Solvability Of Linear Matrix Inequalities Research Articles

Co-design of distributed dynamic event-triggered scheme and extended dissipative consensus control for singular Markov jumping multi-agent systems under periodic Denial-of-Service jamming attacks

This paper introduces a distributed dynamic event-triggered (DDET) controller meticulously crafted to achieve resilient consensus control in singular Markov jumping multi-agent systems (SMJMAs) even in the face of periodic Denial-of-Service (DoS) jamming attacks. With a dual focus on optimizing network resource utilization and fortifying against cyber threats, we propose a distributed dynamic event-triggered scheme (DDETS) grounded in the principles of sampled data consensus. In the presence of cyber attacks, we demonstrate the transformation of the original consensus control challenge within the singular multi-agent system into a robust stability control problem, centering around a singular switching error system governed by the DoS attack signal. Acknowledging the disturbances that typify real-world scenarios, this paper establishes criteria for attaining exponential stability and stochastic admissibility within the singular Markov jumping switching error system under the extended dissipative performance index. Furthermore, we present a hybrid design for the consensus controller and DDETS, delineated through a set of solvable linear matrix inequalities (LMIs). Finally, a comprehensive array of numerical examples meticulously illustrates the compelling effectiveness and unequivocal superiority of our proposed methodology.

Tensor Product Alternatives for Nonlinear Field-Oriented Control of Induction Machines

The paper presents a nonlinear field-oriented control technique based on the tensor product representation of the nonlinear induction machine model and the solvability of linear matrix inequalities. The nonlinear model has 32 quasi linear parameter-varying equivalent variants, and it is shown that only half of the models result in feasible controller. Two control goals are realized: torque control and speed control. The controller is a nonlinear state feedback controller completed by integral action. A new block diagram is investigated for speed control. The controller gains are designed by the solution of linear matrix inequalities to solve the Lyapunov inequality to obtain a stable and fast response and constraints on the control signal. The presented methods are verified and compared by simulations.

A PARAMETER ADJUSTMENT LAW FOR MULTIVARIABLE PID CONTROL SYSTEMS WITH DISTURBANCE ATTENUATION PERFORMANCE

This paper shows a new parameter adjustment law of PID controllers for MIMO linear system with guaranteed disturbance attenuation performance. In the proposed design approach, the design problem of PID parameters is reduced to the problem of static output feedback controllers for MIMO linear systems. In this paper, we show that sufficient conditions for the existence of the proposed PID control system can be reduced to solvability of linear matrix inequalities (LMIs). Finally, a simple numerical example is shown to effectiveness of the proposed PID control system.

T-S fuzzy model based event-triggered change control for product and supply chain systems

Product and supply chain systems are a class of complex nonlinear systems due to the uncertain demand fluctuation and unexpected events, and Takagi–Sugeno (T-S) fuzzy systems are suitable for modelling such product and supply chain systems with different production rates. According to the uncertainty customer demands, different subsystems which describe the corresponding production-inventory processes are orchestrated by the T-S fuzzy rule. Change control is designed to handle the supply chain blocking and event breaking caused by uncertain factors. Then, sufficient conditions are given such that the exponential stability with a prescribed bullwhip effect attenuation level can be guaranteed, and the control synthesis problem is transformed into the solvability of linear matrix inequalities for the product and supply chain systems. An example is introduced to verify the validness and efficiency of the proposed approach.

A random-switch-surface based neural sliding mode framework against actuator attacks of delayed singular semi-Markov jump systems

This article addresses the challenge of actuator attacks in delayed singular semi-Markov jump systems (singular S-MJSs) with uncertainties and exogenous disturbances, operating under conditions of partially unknown transition rate (PUTR) matrix and completely unknown transition rate (CUTR) matrix, respectively. The specifics of actuator attacks and the bounds of disturbances remain elusive during the controller design process. Furthermore, any information regarding unknown elements within the PUTR/CUTR matrix is unattainable. To stabilize systems against actuator attacks, we introduce a distinctive “random switch”-triggered sliding surface, referred to as the random switch surface (RSS). Additionally, H∞ stochastic admissibility sufficient conditions are established under PUTR and CUTR matrices, respectively. Two corresponding algorithms are presented, leveraging solvable linear matrix inequalities (LMIs), to determine the gain matrices. Further, an innovative adaptive H∞ neural sliding mode control (SMC) law is conducted, incorporating an ingenious neural network to approximate actuator attacks. It also enables real-time estimation of unavailable parameter bounds. Finally, we conduct simulations on several examples using our proposed method, as well as other comparison methods, to demonstrate the effectiveness of the proposed approach.

