Improved Reduced-Order Fault Detection Filter Design for Polytopic Uncertain Discrete-Time Markovian Jump Systems with Time-Varying Delays

Lihong Rong,Liangliang Liu,Xiuyan Peng,Biao Zhang

doi:10.1155/2018/9489620

Lihong Rong, Liangliang Liu + Show 2 more

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https://doi.org/10.1155/2018/9489620

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Abstract

The fault detection (FD) reduced-order filtering problem is investigated for a family of polytopic uncertain discrete-time Markovian jump linear systems (MJLSs) with time-varying delays. Under meeting the control precision requirements of the complex systems, the reduced-order fault detection filter can improve the efficiency of the fault detection. Then, by the aid of the Markovian Lyapunov function and convex polyhedron techniques, some novel time-varying delays and polytopic uncertain sufficient conditions in terms of linear matrix inequality (LMI) are proposed to insure the existence of the FD reduced-order filter. Finally, an illustrative example is provided to verify the usefulness of the given method.

Highlights

The past decades have witnessed a boom of advanced studies on theories and applications of Markov jump systems in many fields, such as networks communication systems, automotive systems, energy systems, biological systems, cyber-physical systems, aerospace systems, manufacturing, automation, smart grids, vehicular networking and connected vehicles, power systems, robotics, economic systems, and social systems [1,2,3,4]
The more general and practicable results are derived. (ii) The new designed FD filtering stochastic stability condition for a kind of discretetime Markovian jump linear systems (MJLSs) with time-varying delays and polytopic uncertain transition probabilities (TPs) has been established for the first time. (iii) By applying Wirtinger-based inequality, it has shown the effectiveness of the proposed design approach, which can improve the sensitivity of fault detection and reduce the fault detection rate of false positives
In order to improve the performance of the fault detection system, we introduced the weighting fault signal f(k) which satisfies f(z) = Wf(z)f(z), where the matrix Wf(z) presents a given stable weighting function matrix. f(z) and f(z) denote Laplace transforms of f(k) and f(k), respectively

Summary

Introduction

The past decades have witnessed a boom of advanced studies on theories and applications of Markov jump systems in many fields, such as networks communication systems, automotive systems, energy systems, biological systems, cyber-physical systems, aerospace systems, manufacturing, automation, smart grids, vehicular networking and connected vehicles, power systems, robotics, economic systems, and social systems [1,2,3,4]. As an important factor governing the behaviors of MJLSs, the transition probabilities (TPs) are usually deemed to be certain and completely known, which do not change over time. There are more rational and general MJLSs with the polytopic uncertain TRs. But there are few research literature about fault detection of Markovian jump systems with the exactly known, partially unknown, and uncertain TRs concurrently, and the loss of sensor or actuator information can be efficiently modeled by means of Markov chain frameworks. There are few research literature about fault detection of Markovian jump systems with the exactly known, partially unknown, and uncertain TRs concurrently, and the loss of sensor or actuator information can be efficiently modeled by means of Markov chain frameworks This is the need to solve the main problem, which is one of the motivations for our research

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