Some Unsolved Problems in Stability and Optimal Control Theory of Stochastic Systems

Abstract

In spite of the fact that the theory of stability and optimal control for different types of stochastic systems is well developed and very popular in research, there are some simply and clearly formulated problems, solutions of which have not been found so far. To the readers’ attention six open stability problems for stochastic differential equations with delay, for stochastic difference equations with discrete and continuous time and one open optimal control problem for stochastic hyperbolic equation with two-parameter white noise are offered.

Keywords

• stochastic differential equation
• stochastic difference equation
• stochastic hyperbolic equation
• fading stochastic perturbations
• Lyapunov function
• Linear Matrix Inequality (LMI)