Co-Design of Adaptive Event-Triggered Mechanism and Asynchronous H∞ Control for 2-D Markov Jump Systems via Genetic Algorithm.

This article concerns the co-design scheme of the adaptive event-triggered mechanism (AETM) and asynchronous H∞ control for two-dimensional (2-D) Markov jump systems. First, we introduce a hidden Markov model with the observation that the asynchronous phenomenon is inevitable between the plant mode and the controller mode. Besides, for economizing the communication times, an innovative 2-D AETM is constructed, which can dynamically regulate the event-triggered thresholds to strive for better system performance. Then, by utilizing the 2-D Lyapunov stability theory, nonlinear matrix inequalities are built to ensure the asymptotic mean-square stability with an H∞ performance for the closed-loop 2-D system. To avoid introducing any conservatism when handling the above nonlinear matrix inequalities, a binary-based genetic algorithm (BGA) is exploited to treat some variables as known, such that derive some directly solvable linear matrix inequalities. Finally, a simulation example is provided to verify the effectiveness of the proposed 2-D AETM-based asynchronous controller strategy with a BGA.

Memory Sampled-Data Controller Design for Interval Type-2 Fuzzy Systems via Polynomial-Type Lyapunov–Krasovskii Functional

This study deals with the investigation of the interval type-2 (IT2) fuzzy sampled-data (SD) stabilization problem based on nonlinearities and parameter uncertainties. For the first time, a memory SD control design involving a known signal transmission delay is adapted to address the stabilization problem for IT2 fuzzy systems. New polynomial-type Lyapunov–Krasovskii functionals (LKFs) associated with the state of constant signal transmission delay are introduced to achieve less conservative stability results. To bound the derivative of such LKFs, the Jacobi–Bessel inequality is introduced. Due to this, improved delay-dependent sufficient conditions can be obtained relating to set of linear matrix inequalities (LMIs). Thus, by solving LMIs using the LMI solver in MATLAB, the closed-loop system can be stabilized. The proposed method is verified in the simulation results with a nonlinear permanent-magnet vernier generator (PMVG)-based wind energy model and a Rossler model. Also, the applicability and superiority of the derived sufficient conditions are proved when compared with the existing results.

Observer-based event-triggered sliding mode control of the discrete-time singular networked systems

This article is concerned with the [Formula: see text] observer-based sliding mode control via event-triggered strategy for the discrete-time singular networked systems. To improve network communication efficiency, an event-triggered strategy is introduced. Under the premise of considering the design convenience of the sliding mode surface for discrete-time singular networked systems, the observer is constructed to estimate the states of the system. From the event-triggered strategy–based observer and the sliding mode control technology, the augmented closed-loop discrete-time singular networked system is obtained. Then, new sufficient admissible criteria of discrete-time singular networked systems are derived, satisfying a given [Formula: see text] performance level. The synchronous design method of the event-triggered strategy observer gain and sliding mode control one is provided as solvable linear matrix inequalities. The sliding mode control law is designed to obtain better sliding mode accessibility and less chattering. Finally, two examples are provided to verify the effectiveness of the proposed method.

Fuzzy membership function-dependent switched control for nonlinear systems with memory sampled-data information

In this paper, a fuzzy memory-based coupling sampled-data control (SDC) is designed for nonlinear systems through the switched approach. Compared with the usual SDC scheme, by employing the Bernoulli sequence, a more general coupling switched SDC that involving the signal transmission delay is designed. The Lyapunov–Krasovskii functional (LKF) is presented with the available characteristics of the membership function, and a coupling sampling pattern, for the T-S fuzzy systems. Based on LKF, together with time derivative information of membership function, and the generalized N-order free-matrix-based inequality, the suitable conditions are obtained in terms of linear matrix inequalities (LMIs) for guaranteeing the asymptotic stability and stabilization of the concerned system. Then, the desired fuzzy coupling SDC gain is attained from the solvable LMIs. In the end, two examples are given to validate the derived theoretical results.

