Stability and robust stabilization to linear stochastic systems described by differential equations with markovian jumping and multiplicative white noise

Stochastic linear systems subjected both to Markov jumps and to multiplicative white noise are considered. In order to stabilize such type of stochastic systems, the so-called set of generalized discrete-time algebraic Riccati equations has to be solved. The LMI approach for computing the stabilizing symmetric solution (which is in fact the equilibrium point) of this system is studied. We construct a new modification of the standard LMI approach, and we show how to apply the new modification. Computer realizations of all modifications are compared. Numerical experiments are given where the LMI modifications are numerically compared. Based on the experiments the main conclusion is that the new LMI modification is faster than the standard LMI approach.

Download Full-text

Exact Finite-Difference Schemes ford-Dimensional Linear Stochastic Systems with Constant Coefficients

Journal of Applied Mathematics ◽

10.1155/2013/830936 ◽

2013 ◽

Vol 2013 ◽

pp. 1-6 ◽

Cited By ~ 2

Author(s):

Peng Jiang ◽

Xiaofeng Ju ◽

Dan Liu ◽

Shaoqun Fan

Keyword(s):

Finite Difference ◽

Differential Equations ◽

Stochastic Differential Equations ◽

Symplectic Structure ◽

Stochastic Systems ◽

First Integral ◽

Difference Schemes ◽

Finite Difference Schemes ◽

Linear Stochastic Systems ◽

Constant Coefficients

The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.

Download Full-text

INVARIANT FOLIATIONS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Stochastics and Dynamics ◽

10.1142/s0219493708002421 ◽

2008 ◽

Vol 08 (03) ◽

pp. 505-518 ◽

Cited By ~ 11

Author(s):

KENING LU ◽

BJÖRN SCHMALFUß

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

White Noise ◽

Stochastic Partial Differential Equations ◽

Partial Differential ◽

Invariant Foliation ◽

All Solutions ◽

Multiplicative White Noise ◽

Long Term Behavior

In this paper, we study the existence of an invariant foliation for a class of stochastic partial differential equations with a multiplicative white noise. This invariant foliation is used to trace the long term behavior of all solutions of these equations.

Download Full-text