Linear Matrix Inequality Criterion Research Articles

Synchronization of fractional-order quaternion-valued neural networks with image encryption via event-triggered impulsive control

The finite-time synchronization and impulsive synchronization of fractional-order quaternion-valued neural networks (FOQVNNs) with delay are investigated in this research. To begin, instead of employing a decomposition method, a Lyapunov direct approach is proposed to achieve the finite-time synchronization of FOQVNNs using event-triggered control based on state errors. The settling time is then estimated using a unique fractional differential inequality. The event-triggered impulsive controller, which updates only during triggering instants, is proposed to be more inexpensive and efficient. Then, utilizing fractional Lyapunov theory and the comparison principle, several novel quaternion-valued linear matrix inequalities criteria are defined to assure the impulsive synchronization of the delayed FOQVNNs. Furthermore, the positive lower bound of the inter-event time is obtained to exclude the Zeno behavior. As proof of the feasibility and validity of these theoretical findings obtained, numerical examples are provided. At last, the use of the event-triggered control technique for FOQVNNs in image encryption and decryption is demonstrated and validated.

Admissibility LMI criteria for descriptor fractional-order systems with a changeable number of decision variables

This paper studies the admissibility problem of descriptor fractional-order systems (DFOSs) with order in (0,1). Firstly, an approach to stability for FOSs is derived which is effective for the case of at least two complex matrix variables. Secondly, based on the generalized linear matrix inequality (GLMI) region, a new admissibility criterion for DFOSs with multiple choices for the number of decision variables is presented, which does not involve complex variables and equality constraints. Moreover, all the theorems are necessary and sufficient conditions, and can be described by strict linear matrix inequalities (LMIs). Finally, two numerical examples are provided to verify the validity of theoretical conclusions.

Dissipativity of Stochastic Competitive Neural Networks with Multiple Time Delays

The (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative of stochastic competitive neural networks (SCNNs) with leakage delays and discrete delay is studied. Firstly, Lyapunov–Krasovskii functional is constructed, which studies the relationship between various types of time delays. Secondly, by using integral inequality technique, the linear matrix inequality (LMI) criterion of (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative in the mean square sense of SCNNs is obtained. Furthermore, the obtained LMI criterion is extended to the passivity in the mean square sense, stability in the mean square sense, (Q,R,S)-γ-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q,R,S)-\\gamma -$$\\end{document}dissipative and passivity. Finally, the effectiveness of the obtained results are verified by numerical simulation.

Unified finite‐time fault estimation and fault‐tolerant control for Takagi–Sugeno fuzzy singular systems

SummaryWith the aid of a proportional integral framework, the presented article focuses on the problems of finite‐time boundedness and fault estimation for Takagi–Sugeno fuzzy singular systems subject to time delays, faults and external disturbances. To commence, we conjure up a fuzzy‐dependent intermediate variable and from thereon, a proportional integral‐based fuzzy intermediate estimator is constructed. Moreover, the constructed estimator precisely facilitates for estimating the fault signals and system states in simultaneously. Besides this, the integral term in the proportional integral estimator offers greater design flexibility and higher resilience. Secondly, an intermediate estimator‐based fault‐tolerant control is devised by availing the information from the proportional integral‐based fuzzy intermediate estimator, which aids in effectively compensating the faults arising in the system. Subsequently, by setting up an appropriate Lyapunov–Krasovskii functional, the set of adequate requirements asserting the finite‐time boundedness with the endorsed mixed and passivity performance index is established in terms of linear matrix inequalities. After that, an explicit framework for the requisite gain matrices can be found forth basing on the formed linear matrix inequality criteria. Ultimately, simulation findings are supplied to evaluate the utility and applicability of the theoretical insights.

Generalized Nonlinear Sector Approaches for Takagi-Sugeno Models

The Nonlinear Sector Approach (NLSA) is a way to construct Takagi-Sugeno (T-S) models which exactly represent nonlinear systems with bounded nonlinearities. Generally, the nonlinearities are bounded by a box-shaped set, however, this paper generalizes the NLSA for polytopic and smooth convex bounding sets, providing new ways of reducing the intrinsic conservatism of T-S representations with interdependent scheduling parameters. Some Linear Matrix Inequalities (LMI) criteria for stability analysis of these models are provided throughout the paper.

