A state estimation H∞ issue for discrete-time stochastic impulsive genetic regulatory networks in the presence of leakage,multiple delays and Markovian jumping parameters

In this work, we probes the stability results of H_∞ state estimation for discrete-time stochastic genetic regulatory networks with leakage, distributed delays, Markovian jumping parameters and impulsive effects. Here, we focus to evaluate the true absorption of mRNAs and proteins by calculating the H_∞ estimator in such a way that the estimation error dynamics is stochastically stable during the completion of the prescribed H_∞ disturbance attenuation level. In favor of decreasing the data communion in trouble, the H_∞ system accept and evaluate the outputs that are only transferred to the estimator when a certain case is acroses. Further, few sufficient conditions are formulated, by utilizing the Lyapunov–Krasovskii functional under which the estimation error system is stochastically stable and also satisfied the H_∞ attainment constraint. The estimator is obtained in terms of linear matrix inequalities (LMIs) and these LMIs are attainable, only if the estimator gains can be absolutely given. In addition to that, two numerical examples are exposed to establish the efficiency of our obtained results.     

Event-triggered H∞ state estimation for state-saturated complex networks subject to quantization effects and distributed delays

This paper is concerned with the event-triggered H_∞ state estimation problem for a class of discrete-time complex networks subject to state saturations, quantization effects as well as randomly occurring distributed delays. A series of Bernoulli distributed random variables is utilized to model the random occurrence of distributed delays. For the energy-saving purpose, an event-triggered mechanism is proposed to decide whether the current quantized measurement should be transmitted to the estimator or not. For the state-saturated complex networks, our aim is to design event-triggered state estimators that guarantee both the exponential mean-square stability of and the H_∞ performance constraint on the error dynamics of the state estimation. Stochastic analysis is conducted, in combination with the Lyapunov functional approach, to derive sufficient conditions for the existence of the desired estimators whose gain matrices are obtained by solving a set of matrix inequalities. An illustrative example is exploited to show the usefulness of the estimator design algorithm proposed.     

An event-triggered approach to distributed H∞ state estimation for state-saturated systems with randomly occurring mixed delays

In this paper, the event-triggered distributed H_∞ state estimation problem is investigated for a class of state-saturated systems with randomly occurring mixed delays over sensor networks. The mixed delays, which comprise both discrete and distributed delays, are allowed to occur in a random manner governed by two mutually independent Bernoulli distributed random variables. In order to alleviate the communication burden, an event-triggered mechanism is utilized for each sensor node to decide whether or not its current information should be broadcasted to its neighbors. The aim of this paper is to design event-triggered state estimators such that the error dynamics of state estimation is exponentially mean-square stable with a prescribed H_∞ performance index. By resorting to intensive stochastic analysis, sufficient conditions are first derived to guarantee the existence of the desired estimators, and the parameters of the desired distributed estimators are then obtained in light of the feasibility of a certain set of matrix inequalities. A numerical example is employed to illustrate the usefulness of the proposed distributed estimation algorithm.     

Exponential stabilization and sampled-date H∞ control for uncertain T–S fuzzy systems with time-varying delay

In this paper, the exponential stabilization problem of uncertain T–S fuzzy systems with time-varying delay is emulated by fuzzy sampled-data H_∞ control. Firstly, a novel suitable Lyapunov–Krasovskii function is constructed, which contains all the information about the sampling pattern. Secondly, a less conservative result is achieved by using an extended Jensen inequality, and purposefully using a compact free weighting matrix. In addition, according to the linear matrix inequality (LMI), some sampled-data H_∞ exponential stability sufficient conditions and controller design of T–S fuzzy systems are established. Finally, effectiveness gives some illustrative examples may be used to display the value of the current proposed method as well as a significant improvement.     

H∞ finite-time control for LPV systems with parameter-varying time delays and external disturbance via observer-based state feedback

This paper is concerned with the observer-based H_∞ finite-time control problem for linear parameter-varying (LPV) systems with parameter-varying time delays and external disturbance. The main contribution is to design an observer-based H_∞ finite-time controller such that the resulting closed-loop system is uniformly finite-time bounded and satisfies a prescribed H_∞ disturbance attenuation level in a finite-time interval. By using the delay- and parameter-dependent multiple Lyapunov–Krasovskii functional approach, sufficient criteria on uniform H_∞ finite-time stabilization via observer-based state feedback are presented for the solvability of the problem, which can be tackled by a feasibility problem in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the validity of the proposed theoretical results.     

