Search Results (44)

This paper investigates the asynchronous non-fragile $H_{\infty }$ control problem for a class of Markovian jump singularly perturbed systems (MJSPSs) with time-varying delays. By applying a multi-layer structure method, a non-fragile controller with time delay is designed for the MJSPSs to adapt to disturbances caused by nonstationary quantization and DoS attacks. To model the asynchronous dynamics between the system and the controller mode, an independent Markov chain is employed to capture the asynchronous quantization and control behavior. By constructing mode-dependent Lyapunov–Krasovskii functions, sufficient conditions are derived to ensure stochastic finite-time exponential stability and $H_{\infty }$ performance under conditions of delay, singular disturbances, and quantization uncertainty. The effectiveness of the method is validated using an inverted pendulum system controlled by a DC motor, demonstrating its ability to achieve robust stability and performance in bandwidth-constrained network environments. Full article

The integration of blockchain technology into Cyber–Physical Systems (CPS) offers decentralized resilience against data manipulation. This also introduces stochastic consensus latencies that threaten real-time control stability. We present a Stochastic-Aware Blockchain Predictive Control (SAB-PC) framework, which models blockchain-induced jitter as a state-dependent Markovian process, and embeds it within a Markovian Jump Linear System (MJLS) formulation. Using mode-dependent Linear Matrix Inequalities (LMIs), we derive Mean Square Stability (MSS) conditions, which capture the interaction between decentralized consensus dynamics and closed-loop control behavior. The framework is validated on the Tennessee Eastman Process (TEP) benchmark, using a calibrated stochastic delay model that reflects realistic blockchain congestion patterns. Our results show that standard blockchain-mediated control architectures become unstable under Practical Byzantine Fault Tolerance (PBFT)-induced quadratic latency growth, whereas SAB-PC maintains stable operation across decentralized networks up to 60 validator nodes. The predictive Safety Runway effectively masks long-tail delay distributions, ensuring real-time feasibility and preserving safe Reactor Pressure trajectories. Under coordinated False Data Injection (FDI) attacks, SAB-PC limits pressure deviations to only 1.2 kPa despite an 8.0 kPa adversarial bias, demonstrating cryptographic and control-theoretic resilience. Full article

We study a hybrid stochastic SIS co-infection model for two primary strains and a co-infected class with Crowley–Martin incidence, Markovian regime switching, and Lévy jumps. The model is a four-dimensional regime-switching Lévy-driven SDE system with state-dependent diffusion and jump coefficients. Under natural integrability conditions on the jumps and a mild structural assumption on removal rates, we prove uniform high-order moment bounds for the total population, establish pathwise sublinear growth, and derive strong laws of large numbers for all Brownian and Lévy martingales, reducing the long-time analysis to deterministic time averages. Using logarithmic Lyapunov functionals for the infective classes, we introduce four noise-corrected effective growth parameters ${\lambda }_1,\dots ,{\lambda }_4$ and two interaction matrices $A,B$ that encode the combined impact of Crowley–Martin saturation, regime switching, and jump noise. In terms of explicit inequalities involving ${\lambda }_k$ and the entries of $A,B$, we obtain sharp almost-sure criteria for extinction of all infectives, persistence with competitive exclusion, and coexistence in mean of both primary strains, together with the induced long-term behaviour of the co-infected class. Numerical simulations with regime switching and compensated Poisson jumps illustrate and support these thresholds. This provides, to our knowledge, the first rigorous extinction-exclusion-coexistence theory for a multi-strain SIS co-infection model under the joint influence of Crowley–Martin incidence, Markov switching, and Lévy perturbations. Full article

This paper focuses on the issues of tracking controller enhancement, input delay rectification, and disturbance elimination for dynamical systems characterized as fractional-order semi-Markovian jump processes. In particular, the design of the modified repetitive control technique integrated with the filtered Smith predictor scheme based on the Majhi–Atherton approach guarantees exact tracking performance and disturbance elimination. To be more specific, the active rectification of both external disturbances and delays is safeguarded by the construction of a modified proportional derivative-based active disturbance estimator along with the traditional Smith predictor framework. Also, the modified repetitive control in this framework is able to track the reference signals with multiple periodicities. In accordance with the Lyapunov stability criterion, a group of applicable principles is produced in the structure of matrix inequality constraints. Furthermore, the parameters of the controller block are designed concurrently by way of elucidating the stated matrix inequality constraints. Finally, the simulation results and the comparison analysis between the developed control technique and existing works such as equivalent input disturbance and the truncated predictor feedback control method validate the advantage of the recommended control framework. Full article

