Search

The issues of stability and sliding mode control (SMC) for time-varying delay Markov jump systems (MJSs) with structured perturbations constrained by fractional Brownian motion (fBm) are explored. First, constructing a novel Lyapunov–Krasovskii functional (LKF) with exponential terms that contain the double-integral term, the p th moment exponential stability conditions are derived by utilizing the generalized fractional It o ˆ formula and conditional mathematical expectation. Subsequently, by designing the innovative integral sliding mode surface (SMS) associated with time-varying delay and the SMC law, the state trajectories of the dynamic systems can reach the designed SMS within a finite time. Ultimately, the numerical experiment is executed to confirm and ensure the accuracy and reliability of the obtained results. • Markov jump systems with time-varying delay and structured perturbations driven by fractional Brownian motion are studied. • Exponential terms that contain the double-integral term are considered in the Lyapunov–Krasovskii Function. • An innovative integral sliding mode surface associated with time-varying delay is considered. [ABSTRACT FROM AUTHOR]

This paper delves into the problem of asynchronous fault detection filter (AFDF) for Takagi–Sugeno (T–S) fuzzy singular semi-Markovian jump systems (FSSJSs) with multi-cyber-attacks via dynamic event-triggering mechanism (ETM) and double-quantized schemes (DQS). First, a new design structure is devised by integrating the ETM and DQS into a unified framework to effectively alleviate the communication pressure. In particular, the event-triggered threshold (ETT) is dynamically regulated in line with system information, and not only the data from the plant to the filter but also that from the filter to the plant, are both quantized using different logarithmic quantizers. Second, the hybrid cyber-attacks platform is adopted, of which including the random deception attacks (DAs), random replay attacks (RAs) and DoS attack. Third, leveraging the principles of Lyapunov theory, some sufficient conditions are derived to guarantee the exponential admissibility (EA) of the resulting error dynamics and their adherence to a prescribed H ∞ performance index. Through the utilization of several matrix inequalities, the desired filtering gains are given. Finally, the effectiveness of the achieved results is demonstrated by two examples. [ABSTRACT FROM AUTHOR]

This article aims to address the reliable quantized sampled‐data load frequency control (LFC) synthesis problem for semi‐Markov jump interconnected multi‐area power systems (IMAPSs) suffering from incomplete transition rates (TRs) and actuator failures. Primarily, the semi‐Markov process configurated with incomplete TRs is utilized to model the structural and coefficient switchings of IMAPSs, which enables a more precise representation of reality and a wider range of application. Subsequently, in order to reduce the control cost and facilitate data processing, an aperiodic quantization sampling mechanism is introduced. Furthermore, a mode‐dependent and comprehensive actuator faulty model is scheduled to portray various stochastically occurring actuator failures, which is more in line with practical application. Then, by fully utilizing the state information of sampled intervals, a two‐sided looped functional with some matrices that are not required to be strictly positive is constructed to enhance the flexibility. In what follows, on the basis of stochastic analysis technique and looped functional, sufficient conditions with two scenarios are established in the form of linear matrix inequalities (LMIs) to guarantee the stochastic stability with an H∞$$ {H}_{\infty } $$ performance of the resultant semi‐Markov jump IMAPSs. Finally, the effectiveness of the proposed control synthesis methodology is validated through a numerical simulation. [ABSTRACT FROM AUTHOR]

This paper focuses on the issue of dynamic event‐triggered (DET) asynchronous security load frequency control (LFC) for uncertain semi‐Markov jump interconnected multi‐area power systems (IMAPSs). Initially, the semi‐Markov process which in the presence of partially unknown transition rates (TRs) is exactly introduced to model the switching behaviors of the IMAPSs. Subsequently, the DET mechanism is scheduled to alleviate the transmission frequency and guarantee the desired control performance. Furthermore, the probabilistic deception attacks are taken into consideration, which is much more apt for the practical engineering background. Additionally, a hidden Markov model (HMM) is borrowed to depict the modes asynchronous phenomenon between the security controller and the semi‐Markov jump IMAPSs. Afterwards, on the basis of Lyapunov‐Krasovskii functional method and stochastic analysis technique, sufficient conditions with two cases are derived in the form of linear matrix inequalities (LMIs) to guarantee the stochastic stability with an H∞$$ {H}_{\infty } $$ performance of the semi‐Markov jump IMAPSs. Ultimately, a numerical example is exhibited to verify the solvability and practicability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This study addresses the preassigned-time synchronization for complex-valued memristive neural networks with reaction–diffusion terms and Markov parameters. Employing a preassigned-time stable control strategy, two distinct controllers with varying power exponent parameters are designed to ensure that synchronization can be achieved within a predefined time frame. Unlike existing finite/fixed-time results, a priori specification of the settling time is addressed. Furthermore, Green's formula and boundary conditions are efficiently applied to overcome potential symmetry loss. Additionally, the activation function's constraint range is more lenient compared to existing constraints. Finally, the effectiveness of the presented methods are demonstrated through two examples. [ABSTRACT FROM AUTHOR]

