed H _∞ performance. Through intensive stochastic analysis, sufficient conditions are established for the desired stochastic stability and H _∞ disturbance attenuation, and the addressed non-fragile control problem is then recast as a convex optimisation problem solvable via the semi-definite programme method. An example is finally provided to demonstrate the effectiveness of the proposed design method.

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Non-fragile H _∞ control with randomly occurring gain variations, distributed delays and channel fadings

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