Admissibility and Design Issues for T-S Fuzzy Descriptor Systems With Perturbed Derivative Matrices in the Rules

This article mainly investigates the admissibility analysis and the parallel distributed compensator (PDC) for fuzzy descriptor systems with perturbed derivative matrices in the rules. The standard Takagi–Sugeno (T–S) fuzzy model is generalized into a fuzzy descriptor model with the perturbed derivative matrices existing in each rule, which can be used to represent a larger class of nonlinear and/or uncertain systems. Based on linear matrix inequalities (LMIs) technique, a new admissibility analysis condition for the considered fuzzy descriptor system is first presented, where the new results involve slack matrices for lessening the conservatism. Furthermore, we further cope with the fuzzy PDC synthesis associated with admissibility and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</i> -admissibility assurance for the resulting closed-loop fuzzy descriptor systems. Since all the proposed criteria can be explicitly formulated in terms of LMIs or parametric LMIs, we can handily verify them via current LMI solvers. Finally, illustrative examples are given to demonstrate that the proposed approach is valid and effective.

Local Stabilization for Multiple Input-Delay Systems Subject to Saturating Actuators: The Continuous-Time Case

In this article, the local stabilization problem is dealt with for a class of continuous-time multiple input-delay systems subject to saturating actuators. Using the generalized sector conditions and the piecewise Lyapunov–Krasovskii functional, and carrying out rigorous mathematical deduction, a sufficient condition is established under which the closed-loop dynamics is exponentially stable for admissible initial conditions. Subsequently, the explicit characterization of controller gains is obtained in terms of the solvability of linear matrix inequalities. The special cases concerning the constant and single delays are also discussed. Moreover, optimization problems are proposed to maximize the estimate of the domain of attraction. Finally, two examples are given to show the effectiveness and advantages of the obtained results.

Robust Sliding Mode Control for Stochastic Uncertain Discrete Systems with Two-Channel Packet Dropouts and Time-Varying Delays.

In this paper, the control problem is investigated for discrete time-varying delayed systems with stochastic uncertainty, external disturbance, and two-channel packet dropouts. Sliding mode functions with packet loss probabilities are proposed for the packet loss problem in the sensor–controller channel and the controller–actuator channel. Furthermore, by employing the Lyapunov–Krasovskii functional, some new stability conditions are established in terms of solvable linear matrix inequalities (LMIs), and H∞ performance is analyzed for the sliding mode motion of the system. Meanwhile, a sliding mode controller is designed to drive the system state to the pre-designed sliding surface. Moreover, the designed controller can be robust for two-channel packet dropouts, time-varying delays, stochastic uncertainty and external disturbance. Finally, two numerical examples are given to demonstrate the feasibility of the proposed theoretical method.

Consensus tracking for singular multi‐agent systems with Lipschitz nonlinear dynamics and external disturbances

AbstractThe consensus tracking control problem for singular multi‐agent systems (SMASs) with Lipschitz nonlinearities and unknown disturbances is investigated. An extended state observer using only the relative output information is introduced and then a distributed consensus protocol is proposed, whose performance is analyzed using matrix analysis, singular system theory and Lyapunov stability theory. Sufficient conditions for ensuring consensus tracking with disturbance rejection of linear and Lipschitz nonlinear SMASs are, respectively, obtained under directed networks. Specifically, an equivalent formulation of achieving consensus tracking for SMASs is established, and the design procedures of gain matrices in the proposed consensus protocols are presented by the linear matrix inequality solver. Finally, simulation examples are provided to illustrate the theoretical results.

Dynamic output‐feedback control for discrete time‐delayed systems with actuator saturations under round‐robin communication protocol

AbstractIn this article, the dynamic output‐feedback control problem is investigated for discrete‐time state‐delay systems subject to exogenous disturbances and actuator saturations under the round‐robin communication protocol. Using the switched system approach, the Lyapunov–Krasovskii functional and the modified sector condition, sufficient conditions are first obtained under which the closed‐loop systems can achieve some desirable performance indices such as the boundedness, the performance and the stability in the absence of disturbances. Then, the controller is explicitly characterized by means of the solvability of linear matrix inequalities. For the case without time delays, the corresponding conditions are also presented. Subsequently, the optimization problems about the performance indices are discussed. Finally, the benefit and effectiveness of the proposed results are specifically illustrated via two simulation examples.

