Quantized $H_{\infty }$ Control for Nonlinear Stochastic Time-Delay Systems With Missing Measurements

Abstract

Abstract-In this paper, the quantized H∞ control problem is investigated for a class of nonlinear stochastic timedelay network-based systems with probabilistic data missing. A nonlinear stochastic system with state delays is employed to model the networked control systems where the measured output and the input signals are quantized by two logarithmic quantizers, respectively. Moreover, the data missing phenomena are modeled by introducing a diagonal matrix composed of Bernoulli distributed stochastic variables taking values of 1 and 0, which describes that the data from different sensors may be lost with different missing probabilities. Subsequently, a sufficient condition is first derived in virtue of the method of sector-bounded uncertainties, which guarantees that the closedloop system is stochastically stable and the controlled output satisfies H∞ performance constraint for all nonzero exogenous disturbances under the zero-initial condition. Then, the sufficient condition is decoupled into some inequalities for the convenience of practical verification. Based on that, quantized H∞ controllers are designed successfully for some special classes of nonlinear stochastic time-delay systems by using Matlab linear matrix inequality toolbox. Finally, a numerical simulation example is exploited to show the effectiveness and applicability of the results derived.

A New Design of $H$ -Infinity Piecewise Filtering for Discrete-Time Nonlinear Time-Varying Delay Systems via T–S Fuzzy Affine Models

“…Now, adding the terms on the left-hand side (LHS) of equation (37) to the LHS of (24), together with (27), (28), (31), and (35), we have…”

“…For a more intuitive understanding of the advantages of the above developed synthesis method, in the following, we also present another filter synthesis result based on a conventional decoupling inequality: −Φ T P −1 Φ ≤ P − Φ − Φ T with P > 0, but without using state-augmentation equation (37). For fair comparison purposes, the same piecewise-affine LKF in (21)- (23) is employed.…”

H∞fault estimation with randomly occurring uncertainties, quantization effects and successive packet dropouts: The finite-horizon case

“…It is worth mentioning that there are generally two types of quantized communication models, namely, logarithmic quantization [29] and uniform quantization [5]. The differences between these two algorithms are twofold: 1) the logarithmic one provides a non-uniform partition of the state space while the uniform one is concerned with the uniform partition; and 2) the quantization levels of the logarithmic one become finer in the region that is closer to the origin in a logarithmic way and, for the uniform one, the lengths of each two quantization regions are equal.…”

“…Nowadays, the signal quantization is considered as another source for performance degradation of networked systems and a great number of results have been available in the literature, see e.g. [7,12,29,31]. In particular, the quantization has been described by logarithmic types in [11] which can then be converted into the normbounded uncertainty.…”

On existence and uniqueness of solutions to uncertain backward stochastic differential equations

“…Then, a novel Lyapunov functional is constructed to obtain sufficient conditions, under which the dynamical network is exponentially mean-square stable. In Wang et al [35], a class of nonlinear stochastic time-delay network-based systems with probabilistic data missing is investigated. A nonlinear stochastic system with state delays is employed to model the networked control systems where the measured output and the input signals are quantized by two logarithmic quantizers, respectively.…”