Improvement and extension to “exponential stability and stabilizability in mean square of large-scale stochastic systems”

Abstract

The purpose of this paper is to improve and extend the abovementioned work [1] presented by Boulanger, C. Exponential Stability and Stabilizability in Mean Square of Large-Scale Stochastic Systems. Stoch. Anal. Appl. 1999, 17 (5), 727–747. First, we weaken the fundamental condition in work [1], that is to weaken these coefficient functions of the system equations which are C ₂- functions with bounded derivatives to general continuous functions. Next, we extend the systems by we considered to general stochastic large-scale systems which have time-varying, nonlinear, hierarchical form. Moreover, we improve on the results for exponential stability and stabilizability in mean square to the results on almost sure exponential stability and stabilizability, respectively.

Keywords:

• Stochastic differential equation
• Time-varying hierarchical form
• Exponential stability in mean square
• Almost sure exponential stability
• Feedback law

Acknowledgments