Summary: This article concerns the problem of event‐protocol‐based asynchronous fault detection filtering design for discrete‐time fuzzy singular semi‐Markovian jump systems subjected to system parameters uncertainties, unmatched one‐sided Lipschitz nonlinearities and multi‐cyber‐attacks. First, a well‐designed model structure is proposed to integrate two dynamic quantizers and an improved dynamic event‐triggered protocol into a unified framework to reduce the amount of data in the network transmission and rationalize the use of limited network communication bandwidth resources. Especially, the event‐triggering threshold parameter can be continuously adjusted over the time based on the fluctuation of the network signal. Second, a novel triple‐cyber‐attacks platform is established, of which including random deception attacks, random replay attacks and aperiodic DoS attacks. And with help of the extended decoupling strategy and iterative techniques, the co‐design conditions of the stochastic admissibility with a ℘˘ level of ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance are derived for the fault filtering error systems. Finally, two examples are provided to demonstrate the effectiveness and feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on Interval type-2 (IT2) fuzzy dissipative control for Markov jump nonlinear multiagent systems with partially-known transition rate via dynamic event-triggered protocol (ETP) and double-quantized schemes. Firstly, the integration strategy of dynamic ETP and double-quantized law are proposed as effective methods to reduce the communication frequency, where the dynamic threshold parameter is dynamically adjusted rather than remaining constant, and the input and output data of the controller are quantized by different quantizers in order to reduce conservativeness; Secondly, strictly dissipative performance is taken into account, and the nonlinear features are successfully eliminated by applying a distinctive IT2 T-S fuzzy model with imperfect premise matching; Furthermore, via solving the convex optimization problem, the desired fuzzy feedback controller gains are acquired; Eventually, the utility of the suggested algorithm is demonstrated by an example. [ABSTRACT FROM AUTHOR]

Summary: This article is concerned with the issue of finite‐time analysis for fuzzy semi‐Markovian jump systems (S‐MJSs) with multiple disturbances. Takagi–Sugeno fuzzy method is applied to address the nonlinear problem of closed‐loop systems. Unlike the existing research, delay, multiple disturbances, generally uncertain transition rate, uncertain parameters are all analyzed in a unify S‐MJSs framework. The aim of this study is to construct a composite control strategy for stable operation of S‐MJSs with multiple disturbances on the basis of the actual system requirements. For S‐MJSs, conservatism of analysis method and uncertainty of actual system are both the significant problems need to be solved urgently. First, the sufficient condition of S‐MJSs is obtained to guarantee the finite‐time stable performance through mathematical analysis and matrix inequality derivation. Second, disturbance observer based control and H∞$$ {H}_{\infty } $$ control are combined to deal with the effects of multiple disturbances which contain incomplete information disturbance and norm bounded disturbance. Third, fuzzy controller is designed to satisfy close‐loop systems finite‐time performance. Finally, the actual nonlinear example is presented to verify the accuracy of the approach. [ABSTRACT FROM AUTHOR]

