Practical Fixed-Time Control of Switched Neutral Filippov Systems on Networks

Area of Science:

• Control Theory
• Nonlinear Systems Analysis
• Networked Systems

Background:

• Switched neutral Filippov systems (SNFSs) present challenges due to discontinuous perturbations and neutral logics.
• Existing finite-time control methods often lack practical accuracy in state convergence for real-world applications.

Purpose of the Study:

• To develop practical fixed-time (FxT) control strategies for SNFSs on networks.
• To establish novel stability analysis techniques for systems with discontinuous perturbations and delays.
• To address the limitations of existing finite-time control in achieving accurate state convergence.

Main Methods:

• Development of new Lyapunov inequalities with indefinite functions for settling-time (ST) estimation.
• Establishment of practical FxT stability lemmas with bounded indefinite functions.
• Design of adaptive control strategies using Lyapunov-Krasovskii functionals (LKFs) to handle system delays.

Main Results:

• Novel Lyapunov inequalities provide detailed ST estimations, encompassing existing results.
• Practical FxT stability lemmas with bounded indefinite functions are introduced for the first time.
• Adaptive control successfully achieves FxT and practical FxT synchronization for SNFSs with delays.
• A theoretical deficiency in FxT stability analysis for delayed systems using Lyapunov functions is resolved.

Conclusions:

• The proposed methods offer a more practical approach to FxT control for SNFSs, especially in networked environments.
• The study overcomes key theoretical and practical challenges in analyzing and controlling delayed SNFSs.
• Numerical simulations on an LC transmission line validate the effectiveness of the developed control strategies.