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H_∞ State Estimation for Discrete-Time Nonlinear Singularly Perturbed Complex Networks Under the Round-Robin Protocol.

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Summary

This study addresses H_∞ state estimation for nonlinear singularly perturbed complex networks (SPCNs) using the Round-Robin (RR) protocol. The proposed method ensures stability and performance for systems with a singular perturbation parameter (SPP).

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Area of Science:

Control Systems Engineering
Networked Systems
Nonlinear Dynamics

Background:

Singularly perturbed complex networks (SPCNs) present unique challenges in state estimation due to their multi-time scale nature.
The Round-Robin (RR) protocol introduces periodic switching, complicating stability analysis in networked systems.

Purpose of the Study:

To develop an H_∞ state estimator for discrete-time nonlinear SPCNs operating under the RR protocol.
To guarantee asymptotic stability and H_∞ performance for the state estimation error dynamics.

Main Methods:

A discrete-time nonlinear SPCN model on two time scales is formulated.
A novel Lyapunov function incorporating the singular perturbation parameter (SPP) and transmission order is constructed.
Sufficient conditions for stability and H_∞ performance are derived using a key lemma for SPPs.

Main Results:

Conditions ensuring asymptotic stability and H_∞ performance for the state estimation error are established for any SPP within a bound.
Explicit parameterization of the state estimator is provided via matrix inequalities.
The upper bound of the SPP is determined by the feasibility of these inequalities.

Conclusions:

The proposed H_∞ state estimation scheme effectively handles discrete-time nonlinear SPCNs with RR protocol scheduling.
The method provides a robust framework for analyzing and designing estimators for complex networked systems with singular perturbations.
Numerical validation confirms the efficacy of the designed state estimator.