This study focuses on analyzing the almost sure exponential stability of the split-step $\theta$-method ($SS\theta$-method) when applied to stochastic pantograph differential equations characterized by Markovian switching and jump processes. Initially, we establish the almost sure exponential stability of the system’s trivial solution. Subsequently, under an additional sufficient condition, it is demonstrated that the discrete solutions generated by the $SS\theta$-method also exhibit this stability property. Finally, a computational experiment is conducted to support the theoretical results. Full article

Robust stability/stabilization for discrete-time time-varying Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations is addressed in this paper. Using a scaling technique, we succeed in effectively addressing the multi-perturbations case. We obtain an estimation of the lower bound of the stability radius in terms of the unique bounded and positive semidefinite solutions of adequately defined parameterized backward Lyapunov difference equations. In the time-invariant case, we show that such a lower bound is actually the exact value of the stability radius. Using the obtained result, we effectively address the state-feedback robust stabilization problem. Full article

This paper addresses the problem of extended dissipativity analysis for uncertain neutral-type semi-Markovian jump systems. Two novel parameter-dependent, free-matrix-based integral inequalities are proposed by introducing some adjustable parameters, from which some existing integral inequalities can be covered, such as traditional free-matrix-based integral inequalities and Wirtinger-based integral inequalities. A significant advancement lies in the incomplete slack matrices, with some zero components in these inequalities removed, leading to fully coupled system information. An innovative condition for extended dissipativity is derived, specifically tailored to the systems under investigation and based on the newly formulated inequalities. To demonstrate the efficacy and superiority of the methodologies, two numerical examples are meticulously provided. Full article

This paper aims to find optimal feedback policies for the tracking control of Markovian jump Boolean control networks (MJBCNs) over a finite horizon. The tracking objective is a predetermined time-varying trajectory with a finite length. To minimize the expected total tracking error between the output trajectory of MJBCN and the reference trajectory, an algorithm is proposed to determine the optimal policy for the system. Furthermore, considering the penalty for control input changes, a new objective function is obtained by weighted summing the total tracking error with the total variation of control input. Certain optimal policies sre designed using an algorithm to minimize the expectation of the new objective function. Finally, the methodology is applied to two simplified biological models to demonstrate its effectiveness. Full article

Driven by the rapid development of modern industrial applications, multi-agent systems (MASs), integrating computational and physical resources, have become increasingly important in recent years. However, the performance of MASs can be easily compromised by malicious false data injection attacks (FDIAs) due to the inherent vulnerability of the cyber layer. This work focuses on an event-triggered framework for secure reconstruction and consensus control in MASs subject to both sensor and actuator attacks. First, we introduce a class of Takagi–Sugeno fuzzy multi-agent systems that relax the traditional Lipschitz condition and incorporate realistic system dynamics by considering parameter variations governed by Markovian jump principles. Second, an adaptive fuzzy estimator is developed for the simultaneous reconstruction of states and attacks in MASs. The derived estimates are utilized to design an attack-resilient consensus control strategy that compensates for the effects of FDIAs on the closed-loop consensus error dynamics. Meanwhile, the sufficient conditions for the convergence of both estimation and consensus errors are presented and rigorously proved. Finally, evaluation results on an experimental platform through multiple truck-trailer systems are provided to demonstrate the effectiveness and performance of the proposed approach. Full article

