Nonfragile Finite-Time Stabilization for Discrete Mean-Field Stochastic Systems

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

This paper mainly discusses the robust quadratic stability and stabilization of linear discrete time stochastic systems with state delay and uncertain parameters. By means of the linear matrix inequality (LMI) method, a sufficient condition is respectively obtained for the stability and stabilizability of the considered system. Moreover, an example with simulations is given to verify the effectiveness of our theoretical results.

This paper presents the stabilization problem of a class of discrete-time stochastic linear systems with time delay using an event-triggered control(ETC) strategy. For the general linear systems, we propose a new event triggering mechanism and deduce sufficient conditions for mean square exponentially stabilizability(MSES) and almost sure exponentially stabilizability(ASES) via ETC. The results show that the stability of the system depends on the system parameters (time delay, noise, event trigger threshold parameter, and unstable characteristic value of the original system). When the feedback control is disturbed by low-intensity noise, the unstable system can be stable in the mean square. Finally, the validity of the theoretical results is illustrated through a simulation example.

By the modem time series analysis method, based on the autoregressive moving average (ARMA) innovation models and white noise estimation theory, using the optimal fusion rule weighted by diagonal matrices, a distributed descriptor Wiener state fuser is presented by weighting the local Wiener state estimators for the linear discrete stochastic descriptor systems with multisensor. It realizes a decoupled fusion estimation for state components. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors are presented based on cross-covariances among the local innovation processes, input white noise, and measurement white noises. It can handle the fused filtering, smoothing, and prediction problems in a unified framework. Its accuracy is higher than that of each local estimator. A Monte Carlo simulation example shows its effectiveness and correctness.

The notion of adaptively aggregating a linear discrete time-invariant large-scale stochastic system is presented. It is shown how the eigenstructure of the aggregated system evolves and gains support consistent with specific characteristics of the system being aggregated and with an aggregation matrix functional defined herein. Necessary conditions for the existence of the aggregation matrix functional for the random system components are given. The uniqueness question is addressed. An aggregation performance measure is defined based on certain mild conditions that are imposed on the targeted large-scale system's environmental characteristics.

Reduced-order steady-state descriptor Kalman fuser weighted by block-diagonal matrices

Decoupled distributed Kalman fuser for descriptor systems

In the paper sufficient conditions for stability of nonlinear discrete systems with iterations and for synthesis of discrete Lagrange stable linear time-varying system with iterations, connecting the norm of the operator describing the discrete system, the initial conditions, the perturbations and the parameters of the systems are given and proven with theorems. The results can be used for assessment of discrete iterative processes and systems, like digital microprocessor based controllers.

Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems

In the present paper, a two-stage fault monitoring scheme is proposed and evaluated for discrete linear stochastic systems in the event of sensor noise degradation. In the first stage, fault detection and partial isolation is achieved using simple statistical tests based on the failure effect on the joint pdf of the Kalman-Bucy filter innovations. Complete fault identification (fault size, fault location, time of occurrence) is performed by the subsequent use of generalized likelihood ratio test (GLR). The analysis is verified by computer simulation of a first order discrete stochastic system.

This note deals with the delay-dependent stability and stabilization of linear system with state and input delays. Firstly, for the nominal system, by introducing the augmented Lyapunov functional and some free-weighting matrices, new delay-dependent stability and stabilization criteria of the system are presented. Then, these new conditions are extended to handle norm-bounded uncertain systems with state and input delays, which show less conservativeness. Numerical examples are given to illustrate the effectiveness of the proposed results.

ABSTRACTThe 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, -exact detectability (resp. -exact detectability, -exact detectability, -exact detectability) and -exact observability (resp. -exact detectability, -exact detectability, -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, -exact observability and -exact detectability, respectively.

Robust linear controller design of uncertain discrete systems with time-varying delay

The geometric properties of the canonical parameter space are used to derive necessary conditions for constraining zeros to lie within or on a central circular region of radius α in the z-plane. These necessary conditions are then compared with the sufficient conditions for the stability of linear discrete time systems.

This paper deals with the problem of robust stabilization for linear discrete-time systems under non-linear perturbations. Without limitation to single-input systems and restriction on the structures of both the positive definite matrix and the corresponding variable, a new sufficient condition is presented which guarantees the stability of the closed-loop system and at the same time maximizes the bound on the non-linearity. In addition, our main result is extended to discrete time-delay systems. All the conditions are given within the framework of linear matrix inequalities. The effectiveness of the methods is illustrated with three examples.