This article investigates the problem of adaptive event‐triggered resilient stabilization for nonlinear semi‐Markov jump systems with DoS attacks. In this article, both DoS attacks and event‐triggered transmission strategy (ETTS) are considered. The DoS attacks may disturb the event‐triggered strategy, which implies that the original inequality condition of ETTS will no longer be satisfied. Different from the traditional ETTS, the adaptive ETTS is designed to reduce bandwidth usage. Based on the adaptive ETTS and resilient controller, the sufficient condition for stochastic stability of the closed‐loop system is proposed. Then, the calculation method of controller and observer parameters is given in the form of linear matrix inequality. Finally, the proposed adaptive event‐triggered resilient controller is applied to a single‐link robot arm model, which can show effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article focuses on the issue of nonstationary filtering for uncertain fuzzy Markov switching affine systems (FMSASs) with quantization effects and deception attacks (DAs). The resulting FMSASs are comprised of Markov switching piecewise-affine systems over a set of operating regions. To characterize the multinetwork-induced constraints, the measurement output is quantized before being transmitted, and a compensation scheme is applied to tackle the quantized measurement output loss intermittently. Meanwhile, the randomly occurring DAs are involved, in which the attack behaviors are identified by the bounded stochastic signals. Differently, to deal with the multinetwork-induced constraints, a novel nonstationary region-dependent affine filter strategy is developed. By resorting to a mode-dependent and region-dependent Lyapunov functional and S-procedure theory, sufficient conditions are elicited such that the filtering error system is mean-square exponentially stable. Finally, the practicability of the derived results is verified by a practical tunnel diode circuit model. [ABSTRACT FROM AUTHOR]

In this article, the issue of positive $\mathcal {L}_{1}$ filter design is investigated for positive nonlinear stochastic switching systems subject to the phase-type semi-Markov jump process. Many complicated factors, such as semi-Markov jump parameters, positivity, T–S fuzzy strategy, and external disturbance, are taken into consideration. Practical systems under positivity constraint conditions and unpredictable structural changes are characterized by positive semi-Markov jump systems (S-MJSs). First, by the key properties of the supplementary variable and the plant transformation technique, phase-type S-MJSs are transformed into Markov jump systems (MJSs), which means that, to an extent, these two kinds of stochastic switching systems are mutually represented. Second, with the help of the normalized membership function, the associated nonlinear MJSs are transformed into the local linear MJSs with specific T–S fuzzy rules. Third, by choosing the linear copositive Lyapunov function (LCLF), stochastic stability (SSY) criteria are given for the corresponding system with $\mathcal {L}_{1}$ performance. Some solvability conditions for positive $\mathcal {L}_{1}$ filter are constructed under a linear programming framework. Finally, an epidemiological model illustrates the effectiveness of the theoretical findings. [ABSTRACT FROM AUTHOR]

In this study, an asynchronous H ∞ state feedback controller is devised for Markov jump discrete-time systems (MJDTSs) with time-varying delay. "Asynchronous" means that the system switching mode θ k , the controller mode ϑ k and the quantizer mode λ k are different from each other. The first one is homogeneous and the last two are non-homogeneous. In particular, as a promotion of existing work, we firstly attempt to propose the transition probabilities (TPs) of the three Markov chains (MCs) are not completely known. In addition, the discrete time-varying delay and its infinitely distributed ones are considered. Moreover, according to the Lyapunov stability theory and stochastic process, it is established for the sufficient criterion to ensure the stochastic stability of resulting closed-loop MJDTSs with an H ∞ attenuation performance index. The feasibility and effectiveness of the proposed method are validated by three examples. • It considers unreliable links and mixed time delays. • The system we consider covers asynchronous Markov jump mode knowledge. • The design of asynchronous H ∞ quantized feedback controller is provided. [ABSTRACT FROM AUTHOR]

