Finite-Time H_∞ Filtering for Nonlinear Singular Systems With Nonhomogeneous Markov Jumps.

Area of Science:

• Control Systems Engineering
• Nonlinear Systems Analysis
• Stochastic Systems Theory

Background:

• Singular nonhomogeneous Markov jump systems present challenges due to time-varying and unknown transition probabilities.
• Finite-time H∞ filtering is crucial for systems requiring guaranteed performance bounds within a finite time horizon.
• T-S fuzzy approximation offers a powerful tool for approximating nonlinear systems.

Purpose of the Study:

• To design a finite-time H∞ fuzzy filter for nonlinear singular nonhomogeneous Markov jump systems.
• To address the complexities introduced by time-varying and unknown transition probabilities.
• To develop a less conservative filtering approach compared to existing methods.

Main Methods:

• Utilizing a T-S fuzzy approximation approach for nonlinear system representation.
• Employing a stochastic Lyapunov functional to analyze system stability and boundedness.
• Applying matrix inequality decoupling techniques to derive linear matrix inequality (LMI) conditions.
• Ensuring singular stochastic H∞ finite-time boundedness (SS H∞ FTB) for the filtering error system.

Main Results:

• A sufficient condition for SS H∞ FTB of the filtering error systems is established.
• A novel LMI condition for the existence of the finite-time H∞ fuzzy filter is presented.
• The developed fuzzy filter guarantees SS H∞ FTB for the filtering error system.
• The proposed method demonstrates reduced conservatism, offering greater design freedom.

Conclusions:

• The proposed LMI-based design method effectively addresses finite-time H∞ filtering for complex nonlinear singular Markov jump systems.
• The approach provides less conservative results, enhancing practical applicability.
• Validation through a tunnel diode circuit example confirms the method's effectiveness and advantages.