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This article investigates the problem of finite-time stability and stabilisation (FTSS) in time-varying stochastic systems with multiplicative noise and time-delays. To simplify research process, the method of dimension expansion is employed to transform systems characterised by constant delays into delay-free models, which enables the extraction of the finite-time stability (FTS) of the original systems by leveraging the FTS analysis conducted on the new model. Two distinct approaches are employed to establish criteria for determining FTSS in systems. The first approach leverages the state transition matrix (STM) method to acquire both necessary and sufficient stability conditions for the simplified models. Furthermore, sufficient conditions for the FTS of the original systems can be obtained. For ease of verification, our second approach integrates the Lyapunov equation with linear matrix inequalities (LMIs), offering a framework to obtain control gains. Finally, the proposed results are instantiated through three simulation examples to demonstrate their efficacy. [ABSTRACT FROM AUTHOR]

This work addresses the nonfragile $H_{\infty }$ controller design problem for a class of discrete-time uncertain nonlinear systems. The norm-bounded uncertainty is contained in the nonlinear plant, which is described by the well-known Takagi–Sugeno (T–S) fuzzy model. The controller gain perturbation is also considered. When the input signal is transmitted from the controller to the system through the digital communication channels, it will be quantized by a static quantizer. The main attention is to design the nonfragile $H_{\infty }$ state-feedback controller for the closed-loop quantized uncertain T–S fuzzy system. By introducing some auxiliary scalars and the fuzzy basis-dependent Lyapunov function approach, sufficient conditions are established in the form of linear matrix inequalities (LMIs). The construction for the nonfragile $H_{\infty }$ controller can be completed by solving these LMIs. In the end, the applicability and effectiveness of the proposed method have been illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

This paper revisits the problem of H∞ filter design for singular systems with interval time‐varying delays. Firstly, by state decomposition method (SDM), a novel Lyapunov–Krasovskii functional (LKF) including two augmented nonintegral terms is presented. Secondly, via the constructed LKF and the linear matrix inequality (LMI) technique, sufficient stability conditions with lower conservatism are achieved such that the considered singular system is admissible with specified H∞ performance level. Thirdly, a state decomposition‐recombination approach is first introduced to obtain a desired H∞ filter in terms of matrix component transformation technology. Finally, the validity and superiority of the results obtained are verified via two numerical examples. [ABSTRACT FROM AUTHOR]

This article addresses the H∞ filtering problem for a class of discrete-time nonlinear switched systems. Every subsystem of the considered nonlinear-switched systems is represented by the Takagi–Sugeno fuzzy systems with local nonlinear models. Signal quantization and filter parameter perturbation are considered simultaneously in the H∞ filter design. Both the measurement output signal and the performance output signal are quantized by two static quantizers, respectively, before they are transmitted. Based on the average dwell time approach, sufficient conditions for desired H∞ filters are established in the form of linear matrix inequalities. Under the obtained conditions, the filtering error system is exponentially stable and can achieve a weighted H∞ performance index. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this study, a sampled‐data networked control system over a multipath routing‐enabled network is investigated, where each delivered signal in a path suffers a random delay. For such a system, the mean square stabilisation problem is considered under the joint design of the event‐driven strategy on the actuator side and the control policy on the decision‐maker side. The contributions of this study are twofold. First, by pre‐defining an application time as an event‐triggering parameter, the sampled‐data system is transformed into a stochastic form with input delay and packet dropout. When the probability distribution F(⋅) of random delay is known a priori, the close form of packet dropout rate is proposed and a set of necessary and sufficient stabilisation conditions are developed simultaneously. When F(⋅) is unknown, the reduced system is an uncertain dynamic system. Utilising matrix polynomials, a verifiable criterion is derived for stabilising the uncertain system, which is also necessary and sufficient. Second, for the scalar system, the close form of allowable sampling period bound is developed in terms of F(⋅) and system parameters. [ABSTRACT FROM AUTHOR]

This work focuses on the fault detection for nonlinear networked systems. A fault detection filter is designed to detect the fault signal under the effect of disturbance. The communication channel of the networked system is supposed to be influenced by the limited bandwidth and random data losses. To deal with these, event-triggered scheme and Bernoulli process are employed to describe the problems, respectively. According to the above situation, we employ a formulated random series to describe the input of fuzzy filter. Differential mean value theorem based method is presented to handle the asynchronous membership functions. Synthetically, linear matrix inequality approach is employed to obtain the stability conditions and the filter design process. At last, we verify the performance of this method acting in the simulation example. [ABSTRACT FROM AUTHOR]