This article focuses on the finite-time asynchronous output feedback control scheme for a class of Markov jump systems subject to external disturbances and nonlinearities. The conic-type nonlinearities hold a constraint condition which locates in a known hyper-sphere with an indefinite center. In addition, the asynchronization phenomenon occurs between the system and the controller, which can be represented by means of a hidden Markov model. A sufficient condition is derived not only to guarantee the finite-time boundedness of the acquired closed-loop systems but also to possess a desired $H_{\infty }$ performance on the basis of Lyapunov functional technique. Finally, the validity and feasibility of the proposed method are demonstrated with a dc-motor experiment. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the problem of nonfragile H ∞ control for periodic stochastic systems with probabilistic measurement. A novel Lyapunov–Krasovskii functional is formulated, which makes full use of both delay and its change rate. In view of the measurement signal, the mode-dependent stochastic variables are employed and new sufficient conditions are achieved. Finally, two numerical examples are worked out to demonstrate the effectiveness of the proposed control design. Highlights • A novel Lyapunov–Krasovskii functional is designed in which both delay and its change rate are involved. • Some novel criteria for stabilization analysis of periodic stochastic systems are established. • The mode-dependent stochastic variables are introduced. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the stochastic stability and stabilization problems for a class of semi-Markovian jump systems (SMJSs) with time-varying delay, where the time-varying delay τ (t) is assumed to satisfy τ 1 ≤ τ (t) ≤ τ 2. Based on the flexible terminal approach, the time-varying delay τ (t) is first transformed such that τ 1 (t) ≤ τ (t) ≤ τ 2 (t). By utilizing a novel semi-Markovian Lyapunov Krasoviskii functional (SMLKF) and an improved reciprocally convex inequality (RCI), sufficient conditions are established to guarantee a feasible solution. Two illustrated examples are shown the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of event-triggered control for a class of fuzzy Markov jump systems with general switching policies. A novel event-triggered scheme is proposed to improve the transmission efficiency at each sampling instance. Each transition rate allows to be unknown, known, or only its uncertain domains value is known. With the help of a tailored technique to bind the uncertain terms and an asynchronous operation approach to tackle the fuzzy system and fuzzy controller, sufficient conditions for the resulting fuzzy Markovian jump systems are established in terms of coupled linear matrix inequalities. Finally, an example is given to illustrate the validity of the developed technique. [ABSTRACT FROM PUBLISHER]

This study presents a memory-based sliding mode control for singular semi-Markov jump systems using a novel dynamic-memory event-triggered protocol. Based on the average dwell-time strategy, a deterministic switching signal was developed to adjust the variation of the semi-Markov chains. Randomly occurring deception attacks are considered owing to the existence of an adversary. Furthermore, to enhance transmission efficiency and achieve better control performance, a novel dynamic-memory triggering condition is proposed, in which both historical transmitted data and two auxiliary dynamic variables are implemented. Based on the proposed protocol and Lyapunov theory, some parameter-dependent sufficient criteria are established to guarantee mean-square exponential stability and strictly dissipative performance, and the desired memory-based sliding mode controller is designed. Finally, two simulation examples were presented to verify the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative approach for mitigating the effects of deception attacks in Markov jumping systems by developing an adaptive neural network control strategy. To address the challenge of dual-mode monitoring mechanisms, two independent Markov chains are used to describe the state changes of the system and the intermittent actuator. By employing a mapping technique, these individual chains are amalgamated into a unified joint Markov chain. Additionally, to effectively approximate the unbounded false signals injected by deception attacks, an adaptive neural network technique is skillfully built. A mode monitoring scheme is implemented to design an asynchronous control law that links the mode information between the joint Markov chain and controller with fewer modes. The paper derives sufficient criteria for the mean-square bounded stability of the resulting system based on Lyapunov theories. Finally, a numerical experiment is conducted to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper addresses a finite-time H ∞ fuzzy control problem for a class of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions, which is represented as a Takagi–Sugeno (T–S) fuzzy model. A new homogeneous polynomial of partly uncertain transition rates is chosen. Free-matrix-based and double integral forms of the Wirtinger-based integral inequalities are employed to make the proposed approach less conservative. Then sufficient conditions are derived such that the fuzzy nonlinear Makovian jump delayed system exhibits stochastic finite-time boundedness. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methodology. [ABSTRACT FROM AUTHOR]

The problem of event-triggered reliable control for fuzzy Markovian jump system (FMJS) with mismatched membership functions (MMFs) is addressed. Based on the mode-dependent reliable control and event-triggered communication scheme, the stability conditions and control design procedure are formulated. More precisely, a general actuator-failure is designed such that the FMJS is reliable in the sense of stochastically stable and reduce the utilization of network resources. Furthermore, the improved MMFs are introduced to reduce the conservativeness of obtained results. Finally, simulation results indicate the effectiveness of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of finite-time event-triggered H ∞ boundedness for network-based Markovian jump nonlinear system. An improved model is introduced in terms of network-induced delay. By synthesizing the newly event-triggering conditions, the finite-time H ∞ boundedness for networked Markovian jump nonlinear systems are guaranteed. At last, a numerical example is given to illustrate the effectiveness of proposed theoretical results. [ABSTRACT FROM AUTHOR]

