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This article addresses the adaptive event-triggered nonfragile state estimation for the fractional-order complex networked systems subject to randomly occurring nonlinearities and adversarial network attacks, in which the order of fractional derivative operator satisfies $0 < p < 1$. To reduce unnecessary transmission burden as much as possible in an allowable range, an adaptive event-triggered scheme (AETS) is introduced to determine whether the data released by the sensor should be transmitted to the nonfragile state estimator. First, based on the considerations of the designed AETS and stochastic cyber-attacks, one constructs a newly fractional-order estimation error system model. Then, by employing the Lyapunov functional approach and the properties of Mittag–Leffler (M–L) functions, a sufficient condition is obtained to ensure the augmented error system stochastic mean-square stability; moreover, by making use of matrix’s singular value decomposition (SVD), the desired nonfragile state estimator is designed, and the estimator gains can be obtained by finding the feasible solutions of linear matrix inequality (LMI). Finally, a numerical example and Chua’s circuit model example are given to illustrate the feasibility of the designed nonfragile estimator. [ABSTRACT FROM AUTHOR]

This article develops a generalized $\mathcal {H}$ -representation, which can transforms stochastic systems into deterministic systems. With the help of this new approach, the necessary and sufficient conditions of $p$ th moment asymptotic stability and stabilization of linear stochastic systems are addressed. Meanwhile, the generalized $\mathcal {H}$ -representation method is also applied to investigate $p$ th moment observability and $p$ th moment complete observability for the addressed systems. [ABSTRACT FROM AUTHOR]

Summary: Joint estimation of states and time‐varying parameters of linear stochastic systems is of practical importance for fault diagnosis and fault tolerant control. The known fact is that measurements have outliers. They can significantly degrade the properties of linearly recursive algorithms, which are designed to work in presence of Gaussian noises. This article proposes two kinds of strategies for joint parameter‐state robust estimation of linear stochastic models in presence of all possible faults and non‐Gaussian noises. In the form of Theorem, joint robust algorithm for systems with sensor and component faults, as well as the algorithm for systems with parameter faults are proposed. Because of their good features in robust filtering, Masreliez‐Martin filter represents a cornerstone for realization of the proposed robust algorithms for joint state‐parameter estimation. The good features of proposed robust estimation algorithms, in relation to algorithms based on other widely‐used filters, are illustrated by simulation results. On the other side, intensive research in the field of mathematical modeling of pneumatic servo drives has shown that their mathematical models are nonlinear in which a lot of important details cannot be included in the model. Also, it has been well known that the nonlinear model can be approximated by a linear model with time‐varying parameters. Due to the abovementioned reasons, it can be assumed that the pneumatic cylinder model is a linear stochastic model with variable parameters. The good practical values of the proposed robust joint algorithm to identification of the pneumatic cylinder are illustrated by experimental results. [ABSTRACT FROM AUTHOR]

This paper is engaged in investigating the observer-based event-triggered output feedback control issue for fractional-order cyber–physical systems with stochastic network attacks, where the order scale of the fractional derivative used is 0 < α < 1. An event-triggered scheme (ETS) with output-independent threshold is proposed to renew the observer input so as to reduce the redundant data communications. Considering the effects of the ETS and network attacks, a novel closed-loop fractional-order control system model is constructed. By making use of fractional-order Lyapunov indirect approach, sufficient conditions that can insure the global stochastic asymptotic stability of the established closed-loop control system are obtained. Moreover, according to the singular value decomposition (SVD) of matrix, the co-design of the gains of the desired observer and controller is addressed by finding the solution of the linear matrix inequalities (LMIs). Finally, a numerical example and a diesel engine control system are provided to validate the feasibility of the adopted observer-based control method. • A simplified ETS is proposed for fractional-order CPSs. • A fractional-order state observer model is constructed by taking the ETS and network attacks into consideration. • The observer-based event-triggered output feedback control problem is firstly considered for fractional-order CPSs with network attacks. • A new sufficient condition for the stability analysis of fractional-order CPSs is obtained, and the gains of the observer and controller are also co-designed. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates pth moment regional stability, stabilization, and generalized pole assignment of stochastic systems, which are most useful in many specific systems and applications. With the help of the generalized ℋ‐representation method, the necessary and sufficient conditions of pth moment regional stability and stabilization of stochastic systems are addressed. Meanwhile, the generalized pole assignment of stochastic systems is also considered. Finally, two examples are presented to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This study is concerned with the problem of robust normalisation and stabilisation of singular Markovian jump systems (SMJSs) with time‐varying delays and parameter uncertainties. The main aim is to design a proportional and derivative state feedback controller to realise the normalisation and stabilisation of the delayed SMJSs. Based on the constructed Lyapunov–Krasovskii functional, sufficient conditions are presented in terms of linear matrix inequalities via utilising the free‐weighting matrix method. Illustrative examples including an resistor inductor capacitor (RLC) circuit network are employed to demonstrate the effectiveness and usefulness of the obtained results. [ABSTRACT FROM AUTHOR]