In modern industrial applications, production quality, system performance, process reliability, and safety have received considerable attention. This article proposes a dynamic event-triggered attack estimator for Markovian jump stochastic systems susceptible to actuator deception attacks. Utilizing the developed estimator, the presented attack-tolerant control strategy can tolerate the effects of such attacks and ensure the mean-square convergence of the overall closed-loop system. A dynamic event-triggered mechanism is implemented on the sensor side to optimize communication efficiency. To address the potential threat of deception attacks, a plug-and-play (PnP) secure monitoring and control architecture is introduced. This architecture facilitates the seamless integration of the designed attack-tolerant controller with the nominal feedback controller, thereby enhancing system security without requiring significant modifications to the existing control structure. The practicality and effectiveness of the proposed approaches are demonstrated through experimental results on a switched boost converter circuit. Full article

This paper studies the output feedback $H\infty$ control problem of event-triggered Markov-type networked control systems. Firstly, a new Lyapunov–Krasovskii functional is constructed, which contains an event-triggered scheme, Markovian jump system, and quantified information. Secondly, the upper bound of the weak infinitesimal generation operator of the Lyapunov–Krasovskii function is estimated by combining Wirtinger’s-based integral inequality and reciprocally convex inequality. Finally, based on the Lyapunov stability theory, the closed-loop stability criterion of event-triggered Markov-type networked control systems and the design method of the output feedback $H\infty$ controller for the disturbance attenuation level $\gamma$ are given in the terms of linear matrix inequalities. The effectiveness and superiority of the proposed method are verified using three numerical examples. Full article

This paper concentrates on the finite-time $H_{\infty }$ control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT) $H_{\infty }$ state feedback controller and an SFT $H_{\infty }$ observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov–Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT $H_{\infty }$ boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes. Full article

This study addresses the problem of strictly dissipative stabilization for continuous-time Markovian jump systems (MJSs) with external disturbances and generally uncertain transition rates that contain completely unknown transition rates and their bound values. A stabilization condition is obtained to guarantee strict dissipativity for the MJSs with partial knowledge in terms of the transition rates. To reduce the conservativity of the proposed condition, we used a boundary condition related to the bounds of the transition rate with slack variables. Finally, two simulation results are presented to describe the feasibility of the proposed controller. Full article

Random terms in many natural and social science systems have distinct Markovian characteristics, such as Markov jump-taking values in a finite or countable set, and Wiener process-taking values in a continuous set. In general, these systems can be seen as Markov-process-driven systems, which can be used to describe more complex phenomena. In this paper, a discrete-time stochastic linear system driven by a homogeneous Markov process is studied, and the corresponding linear quadratic (LQ) optimal control problem for this system is solved. Firstly, the relations between the well-posedness of LQ problems and some linear matrix inequality (LMI) conditions are established. Then, based on the equivalence between the solvability of the generalized difference Riccati equation (GDRE) and the LMI condition, it is proven that the solvability of the GDRE is sufficient and necessary for the well-posedness of the LQ problem. Moreover, the solvability of the GDRE and the feasibility of the LMI condition are established, and it is proven that the LQ problem is attainable through a certain feedback control when any of the four conditions is satisfied, and the optimal feedback control of the LQ problem is given using the properties of homogeneous Markov processes and the smoothness of the conditional expectation. Finally, a practical example is used to illustrate the validity of the theory. Full article

This paper provides a detailed analysis of the output voltage/current tracking control of a PWM DCDC converter that has been modeled as a Markov jump system. In order to achieve that, a dynamic sensorless strategy is proposed to perform active disturbance rejection control. As a convex optimization problem, a novel reformulation of the problem is provided to compute optimal control. Accordingly, necessary less conservative conditions are established via Linear Matrix Inequalities. First, a sensorless active disturbance rejection design is proposed. Then, to carry out the control process, a robust dynamic observer–predictive controller approach is introduced. Meanwhile, the PWM DC-DC switching power converters are examined as discrete-time Markovian switching systems. Considering that the system is subject to modeling uncertainties, time delays, and load variations as external disturbances, and by taking partial input saturation into account, the Lyapunov–Krasovskii function is used to construct the required feasibility frame and less conservative stability conditions. As a result, the proposed design provides an efficient control strategy with disturbance rejection and time-delay compensation capabilities and maintains robust performance with respect to constraints. Finally, a PWM DC-DC power converter simulation study is performed in different scenarios, and the obtained results are illustrated in detail to demonstrate the effectiveness of the proposed approach. Full article