This work studies the problem of finite-time stochastic boundedness of discrete-time Markovian jump neural networks with boundary transition probabilities and randomly varying nonlinearities. The partly unknown and uncertain transition probabilities (TPs) are included in the paper, and more general nonlinearities are introduced with both upper and lower bounds due to the nature of its probability information. By employing the free-weighting matrix technique, finite-time stability theory and boundary incomplete TPs, the solvability sufficient conditions of finite-time stochastic boundedness are given. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The issue of finite-time H∞ filtering for singular stochastic Markovian jump systems with time-varying delays is concerned in this paper. H∞ filtering is designed for underlying closed-loop singular Markovian jump system and system state does not exceed a given bound over some finite-time interval. Considering the full information of underlying Markov process, sufficient conditions are obtained to guarantee that the described system is finite-time stability and H∞ filtering finite-time boundedness. By establishing the results of stochastic character and finite-time boundedness, the closed-loop singular Markovian jump system trajectory stays within the given bound. At last, a numerical example is supplied to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the reduced-order filter design method for fuzzy Markov jump affine systems with dynamic event-triggered protocol and uncertain packet dropouts. Aiming at approximating the nonlinearities with high accuracy and broadening practical application, the fuzzy Markov jump affine systems associated with mode-dependent operating regions are developed. A novel nonhomogeneous Markov process is proposed to describe the generalized stochastic jumping among subsystems, whose time-varying transition probabilities are orchestrated by a higher-level deterministic switching signal. Compared with the conventional Markov process with arbitrary switchings, the average dwell-time strategy is adopted in the novel nonhomogeneous Markov process to improve the dynamic performance. A dynamic event-triggered protocol is provided to alleviate the network transmission burden by elongating the interval between any two consecutive events. Based on the variation of state-space partitions, nonsynchronous reduced-order generalized filters are considered. Under this framework, sufficient criteria are attained to ensure stochastic stability and prescribed l 2 − l ∞ performance for the filtering error systems. Eventually, the theoretical findings are verified by two simulation examples. [ABSTRACT FROM AUTHOR]

SUMMARY: This paper is concerned with the problem of finite‐time H ∞  filtering for a class of Markovian jump systems subject to partial information on the transition probabilities. By introducing some slack matrix variables in terms of probability identity, a less conservative bounded real lemma is derived to ensure that filtering Markovian jump systems is finite‐time stable. Finally, the existence criterion of the desired filter is obtained such that the corresponding filtering error system is finite‐time bounded with a guaranteed H ∞  performance index. An example is given to illustrate the efficiency of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a novel method is developed for the finite-time boundedness of Markovian jumping neural networks with time-varying delays. By introducing a newly augmented stochastic Lyapunov-Krasovskii functional and novel activation function conditions, sufficient condition for Markovian jumping neural networks is presented, and the state trajectory remains in a bounded region over a pre-specified finite-time interval. Finally, numerical examples are given to illustrate the efficiency and less conservative of the proposed method. [ABSTRACT FROM AUTHOR]

The problem of H ∞ filtering for a class of discrete-time singular Markovian jump systems with time-varying delays is investigated in this paper. The transition probabilities under consideration are time-varying, i.e., Markovian chain is nonhomogeneous. By using the Lyapunov functional approach and reciprocally convex technique, a less conservative delay-dependent bounded real lemma is developed in terms of linear matrix inequalities. Moreover, a sufficient condition for the existence of the desired filter which guarantees the stochastic admissibility and the H ∞ performance index of the resulting filtering error system is presented. Numerical examples are employed to show the usefulness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of finite-time boundedness of a class of discrete-time Markovian jump systems with piecewise-constant transition probabilities subject to average dwell time switching. Another set of useful regime-switching models has been given for both fixed transition probability Markov switching models and time-varying transition probabilities. Based on the knowledge of average dwell time and multiple Lyapunov function, a novel sufficient condition for finite-time boundedness of H∞ filtering is derived and the system trajectory stays within a prescribed bound. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: An extension of fixed transition probability Markovian switching model to combine time-varying transition probabilities has offered another set of useful regime-switching models. This paper investigated the problem of finite-time filtering for a class of discrete-time Markovian jump systems with switching transition probabilities subject to average dwell time switching. Based on the results of finite-time boundness and average dwell time, a novel sufficient condition for finite-time bounded of filtering is derived and the system trajectory stays within a prescribed bound. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed method. [Copyright &y& Elsevier]