Stability analysis of fractional-order neural networks with time-varying delay utilizing free-matrix-based integral inequalities

The stability problem of fractional-order neural networks in consideration of time-varying delay is addressed by utilizing Lyapunov functional approach in this paper. Firstly, a class of novel Lyapunov-Krasovskii functions are designed to deal with the time-varying delay terms, which reduces the conservatism of the stability criteria. In addition, to estimate the fractional-order derivative of the Lyapunov-Krasovskii functions, a novel free-matrix-based fractional-order integral inequality is then established, which encompasses the Wirtinger one and leads to tractable linear matrix inequality criteria. Then, based on the designed adaptive control and the proposed Lyapunov-Krasovskii functions, some stability criteria depending on time-varying delay information and fractional-order α are deduced. Finally, numerical simulation shows that the presented approach can significantly reduce the conservatism of the existing results and has a broader application prospect.

Alternate Admissibility LMI Criteria for Descriptor Fractional Order Systems with 0 < α < 2

The paper focuses on the admissibility problem of descriptor fractional-order systems (DFOSs). The alternate admissibility criteria are addressed for DFOSs with order in (0,2) which involve a non-strict linear matrix inequality (LMI) method and a strict LMI method, respectively. The forms of non-strict and strict LMIs are brand new and distinguished with the existing literature, which fills the gaps of studies for admissibility. These necessary and sufficient conditions of admissibility are available to the order in (0,2) without separating the order ranges into (0,1) and [1,2). Based on the special position of singular matrix, the non-strict LMI criterion has an advantage in handling the DFOSs with uncertain derivative matrices. For the strict LMI form, a method involving least real decision variables is derived which is more convenient to process the practical solution. Three numerical examples are given to illustrate the validity of the proposed results.

Impulsive control strategies of mRNA and protein dynamics on fractional-order genetic regulatory networks with actuator saturation and its oscillations in repressilator model

In genetic regulatory networks (GRNs), the control strategies of messenger RNA (mRNA) and protein play a key role in regulatory mechanisms of gene expression, especially in translation and transcription. However, the influence of impulsive control strategies on oscillatory gene expression is not well understood. In this article, by considering the impulsive control strategies of mRNA and protein, a novel fractional-order genetic regulatory networks with actuator saturation is proposed. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequalities (LMIs) criteria that guarantee finite-time Mittag-Leffler stabilization problem for fractional-order genetic regulatory networks are given. The derived sufficient conditions can easily be verified by designing impulsive control gains and solving simple LMIs. Finally, to investigate the effectiveness and applicability of the control strategies, an interesting simulation example as a synthetic oscillatory network of transcriptional regulators in Escherichia coli is illustrated.

Lagrange Stability of Fuzzy Memristive Neural Networks on Time Scales With Discrete Time Varying and Infinite Distributed Delays

The existing results of Lagrange stability for neural networks with distributed time delays are scale-free, which introduces conservativeness naturally. A class of Takagi–Sugeno fuzzy memristive neural networks (FMNNs) on time scales with discrete time-varying and infinite distributed delays is brought in this article. First, a new scale-limited Halanay inequality is demonstrated by timescale theory. Next, on the basis of inequality techniques on time scales, some new scale-limited algebraic criteria and linear matrix inequality criteria of Lagrange stability are obtained by comparison strategy and generalized Halanay inequality. All scale-limited sufficient criteria of Lagrange stability for FMNNs not only apply to continuous-time FMNNs and their discrete-time analogs, but also could deal with the arbitrary combination of them. Finally, two numerical simulations are given to verify the validity of the obtained theoretical results.

An improved output feedback controller design for linear discrete‐time systems using a matrix decomposition method

SummaryThis paper presents the design of output feedback controllers for discrete‐time (DT) linear systems. New sufficient LMI conditions are derived for designing static and controllers using decomposition of an auxiliary matrix. The decomposition facilitates linearization of nonlinear term of reduced size to obtain linear matrix inequality criteria. This leads to less conservative results as shown in the numerical examples. In addition, the proposed static output feedback criteria is also used for designing dynamic output feedback controllers for DT systems. Furthermore, a comparative study is also made for the proposed design method with the results existing in the literature. Finally, a DT static output feedback controller is designed for a quarter‐car suspension system. Simulation results are provided to show the efficacy of the proposed design method.

