Absolute stability of the solution of the automatic control stochastic systems with nonlinear feedback and Poisson switching (Q2703339)

The authors consider the system of stochastic differential equations NEWLINE\[NEWLINEdx(t)= [Ax(t)+g\varphi(l^{T}x(t))] dt+ Bx(t) dw(t)+ \int_{U}C(u)x(t)\widetilde\nu(du,dt),NEWLINE\]NEWLINE with condition \(x(0)=\psi\), where \(A,B\) are constant matrices, \(C(u)\) is a matrix-valued function, \(w(t)\) is a standard one-dimensional Wiener process, \(\widetilde\nu(du,dt)\) is the centered Poisson measure, \(\varphi(\sigma)\in R^1\) is a nonlinear function, \(l,g\) are constant vectors. Sufficient conditions of absolute stability in the mean square of the equilibrium position of the given stochastic differential equations system are obtained.