Abstract
The purpose of this paper is to design a positive fault detection filter for positive Markov jump linear systems (MJLSs) using $\ell _{1}$ and $\ell _{-}$ performance indices, which represent respectively, robustness and fault sensitivity. First, by converting the MJLS to an associated deterministic system, sufficient conditions are derived for the positivity, stochastic stability and $\ell _{1}/\ell _{-}$ performance of an augmented system consisting of the original system and the fault detection filter. Then an iterative linear programming (LP) algorithm is provided to solve these bilinear conditions, with two numerical examples presented to show the superiority of the developed approach over the existing ones.
Highlights
In the past decades, tremendous attention has been paid to a class of remarkable systems of great practicality whose state variables and outputs are all nonnegative for all nonnegative initial values and inputs, this class of systems are normally referred to as positive systems
As presented in [4], [5], the design problem of state-feedback controllers for positive systems was investigated by the method of linear matrix inequality (LMI) and linear programming (LP), respectively
This paper investigates the existence of the 1/ − fault detection filter for positive Markov jump linear systems (MJLSs) with time delay
Summary
Tremendous attention has been paid to a class of remarkable systems of great practicality whose state variables and outputs are all nonnegative for all nonnegative initial values and inputs, this class of systems are normally referred to as positive systems. As presented in [4], [5], the design problem of state-feedback controllers for positive systems was investigated by the method of linear matrix inequality (LMI) and LP, respectively. With the increasing complexity of modern systems and accuracy requirements of their components, enormous attention has been received to the research on fault detection problem for several decades so as to deal with frequent failures during industrial processes. A widely-used approach of fault detection problem is to construct a residual generator consisting of the predesigned filter and original plant model. A residual signal, once generated, will be used to compare against a threshold based on the residual
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