This paper addresses the problems of finite-time stochastic stability and stabilization for linear Markovian jump systems subject to partial information on the transition probabilities. By introducing bounded finite time and stochastic character, sufficient conditions that can ensure bounded finite time and H∞ finite-time bounded filtering are derived. Finally, an example is given to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with the problem of finite-time control for a class of Markovian jump systems with mode-dependent time-varying delays via new Lyapunov functionals. In order to reduce conservatism, a new Lyapunov–Krasovskii functional is constructed. Based on the derived condition, the reliable control problem is solved, and the system trajectory stays within a prescribed bound during a specified time interval. Finally, numerical examples are given to demonstrate the proposed approach is more effective than some existing ones. [Copyright &y& Elsevier]

• A more general hidden semi-Markov model is expected. • A novel mode-dependent memory-based event-triggered mechanism is proposed. • A memory asynchronous control strategy is skillfully synthesized. In this paper, the asynchronous control problem is addressed for semi-Markov switching systems with a memory-based event-triggered mechanism. In light of the asynchronous phenomenon between the resulting dynamic modes and the memory controller modes, a more general hidden semi-Markov model is expected. Notably, aiming at decrease the triggering intervals while improving the dynamic performance, a novel mode-dependent memory-based event-triggered mechanism is proposed, whose triggering condition varies with some historic released data. By virtue of the hidden semi-Markov model and historic released data, a memory asynchronous control strategy is skillfully synthesized. By resorting to Lyapunov theory, some criteria are formulated to guarantee the stochastically stable of the resulting dynamic. Eventually, the feasibility of the presented approach is verified by a practical example. [ABSTRACT FROM AUTHOR]

This paper addresses the asynchronous control problem for semi-Markov reaction–diffusion neural networks (SMRDNNs) under probabilistic event-triggered protocol (PETP) scheduling. A semi-Markov process with a deterministic switching rule is introduced to characterize the stochastic behavior of these networks, effectively mitigating the impacts of arbitrary switching. Leveraging statistical data on communication-induced delays, a novel PETP is proposed that adjusts transmission frequencies through a probabilistic delay division method. The dynamic adjustment of event trigger conditions based on real-time neural network is realized, and the responsiveness of the system is enhanced, which is of great significance for improving the performance and reliability of the communication system. Additionally, a dynamic asynchronous model is introduced that more accurately captures the variations between system modes and controller modes in the network environment. Ultimately, the efficacy and superiority of the developed strategies are validated through a simulation example. [ABSTRACT FROM AUTHOR]

This paper considers the problem of the simultaneous finite-time event-triggered control and fault detection for a class of continuous-time singular Markovian jump mixed delay systems (SMJDSs) under asynchronous switching. In order to develop the control and detection objectives, the mode-dependent fault detection filters and dynamic feedback event-triggered-based controllers are designed and the switching signal between the detector/controller unit and subsystems is assumed to be asynchronous. Based on average dwell time (ADT) techniques, some new sufficient conditions for the existence of fault detection/controller unit are presented in the framework of linear matrix inequalities (LMIs) to ensure the control system has singular stochastic finite-time stability (SSFTS). Finally, a numerical example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The problem of asynchronous sliding mode control (SMC) for discrete nonlinear semi-Markov jump models is investigated by the semi-Markov kernel strategy, where asynchronous mechanism means that there is a one-step delay in the controller mode switching related to the system mode. Unlike traditional T-S fuzzy model, the interval type-2 fuzzy model is applied to represent discrete semi-Markov jump systems with uncertain parameters. The main novelty is to design a suitable asynchronous SMC mechanism for the attainment of the quasi-sliding mode, overcoming the difficulty caused by parameter uncertainties. According to the fuzzy Lyapunov function related to the elapsed time and the current mode, the stability criterion of nonlinear model is developed by additional matrix variables, realizing the σ -error mean-square stability of the underlying augmented system. An appropriate fuzzy asynchronous SMC mechanism is established to achieve the accessibility of the quasi-sliding mode. Finally, a tunnel diode circuit model validates the proposed control algorithm. [ABSTRACT FROM AUTHOR]