Exponential Stability for Neutral Stochastic Markov Systems With Time-Varying Delay and Its Applications

Area of Science:

• Control Theory
• Stochastic Systems
• Dynamical Systems

Background:

• Neutral stochastic systems with time-varying delays present significant stability analysis challenges.
• Existing methods often require stringent conditions like delay function differentiability or continuity.
• Markov switching adds complexity to stability investigations.

Purpose of the Study:

• To investigate the exponential stability in the pth moment for neutral stochastic Markov systems with time-varying delays.
• To develop novel delay-independent and delay-dependent stability criteria.
• To apply these criteria to neutral stochastic neural networks and complex dynamical systems.

Main Methods:

• Establishing integral inequalities for delay-independent stability criteria.
• Utilizing functional differential equations theory for delay-dependent stability criteria.
• Employing M-matrix conditions for simplified delay-independent analysis.

Main Results:

• Derived delay-independent criteria using integral inequalities, simplified by M-matrix conditions.
• Developed delay-dependent criteria in algebraic inequalities, providing the least upper bound for delays.
• Demonstrated applicability to neutral stochastic neural networks and complex dynamical systems with Markov switching.

Conclusions:

• The new criteria overcome limitations of previous methods by not requiring delay function differentiability or continuity.
• The results effectively address the complexities introduced by neutral terms and Markov switching.
• Numerical examples validate the effectiveness and potential of the developed theoretical results.