This paper investigates the finite-time stability (FTS) of a linear conformable stochastic differential equation with finite delay (LCSDEwFD). We use Banach fixed point theorem (BFPT) to prove existence and uniqueness solution analyze FTS system using Gronwall inequalities. To demonstrate practical value our approach, we provide two numerical examples that showcase relevance effectiveness theor...

This paper proposes a stochastic finite difference approach, based onhomogenous chaos expansion (SFDHC).The said approach can handle time dependent nonlinear as well as linear systems with deterministic or stochastic initial and boundary conditions. In this approach, included stochastic parameters are modeled as second-order stochastic processes and are expanded using KarhunenLoève expansion, w...

In this paper, we consider a stochastic realization problem with finite covariance data based on “LQ decomposition” in a Hilbert space, and re-derive a non-stationary finite-interval realization ([4, 5]). We develop a new algorithm of computing system matrices of the finiteinterval realization by LQ decomposition, followed by the SVD of a certain block matrix. Also, a stochastic subspace identi...

In this paper, the finite horizon H∞ control problem is solved for a class of linear quantum systems using a dynamic game approach. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem. Then, by solving the finite horizon H∞ control problem for the equivalent stochastic problem using results from a corresponding deterministic ...

We study multigrid for solving the stochastic steady-state diffusion problem. We operate under the mild assumption that the diffusion coefficient takes the form of a finite Karhunen-Loéve expansion. The problem is discretized using a finite element methodology using the polynomial chaos method to discretize the stochastic part of the problem. We apply a multigrid algorithm to the stochastic pro...

In this paper, we provide for the first time an automated, correct-by-construction, controller synthesis scheme for a class of infinite dimensional stochastic hybrid systems, namely, hybrid stochastic retarded systems. First, we construct finite dimensional abstractions approximately bisimilar to original infinite dimensional stochastic systems having some stability property, namely, incrementa...

In this paper, global finite-time stabilization via output-feedback is investigated for a class of stochastic nonlinear systems. By introducing a homogeneous observer, we design an output-feedback control law by adding one power integrator technique and homogeneous domination approach. Based on stochastic finite-time stability theorem, it is proved that the closed-loop system is globally finite...

The main objective of this study is estimating acceleration time history of 16 September 1978 Tabas earthquake incorporating the seismological/geological source-path and site model parameters by using finite-fault simulation approach. The method generalizes the stochastic ground-motion simulation technique, developed for point sources, to the case of finite faults. It subdivides the fault plane...