Abstract
This paper deals with the problem of stochastic stability for a class of neutral distributed parameter systems with Markovian jump. In this model, we only need to know the absolute maximum of the state transition probability on the principal diagonal line; other transition rates can be completely unknown. Based on calculating the weak infinitesimal generator and combining Poincare inequality and Green formula, a stochastic stability criterion is given in terms of a set of linear matrix inequalities (LMIs) by the Schur complement lemma. Because of the existence of the neutral term, we need to construct Lyapunov functionals showing more complexity to handle the cross terms involving the Laplace operator. Finally, a numerical example is provided to support the validity of the mathematical results.
Highlights
Time-delay models are popular in all kinds of fields such as demography, biology, economics, and chemistry
Neutral systems as a special type of time-delay systems are often encountered because these systems have a wider application value than the general time-delay systems in many dynamical systems such as bioengineering systems, dynamic systems of offshore platform, and dynamic economic models
The systems inevitably receive the impact of sudden changes in the environment, abrupt failure of components, unexpected changes in system parameters, and so on. ese random diversifications usually follow the law of Markov jump. ese systems are called Markovian jump systems
Summary
Time-delay models are popular in all kinds of fields such as demography, biology, economics, and chemistry. Stability analysis for neutral Markovian jump systems with partially unknown transition probabilities has been proposed in [34, 35]. Finite-time stochastic stability and control of Markovian jump systems with general incomplete transition probabilities have been discussed in [41,42,43,44]. Stabilization of discrete-time Markovian jump systems with partially unknown transition probabilities was probed in [45]. We are considering the problem of stochastic stability of a class of Markovian jumping neutral distributed parameter systems in this paper. E linear matrix inequality approach together with the Lyapunov functional method is employed to develop stochastic stability criteria for the described systems. ZW(x, t) 0, (x, t) ∈ zΩ ×[− c, +∞), zn where c max{σ, τ} and σ > 0 and τ > 0 are constants. n is the unit outward normal vector of zΩ, and ψ(x, t) is the smooth function. τ > 0, σ > 0, and D(r(t)) > 0 are constants; A(r(t)), C(r(t)), and A1(r(t)) are constant matrices
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
