Exponential Stability Analysis of Stochastic Semi-Linear Systems With Lèvy Noise

Abstract

The exponential stability of semi-linear stochastic partial differential equations (SPDEs) involving Lèvy type noise is investigated in this paper. By constructing an appropriate Lyapunov function, a new set of sufficient conditions are established in terms of linear matrix inequalities (LMIs) which ensures the mean-square exponentially stability (MSES) of given system with Neumann boundary conditions. Then the H ∞ performance index is introduced to eliminate the disturbance which occurs in the considered system. The boundary control gain is obtained by solving the LMI conditions using the standard MATLAB software. Finally, a numerical example is provided to demonstrate the usefulness of the proposed methods.

Exponential mean‐square string stability of vehicular platoon with stochastic disturbance and time delay

“…30 Noteworthy studies on stochastic disturbance include the work of Xu et al, 31 who investigated spacing errors between vehicles in a longitudinal following system with stochastic disturbance, and Hu et al, 32 who applied stochastic programming to address stochastic disturbances in vehicle platoons. Mathiyalagan et al had contributed to the establishment of conditions for mean-square and almost sure exponential stability in both semi-linear stochastic partial differential systems affected by Lévy noise using linear matrix inequalities (LMIs), 33 and in linear stochastic neutral systems with general time-delays governed by Stieltjes integrals. 34 Zhang and Li 35 investigate the delay-dependent exponential stability of linear stochastic neutral systems with general delays, utilizing Stieltjes integrals to provide a unified approach in determining stability through spectral radius and linear matrix inequalities.…”