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This paper investigates the problem of disturbance attenuation and rejection for a class of switched nonlinear systems subject to input and sensor saturations, in which exosystem generated disturbances and H2-norm bounded disturbances are considered. The full-order and reduced-order observers are designed according to whether the system states are available or not. Based on the estimating values of the system states and exosystem generated disturbances, the design schemes for the composite controllers are put forward based on the full-order and reduced-order observers, respectively. For a switched system, the input and sensor saturations would influence the effective synthesis of observer and controller. By sector nonlinearity technology, the stability of the augmented closed-loop systems under the proposed composite controllers are analyzed, and the conditions of synthesis of the observers and controllers are further presented to ensure the augmented systems to be robustly asymptotically stable with a weighted H∞ performance level. An example is given to guarantee the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of static anti-windup design for uncertain continuous-time Markovian jump systems with partially unknown transition rates in the face of actuator saturation. The underlying system is subject to time-varying and norm-bounded parameter uncertainties in both the state and input matrices. It is assumed that a set of stabilizing dynamic output-feedback controllers have been designed for the system in the absence of control saturation. The objective is to design anti-windup compensation gains for the given controllers such that the system can still be stabilized, irrespective of whether actuator saturation appears or not. To obtain a maximum estimation of the domain of attraction of the resulting closed-loop system, a convex optimization problem in the linear matrix inequality framework is formulated. Furthermore, the results are extended to the cases of the systems with completely known transition rates and with completely unknown transition rates. Finally, the usefulness of the developed method is demonstrated through simulation examples. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of the disturbance observer based control for a class of continuous-time uncertain systems subject to input saturation and nonlinearity. The input of the system includes two parts, the control input and the disturbance input. The nonlinearity of the system, which satisfies a global Lipschitz condition, is considered as two cases of known nonlinearity and unknown nonlinearity. By virtue of the technique of the disturbance observer based controller, the anti-disturbance controllers are designed respectively with both the polytopic and dead-zone representations of the saturation function, which ensure that the resulting closed-loop systems are asymptotically stable with an estimation of the domain of attraction described by the level set of the Lyapunov function. Further, an iterative optimization method is used to obtain the maximum estimation of the domain of the set of initial states. An example of application design for a flight control system illustrates the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper carries out a study on the design of anti-windup gains for uncertain discrete-time Markovian jump systems subject to both actuator saturation and partially known transition probabilities. The parameter uncertainties appearing in both the state and input matrices are assumed to be time-varying and norm-bounded. Under the assumption that a set of linear dynamic output feedback controllers have been designed to stabilise the Markovian jump system in the absence of actuator saturation, anti-windup compensation gains are designed for maximising the domain of attraction of the closed-loop system with actuator saturation. Then, by solving a convex optimisation problem with constraints of a set of linear matrix inequalities, the anti-windup compensation gains are obtained. A simulation example is provided to illustrate the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of non-fragile and mode-dependent $$H_{\infty }$$ filter design for a class of nonlinear stochastic Markovian jump systems with mode-dependent time-varying delays and norm-bounded parameter uncertainties. The non-fragile and mode-dependent filter to be designed is assumed to include multiplicative gain variations which result from inaccuracies in filter implementation, and the desired filter ensures the filtering error system is not only exponentially mean-square stable, but also satisfies a prescribed $$H_{\infty }$$ -norm level for all admissible uncertainties. A stochastic Lyapunov-Krasovskii function is proposed to reflect the information of Markovian jump modes and the mode-dependent time-varying delays, and a set of strict linear matrix inequalities are utilized to derive sufficient conditions that guarantee the desired filter can be constructed. A numerical example and a vertical take-off and landing (VTOL) helicopter system are utilized to illustrate the effectiveness and usefulness of the main results obtained. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of robust stabilization for uncertain switched non-linear systems subject to actuator saturation and time-varying norm-bounded parameter uncertainties. Centred on the problem, a survey on both continuous and discrete-time domains has been made. The non-linearities in the state equations meet with the global Lipschitz conditions. In this paper, we are trying to work out a design of state feedback controllers and a state-dependent switching law so as to make the resulting closed-loop system robustly asymptotically stable at the origin with a large domain of attraction. Using the multiple Lyapunov functions method, some sufficient conditions for robust stabilization are derived. Furthermore, a group of static feedback controllers and a state-dependent switching law are designed, respectively, with an estimation of domain of attraction by solving a optimization problem, which are based on the solutions of certain linear matrix inequalities. Finally, a simulation example is presented to illustrate the effectiveness of the proposed results. [ABSTRACT FROM PUBLISHER]

