Gain Scheduled Fault Detection Filter for Markovian Jump Linear System with Nonhomogeneous Markov Chain

Leonardo Carvalho (), Jonathan M. Palma, Cecília F. Morais, Bayu Jayawardhana and Oswaldo L. V. Costa
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Leonardo Carvalho: Departamento de Engenharia de Telecomunicacções e Controle, Escola Politécnica na Universidade de São Paulo, São Paulo 05508-010, SP, Brazil
Jonathan M. Palma: Facultad de Ingeniería, Universidad de Talca, Curico 3340000, Maule, Chile
Cecília F. Morais: Pontifical Catholic University of Campinas (PUC-Campinas), Center for Exact, Environmental and Technological Sciences (CEATEC), Postgraduate Program in Telecommunication Networks Management, Campinas 13086-900, SP, Brazil
Bayu Jayawardhana: Engineering and Technology Institute Groningen, Faculty of Science and Engineering, Rijksuniversiteit Groningen, 9747 AG Groningen, The Netherlands
Oswaldo L. V. Costa: Departamento de Engenharia de Telecomunicacções e Controle, Escola Politécnica na Universidade de São Paulo, São Paulo 05508-010, SP, Brazil

Mathematics, 2023, vol. 11, issue 7, 1-21

Abstract: In a networked control system scenario, the packet dropout is usually modeled by a time-invariant (homogeneous) Markov chain (MC) process. However, from a practical point of view, the probabilities of packet loss can vary in time and/or probability parameter dependency. Therefore, to design a fault detection filter (FDF) implemented in a semi-reliable communication network, it is important to consider the variation in time of the network parameters, by assuming the more accurate scenario provided by a nonhomogeneous jump system. Such a premise can be properly taken into account within the linear parameter varying (LPV) framework. In this sense, this paper proposes a new design method of H ∞ gain-scheduled FDF for Markov jump linear systems under the assumption of a nonhomogeneous MC. To illustrate the applicability of the theoretical solution, a numerical simulation is presented.

Keywords: fault-detection filter; Markovian jump linear system; H ? norm; LMI relaxations; nonhomogeneous Markov chains (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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