H∞ reduced-order observer-based controller synthesis approach for T-S fuzzy systems

For continuous-time nonlinear systems represented by Takagi–Sugeno fuzzy models, a new H_∞ reduced-order-observer based controller synthesis structure is investigated in this paper. By the fuzzy reduced-order observer and fuzzy controller, an augmented error system composed of the estimation and control errors is obtained. The fuzzy modeling residual terms are seen as part of the external disturbance, and an extra design matrix is added to facilitate the design process. The robustness and stability conditions are given based on Lyapunov function approach, then the conditions are transformed into convex form to facilitate the numerical solving process. Finally, by the comparison with existing methods in simulation section, the control performance and conservativeness reduction effects of the proposed methods are verified.     

Finite-horizon H∞-consensus control for multi-agent systems with random parameters: The local condition case

This paper is concerned with the distributed H_∞-consensus control problem over the finite horizon for a class of discrete time-varying multi-agent systems with random parameters. First, by utilizing the proposed information matrix, a new formula is established to calculate the weighted covariance matrix of random matrix. Next, by allowing every agent to track the average of the neighbor agents, a novel local H_∞-consensus performance constraint is presented to cater to the local performance analysis. Then, by means of the proposed definition of the stochastic vector dissipativity-like over the finite horizon, a set of sufficient conditions for every agent is obtained such that the controlled outputs of the closed-loop multi-agent systems satisfy the proposed H_∞-consensus performance constraint. As a result, the proposed consensus control algorithm can be executed on each agent in an indeed distributed manner. Finally, a simulation example is employed to verify the effectiveness of the proposed algorithm.     

Robust H∞ persistent dwell time control for switched discrete-time T–S fuzzy systems with uncertainty and time-varying delay

This paper is concerned with the controller synthesis for switched Takagi–Sugeno (T–S) fuzzy systems with time-varying delays, parameter uncertainties and process disturbances. A persistent dwell time (PDT) based control law is mainly proposed for the T–S fuzzy systems in presenting of high-frequency motion switches. Different with the most existing literatures, the dynamics of local subsystems are allowed to be unstable during fast switching time intervals as well as the jump time instants. In addition, the maximal period of persistence time is not limited. Under the influences of the time-varying delays, uncertainties and disturbances, the proposed method ensures the overall closed-loop system to be globally uniformly exponentially stable. Moreover, a pre-given H_∞ performance can be simultaneously guaranteed. Numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Fractional-order adaptive neuro-fuzzy sliding mode H∞ control for fuzzy singularly perturbed systems

This paper investigates the fractional-order (FO) adaptive neuro-fuzzy sliding mode control issue for a class of fuzzy singularly perturbed systems subject to the matched uncertainties and external disturbances. Firstly, a novel FO fuzzy sliding mode surface is presented. Secondly, by introducing an appropriate ε-dependent Lyapunov function, some H_∞ performance analysis criteria are given, which also ensure the robust stability of the sliding mode dynamics. Furthermore, a hybrid neuro-fuzzy network system (HNFNS) is introduced to estimate the matched uncertainty. Moreover, an FO adaptive fuzzy sliding mode controller is designed to drive the state trajectories of fuzzy singularly perturbed systems to the predefined FO sliding mode surface within a finite-time. Finally, two verification examples are presented to illustrate the validity of the proposed FO control scheme.     

Finite-time synchronization for periodic T–S fuzzy master-slave neural networks with distributed delays

Finite-time (FT) synchronization for periodic T–S fuzzy master-slave neural networks (NNs) with distributed delays is addressed in this work. A fuzzy controller is designed for the salve NNs to synchronize the master NNs in FT and a synchronization error system (SES) is derived. Sufficient conditions are established to guarantee that the SES is FT bounded by using the mode and fuzzy basis dependent Lyapunov function. A new algorithm is proposed to obtain the suboptimal boundary of the SES to analyze how the periodic characteristics affect the system boundary. Finally, a numerical example is provided to demonstrate the validity of the fuzzy controller and the iterative algorithm for the boundary.     