This paper studies the problems of the finite‐time stochastic boundedness (FTSB) and stabilisation for a class of discrete‐time Markovian jump non‐linear quadratic systems with incomplete information on transition probabilities. It is shown that the FTSB of the system can be ensured under some sufficient conditions derived. As a corollary, some sufficient conditions of the finite‐time stochastic stability for the non‐linear quadratic systems without exogenous disturbance are also established. Based on these results, stabilising mode‐dependent state feedback controllers are designed for Markovian jump non‐linear quadratic systems with/without exogenous disturbance, respectively. Consequently, the finite‐time stochastic stabilisation problem is resolved. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed theory. [ABSTRACT FROM AUTHOR]

In this work, the problem of passivity-based synchronization for coupled chaotic neural networks with randomly occurring time delays is addressed. The topology switching of the networks is subject to the semi-Markov process. Some Bernoulli random variables are used to simulate the randomly occurring phenomena of the aforesaid networks. Furthermore, the main objective is to develop the synchronization criteria such that the considered networks can achieve global stochastic synchronization and conform to the passive performance index. Subsequently, by using some relatively advantageous inequalities and reasonable matrix transformation techniques, some available synchronization criteria are derived. Ultimately, an example is presented to illustrate the applicability and availability of the method proposed. [ABSTRACT FROM AUTHOR]

This work investigates the dissipativity and stability analysis problems for Markov jump generalized neural networks subject to time-varying interval delays. The aim of the present study is to determine whether the new dissipativity and stability criteria with less conservatism could be established for Markov jump generalized delayed neural networks or not. In this connection, a more general dissipative property index inequality is firstly introduced. On basis of fully considering mode-dependent matrices in the Lyapunov–Krasovskii functional, some advantageous negative terms ignored in some existing works are taken into account. By employing some novel integral inequalities and stochastic analysis theory, some available less conservative criteria are developed. Three compared examples are finally shown to explain the reduced conservatism and superiority of the presented criteria for Markov jump generalized delayed neural networks. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of dissipative filtering for a class of nonlinear singular Markovian Jump systems (SMJSs) with time-varying delays. Our consideration is centered on the design of a mixed filter that can contain both mode-dependent and mode-independent filters in a unified framework. By using a delay-decomposition approach and constructing a mode-dependent stochastic Lyapunov–Krasovskii functional, sufficient delay-dependent conditions are derived in terms of linear matrix inequalities, which guarantee the considered nonlinear SMJSs to be stochastically admissible with a dissipativity performance γ . Based on the conditions, the existence conditions and parameters of the desired filter are obtained. Two numerical examples are given to illustrate the reduced conservatism and the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of quantized output feedback control for uncertain discrete-time systems with input saturation. Input quantization case and output quantization case are studied, respectively. The purpose of the study was to design of dynamic output feedback controllers such that all the trajectories of the closed-loop system converge to a small ellipsoid for every initial condition starting from large admissible domain. By solving the optimization problem, the corresponding domains can be obtained. Finally, two simulation examples are provided to demonstrate the applicability of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of adaptive neural control for a class of strict-feedback stochastic nonlinear systems with multiple time-varying delays, which is subject to input saturation. Via the backstepping technique and the minimal learning parameters algorithm, the problem is solved. Based on the Razumikhin lemma and neural networks' approximation capability, a new adaptive neural control scheme is developed. The proposed control scheme can ensure that the error variables are semi-globally uniformly ultimately bounded in the sense of four-moment, while all the signals in the closed-loop system are bounded in probability. Two simulation examples are provided to demonstrate the effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

Summary: In this article, the adaptive tracking control problem is considered for a class of uncertain nonlinear systems with input delay and saturation. To compensate for the effect of the input delay and saturation, a compensation system is designed. Radial basis function neural networks are directly utilized to approximate the unknown nonlinear functions. With the aid of the backstepping method, novel adaptive neural network tracking controllers are developed, which can guarantee all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the system output can track the desired signal with a small tracking error. In the end, a simulation example is given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract For complex dynamic networks subject to switching topologies, an H ∞ event-triggered control scheme is developed to deal with the finite-time synchronization problem. A semi-Markov process is employed to govern the switching of the networks topologies. The purpose focuses on designing a controller via the event-triggered scheme, which guarantees that the resulting error networks are finite-time bounded with a prescribed level of the H ∞ performance. By utilizing the stochastic analysis theory and finite-time synchronization concept, some sufficient conditions are deduced to determine whether the desired controller will exist or not for the complex dynamic networks. Eventually, an illustrated example is proposed to explain the validity and practicability of this method. [ABSTRACT FROM AUTHOR]

