Filter for Positive Stochastic Nonlinear Switching Systems With Phase-Type Semi-Markov Parameters and Application

In this article, the issue of positive L-1 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 L-1 performance. Some solvability conditions for positive L-1 filter are constructed under a linear programming framework. Finally, an epidemiological model illustrates the effectiveness of the theoretical findings.

Automated summary

This article investigates the positive L-1 filter design for positive nonlinear stochastic switching systems subject to phase-type semi-Markov jump process. The paper considers various complex factors such as semi-Markov jump parameters, positivity, T-S fuzzy strategy, and external disturbance. By transforming phase-type semi-Markov jump systems into Markov jump systems and utilizing normalized membership function, the paper presents criteria for stochastic stability with L-1 performance and constructs solvability conditions for positive L-1 filter under a linear programming framework.