Adaptive sliding mode observers for sector‐bounded nonlinear systems

SummaryThis article introduces a novel sliding mode observer design for sector bounded nonlinear systems. The proposed observer can simultaneously estimate both states and unknown parameters in the presence of disturbances and measurement noise. The observer is developed by using a time‐averaged Lyapunov (TAL) functional to analyze the effect of noise (Gaussian) and to adequately reduce its effect on the system. The TAL averages the Lyapunov analysis over a small finite time interval, allowing for intuitive analysis of noises and disturbances acting on the system. The TAL is shown to satisfy all the requirements of a Lyapunov candidate function. The article focuses on the observer design for sector bounded nonlinear systems since several nonlinearities can be modeled using a sector bound. An optimization approach is also developed to provide a tight bound on the effect of the uncertainty on the estimated parameters. The conditions for the existence of the observer are presented in the form of linear matrix inequality (LMI), which can be explicitly solved offline using commercial LMI solvers. Furthermore, the LMI design is also extended to a specific case of a dissipative nonlinear system. The observer design has also been extended to the case where the input disturbance is correlated with the sensor noise.

Consensus control for nonlinear multi-agent systems with event-triggered communications

This paper investigates the consensus problems for a class of nonlinear multi-agent systems (MASs) by distributed event-based control protocols. Firstly, we design the static distributed event-triggered control protocols to achieve leader-follower and leaderless consensus problems, respectively, and the systems exclude Zeno behavior under the proposed control schemes. In order to avoid utilizing the global information of the system networks, that is, the minimum eigenvalues of the correlation matrices. Then, the fully distributed event-based control schemes are designed by introducing the time-varying coupling weights to achieve the leader-follower and leaderless consensus problems, respectively. It has been shown that the Zeno behavior is ruled out in the MASs under the fully distributed event-based control protocols. All static and dynamic event-based control schemes are able to be constructed based on the solvability of linear matrix inequalities (LMIs). Finally, the rationality of the theoretical results is illustrated by the example.

Observers of Disturbances and Measurement Noises for Sector-bound Nonlinear System

Observers of disturbances and measurement noises are developed for dynamical systems with sector-bound nonlinearity and parametric uncertainty. Conditions for the existence of these observers are proposed in the form of solvability of linear matrix inequalities (LMIs). Using the observers, a control law is designed to ensure system stabilization. The proposed algorithm is experimentally studied on a stand for multi-machine power systems control.

A Robust Formation Control Strategy for Multi-Agent Systems with Uncertainties via Adaptive Gain Robust Controllers

This paper deals with a design problem of an adaptive gain robust controller which achieves consensus for multi-agent system (MAS) with uncertainties. In the proposed controller design approach, the relative position between the leader and followers are considered explicitly, and the proposed adaptive gain robust controller consisting of fixed gains and variable ones tuned by time-varying adjustable parameters can reduce the effect of uncertainties. In this paper, we show that sufficient conditions for the existence of the proposed adaptive gain robust controller are reduced to solvability of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed robust formation control system is verified by simple numerical simulations. A main result of this study is that the proposed adaptive gain robust controller can achieve consensus and formation control giving consideration to relative distance in spite of uncertainties.

Memory sampled data control for switched-type neural networks and its application in image secure communications

The present study focuses on designing the memory-based sampled data control approach to achieve the desired performance from switched-type of neural networks. The overall contribution of the study can be viewed from two directions. The first part is to derive the theoretical-based sufficient stability conditions that ensure the synchronization of uncontrolled and controlled systems. The idea behind the synchronization analysis is because of time complexity and computational cost. Once, we derive the closed-loop system then user can employ them in any practical application without interruptions. The existence of time-delays during the information transmission is inevitable, and in a practical sense, the delays, which are a function of time are well-effective. Besides, the sufficient conditions are derived in terms of solvable linear matrix inequalities (LMIs), which can be solved to ensure the global asymptotical stability of the error system, derived from uncontrolled–controlled systems. Technically, the work integrates with the new type of discontinuous Lyapunov–Krasovskii functional candidate with integral terms, several delay-dependent stability conditions, and Wirtinger-based integral inequality. The second part works on utilizing the controlled system into a real-life application, say, encryption/decryption process. To an evident, the proposed controlled system is considered as crypto-system in the encryption/decryption process.

Exponential sampled‐data fuzzy stabilization of nonlinear systems and its application to basic buck converters

This study focuses on the exponential stability and stabilization of nonlinear systems via fuzzy sampled-data control technique. The stability and stabilization conditions are obtained through constructing suitable Lyapunov functional which contains the sampling information and the solvable linear matrix inequalities. Then, the dynamics of the nonlinear buck converter system and Lorenz system with the sampled-data controller is analyzed and designed. Finally, the proposed method is validated with a basic buck converter system model designed to reflect the characteristics of the power metal-oxide-semiconductor field-effect transistors in the numerical section. In addition, the superiority of the sufficient conditions obtained is shown by comparing with the existing methods of the Lorentz system.