Abstract In this work, a kind of switched gene regulatory networks with packet dropout and uncertainties are constructed by switched coupled nonlinear difference equations. In comparison, a more comprehensive switching regulation, persistent dwell-time, is employed to it. The aim is to construct a mixed mode-dependent and mode-independent estimator for the before-mentioned gene regulatory networks with a view to the loss of system modal information. Thereafter, the augmented system is established. After that, the sufficient conditions of the exponential stability and mixed H ∞ / l 2 − l ∞ performance for the augmented system are deduced by the switching Lyapunov theory. Finally, a numerical example is employed to elucidate the validity of the estimator gains decoupled by the congruent transformation. [ABSTRACT FROM AUTHOR]

The saturation input control problem of discrete-time networked systems via adaptive event-triggered communication scheme is discussed in this paper. The criteria are derived by utilising a new Lyapunov functional to guarantee that the considered networked system with randomly occurring infinite distributed delays, random packet losses and sensor saturation is exponentially stable in mean square sense. A novel adaptive event-triggered law is proposed, which is dependent on the exponentially stable index α. The effectiveness of our proposed method is illustrated by both theoretical analysis and numerical simulations. [ABSTRACT FROM AUTHOR]

The estimate of Mittag-Leffler function has been widely applied in the dynamic analysis of fractional-order systems in some recently published papers. In this paper, we show that the estimate for Mittag-Leffler function is not correct. First, we point out the mistakes made in the estimation process of Mittag-Leffler function and provide a counterexample. Then, we propose some sufficient conditions to guarantee that part of the estimate for Mittag-Leffler function is correct. Meanwhile, numerical examples are given to illustrate the validity of the two newly established estimates. [ABSTRACT FROM AUTHOR]

This paper deals with stability analysis and control synthesis for positive semi-Markov jump systems (S-MJSs) with time-varying delay, in which the stochastic semi-Markov process related to nonexponential distribution is considered. The main motivation for this paper is that the positive condition sometimes needs to be considered in S-MJSs and the controller design methods in the existing have some conservation. To deal with these problems, the weak infinitesimal operator is firstly derived from the point of view of probability distribution under the constraint of positive condition. Then, some sufficient conditions for stochastic stability of positive S-MJSs are established by implying the linear Lyapunov–Krasovskii functional depending on the bound of time-varying delay. Furthermore, an improved stabilizing controller is designed via decomposing the controller gain matrix such that the resulting closed-loop system is positive and stochastically stable in standard linear programming. The advantages of the new framework lie in the following facts: (1) the weak infinitesimal operator is derived for S-MJSs with time-varying delay under the constraint of positive condition and (2) the less conservative stabilizing controller is designed to achieve the desired control performance. Finally, three examples, one of which is the virus mutation treatment model, are given to demonstrate the validity of the main results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of reachable set estimation for a class of uncertain singular systems with time-varying delays from a new point of view. Our consideration is centered on the design of a proportional-derivative state feedback controller (PDSFC) such that the considered singular system is robustly normalizable and all the states of the closed-loop system can be contained by a bounded set under zero initial conditions. First, a nominal singular time-delay system is considered and sufficient conditions are obtained in terms of matrix inequalities for the existence of a PDSFC and an ellipsoid. In this case, the considered system is guaranteed to be normalizable and the reachable set of the closed-loop systems is contained by the ellipsoid. Then, the result is extended to the case of singular time-delay systems with polytopic uncertainties and relaxed conditions are derived by introducing some weighting matrix variables. Furthermore, based on the obtained results, the reachable set of the considered closed-loop singular system can be contained in a prescribed ellipsoid. Finally, the effectiveness of our results are demonstrated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of controller design for time-delay system with stochastic disturbance and actuator saturation. By use of more appropriate Lyapunov–Krasovskii functional (LKF) and a new criterion for the domain of attraction, less conservative conditions for stochastic stability are proposed. Then, the difficulties of the domain of attraction confronted in system analysis and synthesis can be overcome. These sufficient conditions are derived in terms of linear matrix inequality (LMI). Finally, two practical examples demonstrate the validity of the given results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the adaptive finite-time flocking problem for a class of second-order nonlinear multi-agent systems with parameter uncertainties. The states of all agents can achieve finite-time consensus by using the proposed control algorithm under an undirected graph. It is shown that connectivity preservation is guaranteed by choosing an appropriate Lyapunov potential function. A numerical example is presented to illustrate the effectiveness of the proposed consensus protocol. [ABSTRACT FROM AUTHOR]

