Robust Filtering for Nonlinear Nonhomogeneous Markov Jump Systems by Fuzzy Approximation Approach

Area of Science:

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

Background:

• Markov jump systems (MJSs) are crucial for modeling systems with abrupt changes.
• Nonlinear systems with uncertainties pose significant challenges in control and filtering.
• Existing fuzzy filtering methods often face limitations in handling nonhomogeneous MJSs.

Purpose of the Study:

• To develop a robust fuzzy L2-L∞ filter for uncertain nonlinear discrete-time MJSs with nonhomogeneous jump processes.
• To address the conservation issue in filtering by employing a polytope Lyapunov function.
• To ensure stochastic stability and a prescribed L2-L∞ performance for the filtering error dynamics.

Main Methods:

• Utilizing the Takagi-Sugeno fuzzy model to represent nonlinear nonhomogeneous MJSs with norm-bounded parameter uncertainties.
• Designing a mode-dependent and variation-dependent fuzzy filter incorporating membership functions.
• Employing a polytope Lyapunov function that evolves as a convex function to reduce conservatism.

Main Results:

• A sufficient condition is derived to guarantee the stochastic stability of the filtering error dynamic system.
• The proposed filter ensures the filtering error system achieves a prescribed L2-L∞ performance index.
• The effectiveness and advantages of the proposed filtering techniques are demonstrated through two simulated examples.

Conclusions:

• The developed fuzzy L2-L∞ filtering approach effectively handles robust filtering for uncertain nonlinear discrete-time MJSs with nonhomogeneous jumps.
• The proposed method offers improved performance and reduced conservatism compared to existing techniques.
• The findings provide a valuable contribution to the field of robust filtering for complex dynamic systems.