Classical and Resilient Filtering

  • Lixian ZhangEmail author
  • Ting Yang
  • Peng Shi
  • Yanzheng Zhu
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 54)


This chapter concerns the problem of \(H_{\infty }\) estimation for a class of Markov jump linear system (MJLS) with time-varying transition probabilities (TPs) in discrete-time domain. The time-varying character of TPs is also considered as finite piecewise homogeneous and the variations in the finite set are considered as two types: arbitrary variation and stochastic variation, respectively. The latter means that the variation is subject to a higher-level transition probability matrix (TPM). The mode-dependent and variation-dependent \(H_{\infty }\) filter is designed such that the resulting closed-loop systems are stochastically stable and have a guaranteed \(H_{\infty }\) filtering error performance index. Using the idea of partially unknown TPs for the traditional MJLS with homogeneous TPs, a generalized framework covering the two kinds of variation is proposed. Then, the derived results are extended to the study of the resilient \(H_{\infty }\) filtering problem for a class of discrete-time Markov jump neural networks (MJNNs) with time-varying delays, unideal measurements and multiplicative noises. The transitions of neural networks modes and desired mode-dependent filters are considered to be asynchronous, and a nonhomogeneous mode TPM of filters is used to model the asynchronous jumps to different degrees that are also mode-dependent. The unknown time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. The unideal measurements model includes the phenomena of randomly occurring quantization and missing measurements in a unified form. The desired resilient filters are designed such that the filtering error system is stochastically stable with a guaranteed \(H_{\infty }\) performance index. A monotonicity is disclosed in filtering performance index as the degree of asynchronous jumps changes. Numerical examples are provided to demonstrate the potential and validity of the theoretical results.


Stochastic Variation TPMTransition Probability Matrix Multiplicative Noise Filter Mode Arbitrary Variation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Lixian Zhang
    • 1
    Email author
  • Ting Yang
    • 1
  • Peng Shi
    • 2
    • 3
  • Yanzheng Zhu
    • 1
  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina
  2. 2.School of Electrical and Electronic EngineeringThe University of AdelaideAdelaideAustralia
  3. 3.College of Engineering and ScienceVictoria UniversityMelbourneAustralia

Personalised recommendations