• A novel distributed filtering compensation algorithm is presented in terms of the available transmitted data. • The expression form of minimized upper bound of filtering error covariance matrix and the desired filter gain are established. • The filtering algorithm performances are analyzed by providing the theoretical proofs regarding the boundedness. This paper investigates the distributed filtering (DF) issue for a class of time-varying state-saturated systems with packet disorders (PDs) via the event-triggered communication mechanism (ETCM). The random transmission delays, which can be characterized by a set of random variables obeying certain probability distribution, cause the phenomenon of PDs. In addition, for the sake of decreasing the consumption of network resources, the ETCM is used to arrange the data transmission. On the basis of the measurable data information, a novel distributed filter is constructed that can ensure the existence of the upper bound matrix (UBM) regarding the filtering error (FE) covariance and then the trace of the presented UBM is minimized via constructing the suitable filter gain. Afterwards, the boundedness analysis of FE dynamics is provided to evaluate the filtering algorithm performance. Finally, the validity of the designed DF scheme is illustrated through a numerical experiment. [ABSTRACT FROM AUTHOR]

This paper deals with the decentralised output feedback stabilisation problem for a class of large-scale stochastic time-delay nonlinear systems. A general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time-delay systems. In addition, a stochastic version of the well-known LaSalle-Yoshizawa theorem with time-varying delay is initially proposed for the controller design and stability analysis. Then, for a class of large-scale stochastic systems with time-varying delays, totally decentralised adaptive delay-dependent controllers are designed by using K-filter and backstepping approach. Via LaSalle-Yoshizawa-type theorem and constructing a general Lyapunov function, it is shown that all signals in the closed-loop system are bounded almost surely and the solution is almost surely asymptotically stable. Finally, a simulation example is given to illustrate the effectiveness of the results of this paper. [ABSTRACT FROM AUTHOR]

H ∞ finite-time control for uncertain system with the unmeasurable state via the sliding mode control (SMC) approach is discussed in this article. Our attention is to design an appropriate finite-time SMC law to attenuate the influences of parametrical uncertainty and external disturbance. First, an appropriate non-fragile observer-based finite-time SMC law is designed such that the state trajectories can arrive at the specified sliding surface during the finite-time interval. Then, finite-time boundedness (FTBs) is well implemented by partitioning strategy and sufficient conditions are given to realize FTBs for the augment system with H ∞ performance. Next, the controller gain and observer gain are obtained by solving the corresponding linear matrix inequalities (LMIs). Finally, a RLC series circuit shows the effectiveness of the proposed SMC approach. [ABSTRACT FROM AUTHOR]

This paper investigates the issue of robust stabilization for delayed semi-Markov jump T-S fuzzy systems via sliding mode control (SMC). In order to reduce some conservativeness, an integral sliding mode surface (ISMS) is designed without assumption that the input matrices are plat-rule independent with full column rank, which is one of the critical factors for system performance. Based on Lyapunov functional theory, sufficient condition is provided for stochastic stability of the closed-loop system, and then extended to the case where the input matrices are independent of plant-rule. In addition, a fuzzy SMC controller is established to guarantee the finite time reachability of the predetermined fuzzy manifold. Finally, the superiorities of the proposed method are validated by a single-link robot arm model. [ABSTRACT FROM AUTHOR]

Exponential mean-square stability for delayed switched systems with Markov jump parameters and generally incomplete transition rates is discussed. The switching dynamics among the operation modes are considered to be governed by a high level with average dwell time switching (ADTS) and a low level with stochastic Markov switching. Many practical systems such as general economic model subject to unpredictable structural changes can be described by switching Markov jump systems (SMJSs) with generally incomplete transition rates. By resorting to average dwell time switching approach, sufficient conditions are proposed to ensure the underlying system exponentially mean-square stable. Finally, the theoretical results are applied to a general economic model to demonstrate the effectiveness, applicability and superiority of the main results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of disturbance-observer-based control (DOBC) for semi-Markovian jump systems (S-MJSs) with generally uncertain transition rate (TR) and saturation nonlinearity. Unlike the existing theories, the proposed method considers the external disturbance and saturation nonlinearity in S-MJSs with more general TR. First of all, to study this DOBC problem, the sufficient condition for stochastic stability of the system is derived by the use of Lyapunov–Krasovskii functional. Then, the design methods of the anti-disturbance controller and the disturbance observer are proposed based on the given stability condition of the closed-loop system. Furthermore, the maximum domain of attraction is estimated by solving an optimization iterative algorithm. Finally, two numerical examples are given to prove the correctness of the proposed results. [ABSTRACT FROM AUTHOR]