Mean square detectability of multi-output discrete-time systems over stochastic multiplicative noise channels
WU Yi-lin
SHEN Zhi-ping
ZHANG Jin
Abstract：This study discusses the detectability of multiple output discrete-time systems under multiplicative noise constraints.It is assumed that the capacities of sub-channels are fixed prior and cannot be arbitrarily allocated.First,a multiplicative noise is used to model the communication channel,and the dynamic equation of the systems is established by virtue of the coding/observer co-design idea.Second,according to the properties of majorization and controllable decomposition technique,a sufficient condition for the detectability of the networked control systems(NCSs)is given.Meanwhile,based on the cyclic decomposition technique,the optimal complementary sensitivity and the majorization theory,a necessary condition for the detectability of the NCSs is also obtained.The sufficient and necessary conditions can be expressed by the form of majorization,which is composed of the topology entropy of the open loop system and the channel capacities of sub-channels.Finally,the rationality of the conclusion is verified by numerical examples and simulation.
Keywords：discrete time control systemschannel capacitymean square detectabilitymajorizationmultiplicative noise
Publication Date：2024-08-28
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：8( 1487-1494 )