This study investigates the stability and stabilisation problems for a class of neutral stochastic systems with Markovian jumping parameters. First, stability conditions are derived based on mode‐dependent Lyapunov–Krasovskii functionals. Second, a novel delay state‐feedback controller is considered to stabilise the stochastic system; novel conditions for designing desired controllers are presented in terms of linear matrix inequalities. The results are then extended to the robust stabilisation problem for uncertain neutral Markovian jump systems. Finally, numerical examples and simulation results are provided to show the effectiveness of the proposed design methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of stochastic stability analysis for a class of genetic regulatory networks with Markovian jump parameters and time-varying delays. A delay-dependent stability criterion is derived by using a novel mode-dependent Lyapunov functional. The derived stability criterion is expressed in terms of linear matrix inequalities and is less conservative than the existing ones in the literature. A numerical example is provided to demonstrate the effectiveness of the proposed stability criterion. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the robust and deconvolution filtering problems for stochastic systems with polytopic uncertainties. The purpose is to design a full-order deconvolution filter such that (i) the deconvolution error system is robustly exponentially mean-square stable with a prescribed decay rate and (ii) an or performance of the deconvolution error system is guaranteed. Based on a homogeneous polynomial parameter-dependent matrix (HPPDM) approach, sufficient conditions for the solvability of these problems are given in terms of linear matrix inequalities (LMIs). Such conditions are dependent on the decay rate, which enables one to design robust deconvolution filters by selecting the decay rates according to different practical conditions. In addition, when these LMIs are feasible, a design procedure of the desired filters is developed and an exponential estimate for the deconvolution error system is given. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed design methods. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the delay-dependent stabilization problem for a class of time-delay stochastic fuzzy systems. The time delays are assumed to appear in both the state and the control input. The purpose is the design of a state-feedback fuzzy controller such that the resulting closed-loop system is asymptotically stable in the mean square. A delay-dependent condition for the solvability of this problem is obtained in terms of relaxed linear matrix inequalities (LMIs). By solving these LMIs, a desired controller can be obtained. Finally, a numerical example is given to demonstrate the effectiveness of the present results. [Copyright &y& Elsevier]

The problem of state robust H ∞ tracking control for uncertain stochastic systems with interval time-varying delay is considered in this paper. The target is to design a memory state feedback controller such that the resulting closed-loop augmented system is robustly stochastically asymptotically stable and the states of original systems can follow the reference signal with given H ∞ performance. Firstly, by constructing delay-partitioning-dependent Lyapunov–Krasovskii functional with reciprocally convex approach, a delay-dependent condition guaranteeing the robust H ∞ tracking performance is proposed in a set of matrix inequalities. Secondly, new stability criteria for stochastic systems with time-varying delay are given with less conservativeness than some recent results. Thirdly, memory state feedback controller is designed via a set of linear matrix inequalities (LMIs) which can be solved by Matlab LMI toolbox. At last, numerical simulations are addressed to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]