A unified framework for asymptotic and transient behavior of linear stochastic systems

作者：Yan, Zhiguo; Park, Ju H.^*; Zhang, Weihai

来源：Applied Mathematics and Computation, 2018, 325: 31-40.

DOI：10.1016/j.amc.2017.12.023

• Stochastic systems
• Mean square (gamma alpha)-stability
• Asymptotic and transient behavior
• Matrix inequality

This paper is concerned with a unified framework for asymptotic and transient behavior of stochastic systems. In order to explain this problem explicitly, a concept of mean square (gamma,alpha)-stability is first introduced and two stability criteria are derived. By utilizing an auxiliary definition of mean square (gamma,T)-stability, the relations among mean square (gamma,alpha)-stability, mean square (gamma,T)-stability and finite-time stochastic stability are established. Subsequently, two new sufficient conditions for the existence of state and output feedback mean square (gamma,alpha)-stabilization controllers are presented in terms of matrix inequalities. A numerical algorithm is given to obtain the relation between gamma(min) and alpha. Finally, an example is given to illustrate our results.

• 出版日期2018-5-15
• 单位重庆师范大学; 山东科技大学