Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems withmultiplicative noise

作者：Zhang, Weihai; Zheng, Wei Xing^*; Chen, Bor-Sen

来源：International Journal of Control, 2017, 90(11): 2490-2507.

DOI：10.1080/00207179.2016.1257152

• Discrete-time time-varying stochastic systems
• generalised Lyapunov equations
• uniform detectability
• exact detectability
• exact observability

The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability, K-infinity-exact detectability (resp. K-WFT-exact detectability, K-FT-exact detectability, K-N-exact detectability) and K-infinity-exact observability (resp. K-WFT-exact detectability, K-FT-exact detectability, K-N-exact detectability) are introduced, respectively, and nice properties associated with uniform detectability, exact detectability and exact observability are also obtained. Moreover, some Lyapunov-type theorems associated with generalised Lyapunov equations and exponential stability in mean square sense are presented under uniform detectability, K-N-exact observability and K-N-exact detectability, respectively.

• 出版日期2017
• 单位山东科技大学; 清华大学