Networked H∞ filtering for Takagi–Sugeno fuzzy systems under multi-output multi-rate sampling

This paper studies networked H_∞ filtering for Takagi–Sugeno fuzzy systems with multi-output multi-sensor asynchronous sampling. Different output variables in a dynamic system are sampled by multiple sensors with different sampling rates. To estimate the signals of such a system, a continuous multi-rate sampled-data fusion method is proposed to design a novel networked filter. By considering a class of decentralized event-triggered transmission schemes, multi-channel network-induced delays, and the updating modes of the MOMR sampled-data, a networked jumping fuzzy filter is proposed to estimate system signals based on the transmitted multi-rate sampled-data of fuzzy system and the multi-rate sampled states of filter, and the jumping among filter modes is governed by a Markov process which depends on the arrival times of sampled output sub-vectors. To deal with asynchronous membership functions, the networked fuzzy filtering system is modeled as an uncertain fuzzy stochastic system with membership function deviation bounds. Based on stability and H_∞ performance analysis, several membership-function-dependent conditions are presented to co-design the event-triggered transmission schemes and the fuzzy filter such that the filtering error system is robustly mean-square exponentially stable with a prescribed H_∞ attenuation level. Finally, the improvement in estimation performance and comparison with the existing filtering methods are discussed through simulation examples.     

Adaptive event-triggered H∞ fuzzy filtering for interval type-2 T–S fuzzy-model-based networked control systems with asynchronously and imperfectly matched membership functions

This paper is concerned with the network-based H_∞ fuzzy filtering for non-linear systems with parameter uncertainties under a novel adaptive discrete event-triggered communication scheme (DETCS). Based on interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model, the non-linear systems with parameter uncertainties are represented as a class of IT2 T–S fuzzy systems. In the design process, a novel adaptive DETCS is proposed to reduce the usage of system resources and adapt the variation of plant output, and a novel networked IT2 T–S fuzzy filter is applied to improve the flexibility of filter design. By employing the time-delay systems modeling method, the filtering-error-system is modeled as a class of interval time-varying delayed IT2 T–S fuzzy systems with asynchronously and imperfectly matched membership functions, and further conditionally expressed as a favorable form. Then, some relaxed stability criteria are established to determine that this class of delayed IT2 T–S fuzzy systems is asymptotically stable with a prescribed H_∞ disturbance attenuation performance. Also, the co-design of parameter matrices of adaptive DETCS and filter is implemented. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Robust delay-dependent H∞ filtering for uncertain Takagi–Sugeno fuzzy neutral stochastic time-delay systems

This paper addresses the robust H_∞ filter design problem for a class of uncertain fuzzy neutral stochastic system with time-delay through Takagi–Sugeno (T–S) fuzzy model. By constructing an augmented Lyapunov–Krasovskii functional, some novel delay-dependent stability criteria for uncertain fuzzy neutral stochastic system with time varying delay are obtained in terms of linear matrix inequalities. By using the integral inequality in the neutral stochastic setting combined with delay decomposition approach, the H_∞ fuzzy filter is designed to guarantee the corresponding filtering error systems robustly asymptotically stable with a specified H_∞ performance index. At last, two numerical examples are presented to show the less conservatism than the previous results.     

An adaptive state tracking control scheme for T–S fuzzy models in non-canonical form and with uncertain parameters

This paper develops a novel adaptive state tracking control scheme based on Takagi–Sugeno (T–S) fuzzy models with unknown parameters. The proposed method can deal with T–S models in a non-canonical form and allows the number of inputs to be less than state variables, which is more practical and has wider applications. The needed matching conditions for state tracking are relaxed by using a T–S fuzzy reference model to generate desired state reference signals. A new fuzzy estimator model is constructed whose states are compared with those of the T–S fuzzy model to generate the estimator state error which is used for the parameter adaptive law. Based on the Lyapunov stability theory, it has been proven that all the signals in the closed-loop system are bounded and the asymptotic state tracking can be achieved. The effectiveness of the proposed scheme is demonstrated through a magnetic suspension system and a transport airplane model.     

Non-fragile quantized H∞ output feedback control for nonlinear systems with quantized inputs and outputs

This paper is concerned with non-fragile $H_{\infty }$ control problems for a class of continuous-time nonlinear systems with unknown nonlinearity and quantized inputs and outputs. The construction of both static output feedback (SOF) and observer-based output feedback (OBOF) control laws in the presence of additive interval-bounded controller coefficient variations can be divided into two parts, linear and nonlinear parts. The linear part plays a role in achieving the $H_{\infty }$ performance, while the nonlinear part is used to reduce the quantization effect. However, it should be pointed out that the effect of input and output quantization can be eliminated fully for SOF case by requiring knowledge of all signs of the states, but only the effect of input quantization can be eliminated for OBOF case. It is worth mentioning that three novel alternative methods with strict linear matrix inequality (LMI) conditions are proposed to design both SOF and OBOF controllers. In particular, these three new methods do not introduce any other auxiliary constraints as many existing results do where a matrix equality constraint between system matrix and Lyapunov matrix is often inserted. Finally, the effectiveness and advantages of the proposed control methods are demonstrated by a numerical example.