Exact detectability of linear discrete-time time-varying stochastic systems

Abstract

This paper mainly studies exact detectability of linear discrete-time time-varying stochastic systems. Some new concepts such as K ∞ -exact detectability, K W F T -exact detectability, K F T -exact detectability and K N -exact detectability are introduced. Some nice properties of these new concepts are derived and their inherent relationship are also discussed. As an application, a Lyapunov-type theorem associated with generalized Lyapunov equations and exponential stability in mean square sense is presented under K N -exact detectability.

Robust H 2 / H ∞ control for periodic stochastic difference systems with mutiplicative noise

“…Assume that system (3) is a periodic system with the period τ > 0, namely, in system (1), F ( t + τ ) = F ( t ), G ( t + τ ) = G ( t ), M ( t + τ ) = M ( t ) and N ( t + τ ) = N ( t ). The following lemma generalises Proposition 4.1 in [13] to the stochastic case, for which its proof can be seen in [14]. Lemma 2 Assume that system (3) is a periodic system with a period τ > 0.…”

Expansion modelling of discrete grey model based on multi-factor information aggregation

“…Recently, a lot of improved models have been constructed, and forecasting precision of sequences was obviously improved [2][3][4][5][6][7][8]. In the literature, different kinds of improved GM(1, 1) models, such as the discrete grey forecasting model GM (1, 1|τ, γ), non-equipgap GM(1, 1) model, nonhomogeneous discrete grey model (NDGM), were proposed [7][8][9][10][11][12][13][14][15][16]. Properties of these improved models were also analyzed and discussed [17][18][19][20].…”