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

• Published in: Mathematics (Basel) Vol. 11; no. 7; p. 1713
• Main Authors: Carvalho, Leonardo, Palma, Jonathan M., Morais, Cecília F., Jayawardhana, Bayu, Costa, Oswaldo L. V.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.04.2023
• Subjects: <named-content content-type="inline-formula"><mml:math id="mm1111"><mml:mi mathvariant="script">H</mml:mi>∞</mml:math></named-content> norm; Design parameters; Fault detection; Fault location (Engineering); fault-detection filter; H-infinity control; Linear systems; LMI relaxations; Markov analysis; Markov chains; Markov processes; Markovian jump linear system; Mathematical models; Methods; Network control; nonhomogeneous Markov chains; Numerical analysis; Probability; Simulation; Systems stability; Brazil
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math11071713

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.