Robust Finite-Time Stability for Uncertain Discrete-Time Stochastic Nonlinear Systems with Time-Varying Delay

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Stochastic Systems Analysis

Background:

• Ensuring finite-time stability (FTS) is critical for discrete-time stochastic nonlinear systems (DSNSs), especially with time-varying delays (TVD) and multiplicative noise.
• Existing methods may be conservative or insufficient for complex DSNSs under these conditions.

Purpose of the Study:

• To develop novel, less conservative criteria for finite-time stability (FTS) in uncertain discrete-time stochastic nonlinear systems (DSNSs) with time-varying delay (TVD).
• To address the challenges posed by multiplicative noise and time-varying delays in stability analysis.

Main Methods:

• Construction of a Lyapunov-Krasovskii function (LKF) incorporating forward differences.
• Formulation and solution of a series of linear matrix inequalities (LMIs).
• Development of FTS criteria for both general uncertain DSNSs and a stochastic nominal system.

Main Results:

• Less conservative stability criteria for FTS in DSNSs with TVD and multiplicative noise were derived.
• Sufficient conditions for FTS were obtained by solving LMIs.
• Finite-time stability was demonstrated for a stochastic nominal system.

Conclusions:

• The proposed methods provide effective and improved sufficient conditions for finite-time stability analysis of uncertain discrete-time stochastic nonlinear systems.
• Simulation examples validate the effectiveness and advancements of the presented techniques.