The main focus of this paper is to explore the finite-time stabilization of mean-field time-varying stochastic systems that are affected by uncertain parameters, multiple disturbances, and delays. In contrast to prior studies, we present a set of sufficient conditions for achieving finite-time stability in the closed-loop model. Notably, these conditions are established based on the analysis of the state transition matrix (STM). Additionally, we address a sufficient condition based on the Lyapunov function, where the STM significantly simplifies the selection process of the Lyapunov function. Finally, we introduce a linear matrix inequality (LMI)-based approach that facilitates the computation of non-fragile controllers. The effectiveness of the developed theoretical results is verified through a stock investment model. [ABSTRACT FROM AUTHOR]

This paper addresses the finite-time state estimation problem for semi-Markovian jump neural networks with sensor nonlinearities under the consideration of leakage delay and time-varying delay. The modes of original system and desired estimator are supposed to be asynchronous. Some sufficient conditions are proposed to guarantee the finite-time boundedness as well as mixed H ∞ and passive performance of the error system in terms of constructing Lyapunov–Krasovskii functionals. By utilizing affine Bessel-Legendre inequalities, a less conservative result can be achieved. By virtue of linear matrices inequalities approach, the asynchronous state estimator gains are obtained. Two numerical examples are provided to demonstrate the less conservativeness and effectiveness of our method. [ABSTRACT FROM AUTHOR]

• The observer design problem for nonlinear switched systems with quantization has been investigated. • A more practical and complex situation that is the uncertainties existing in system parameters and observer gains simultaneously has been studied. • New suficient conditions have been obtained. This paper addresses the nonfragile H ∞ observer design problem for uncertain nonlinear switched systems with quantization. The measurement output signals are quantized by a static quantizer before being transmitted. The sector bound approach is applied to obtain the quantization error. To address the problem of observer parameter perturbation, a set of observers with gain variations are constructed. Considering uncertainties existing both in switched systems and observer gains, our purpose is to design a set of robust nonfragile observers such that the observer error systems are globally exponentially stable and satisfy a weighted H ∞ performance index. Based on the average dwell time (ADT) switching approach and some lemmas, sufficient conditions for the desired observers are established in form of linear matrix inequalities (LMIs). Finally, an example is provided to illustrate the applicability of the obtained results. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the problem of non-fragile delay feedback control for neutral stochastic Markovian jump systems (NSMJSs) with time-varying delays. The main aim is to design non-fragile and mode-dependent delay feedback controller (DFC) both in the drift part and in the diffusion part to realize closed-loop NSMJS is stochastically stable. By constructing mode-dependent and delay-dependent comprehensive Lyapunov-Krasovskii functional, the stabilization conditions are provided in terms of linear matrix inequalities (LMIs). Simulation examples including a lossless transmission line model (LTLM) are utilized to verify the validity and usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract This paper is concerned with the output-feedback stabilization problem for a class of singular linear parameter-varying (LPV) systems. The objective is to design a dynamic output-feedback controller such that the resulting closed-loop system is robustly admissible. Different from the classical gain-scheduling techniques, it is assumed in this paper that the scheduling parameters involved in the plant model are not exactly available for the controller. First, a sufficient and necessary condition for the solvability of the underlying stabilization problem is obtained in the form of general parameter-dependent matrix inequalities. Second, an equivalent transformation is developed to convert the general parameter-dependent conditions into parameter-dependent linear matrix inequalities (LMIs). Third, the singular LPV system whose coefficient matrices take a polytopic form is considered, and the finite LMI-based conditions are derived. Finally, an illustrative example is provided to show the effectiveness of the proposed design methods. [ABSTRACT FROM AUTHOR]

In this paper, a partially mode-dependent dissipative filter design method is presented for uncertain Markovian jump systems with mixed delays and unknown transition rates. The uncertainty is assumed to be time-invariant which belongs to a ploytope. By constructing a mode-dependent and parameter-dependent Lyapunov–Krasovskii functional based on delay-partitioning approach, we propose a sufficient condition for the existence of a partially mode-dependent dissipative filter, which ensures that the resulting filtering error system is stochastically stable and dissipative. The filter parameters can be derived by using feasible solutions to a certain set of linear matrix inequalities. Finally, two simulation examples are provided to illustrate the effectiveness of the filter design technique. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of α -dissipativity filtering for singular Markovian jump systems (SMJSs) with distributed delays. Sufficient delay-dependent conditions are developed for the stochastic admissibility and the dissipativity analysis of SMJSs with distributed delays by using an integral partitioning technique. Then, based on these conditions, both mode-dependent and mode-independent filters are designed such that the filtering error SMJSs with distributed delays are stochastically stable and strictly ( Q , S , R ) - α -dissipative. The criteria are established in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]