Detectability, Observability and Lyapunov-Type Theorems of Linear Discrete Time-Varying Stochastic Systems with Multiplicative Noise

2015/09/15 by Weihai Zhang, Wei Xing Zheng, Zhang, Weihai +3
Engineering · #Control Systems and Identification #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1509.04379

openalex publication_date 2015/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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, \cal K^∞-exact detectability (resp. \cal K^WFT-exact detectability, \cal K^FT-exact detectability, \cal K^N-exact detectability) and \cal K^∞-exact observability (resp. \cal K^WFT-exact observability, \cal K^FT-exact observability, \cal K^N-exact observability) 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 generalized Lyapunov equations and exponential stability in mean square sense are presented under uniform detectability, \cal K^N-exact observability and \cal K^N-exact detectability, respectively.

Citations

• Uniform stabilization of discrete-time switched and Markovian jump linear systems

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