1. Filter for Positive Stochastic Nonlinear Switching Systems With Phase-Type Semi-Markov Parameters and Application
- Author
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Wenhai Qi, Jinde Cao, Ju H. Park, Jun Cheng, and Guangdeng Zong
- Subjects
Lyapunov function ,0209 industrial biotechnology ,Markov chain ,02 engineering and technology ,Fuzzy logic ,Computer Science Applications ,Human-Computer Interaction ,Filter design ,Nonlinear system ,symbols.namesake ,020901 industrial engineering & automation ,Control and Systems Engineering ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Jump ,Applied mathematics ,020201 artificial intelligence & image processing ,Electrical and Electronic Engineering ,Jump process ,Software ,Membership function ,Mathematics - Abstract
In this article, the issue of positive L₁ filter design is investigated for positive nonlinear stochastic switching systems subject to the phase-type semi-Markov jump process. Many complicated factors, such as semi-Markov jump parameters, positivity, T-S fuzzy strategy, and external disturbance, are taken into consideration. Practical systems under positivity constraint conditions and unpredictable structural changes are characterized by positive semi-Markov jump systems (S-MJSs). First, by the key properties of the supplementary variable and the plant transformation technique, phase-type S-MJSs are transformed into Markov jump systems (MJSs), which means that, to an extent, these two kinds of stochastic switching systems are mutually represented. Second, with the help of the normalized membership function, the associated nonlinear MJSs are transformed into the local linear MJSs with specific T-S fuzzy rules. Third, by choosing the linear copositive Lyapunov function (LCLF), stochastic stability (SSY) criteria are given for the corresponding system with L₁ performance. Some solvability conditions for positive L₁ filter are constructed under a linear programming framework. Finally, an epidemiological model illustrates the effectiveness of the theoretical findings.
- Published
- 2022