Output-feedback photovoltaic WADC by H∞ criterion using auxiliary function

The wide-area damping controller (WADC) is vital in suppressing wide-area oscillations. However, the power system is now developing very fast, traditional output-feedback linear matrix inequality (LMI) criteria adopted in this field may not be very applicable. This paper proposes an output-feedback H∞ robust criterion to design a WADC installed in the photovoltaic plant considering the wide-area signal delay. We use the auxiliary function technique, and adopt Lyapunov functions containing triple summation, augmented variables and cross terms to deduce a stability analysis criterion followed by the corresponding controller design criterion. The low conservatism and control performance of the proposed criteria are verified in a 68-bus 16-machine test system. In addition, as system parameters often change, the control performance of integrating the proposed controller design criterion into a gain scheduling algorithm to handle the system parameter variance is validated.

Impulsive stabilization and stability analysis for Gilpin–Ayala competition model involved in harmful species via LMI approach and variational methods

Firstly, a dynamic analysis for reaction–diffusion Gilpin–Ayala competition model involved in harmful species is considered under Dirichlet boundary value condition. Existence of multiple stationary solutions is verified by way of Mountain Pass lemma, and the local stability result of the null solution is obtained by employing linear approximation principle. Secondly, the authors utilize variational methods and linear matrix inequality (LMI) technique to deduce the LMI-based global exponential stability criterion on the null solution which becomes the unique stationary solution of a Markovian jumping ecosystem with delayed feedback under a reasonable boundedness assumption on population densities. Particularly, LMI criterion is involved in free weight coefficient matrix, which reduces the conservatism of the algorithm. In addition, a new impulse control stabilization criterion is also derived, in which no differentiable assumptions on time-delayed functions are proposed. Finally, three numerical examples show the effectiveness of the proposed methods. It is worth mentioning that the obtained stability criteria of null solution presented some useful hints on how to eliminate pests and bacteria.

Global asymptotic stability of fractional-order complex-valued neural networks with probabilistic time-varying delays

The stability of fractional-order complex-valued neural networks (FOCVNNs) with probabilistic time-varying delays is investigated in this paper. By constructing suitable Lyapunov–Krasovskii functional and utilizing inequality technique, a complex-valued linear matrix inequality (LMI) criterion guaranteeing the global asymptotic stability of the proposed FOCVNNs is deduced. A numerical example with simulations is provided to demonstrate the feasibility and availability of the obtained theoretical result.

Impulsive Synchronization of Unbounded Delayed Inertial Neural Networks With Actuator Saturation and Sampled-Data Control and its Application to Image Encryption.

The article considers the impulsive synchronization for inertial neural networks with unbounded delay and actuator saturation via sampled-data control. Based on an impulsive differential inequality, the difficulties caused by unbounded delay and impulsive effect may be effectively avoid. By applying polytopic representation technique, the actuator saturation term is first considered into the design of impulsive controller, and less conservative linear matrix inequality (LMI) criteria that guarantee asymptotical synchronization for the considered model via hybrid control are given. As special cases, the asymptotical synchronization of the considered model via sampled-data control and saturating impulsive control are also studied, respectively. Numerical simulations are presented to claim the effectiveness of theoretical analysis. A new image encryption algorithm is proposed to utilize the synchronization theory of hybrid control. The validity of image encryption algorithm can be obtained by experiments.

Impulsive Stabilization of Nonlinear Time-Delay System With Input Saturation via Delay-Dependent Polytopic Approach

The impulsive stabilization of nonlinear time-delay system with input saturation via delay-dependent polytopic approach is studied in this article. Different from polytopic representation technique, delay-dependent polytopic technique is able to estimate a larger domain of attraction. Based on this approach, the actuator saturation term is first introduced into the design of impulsive controller, which is expressed as a convex combination of the product of delay-dependent state vectors and auxiliary matrices. By applying delay-dependent polytopic technique and delay-dependent Lyapunov–Krasovskii functional (LKF) approach, a new series of less conservative linear matrix inequality (LMI) criteria are obtained to ensure the stability of the established model. Finally, two examples are presented to claim the effectiveness of theoretical analysis results.

Robust state estimation for fractional-order complex-valued delayed neural networks with interval parameter uncertainties: LMI approach

Without separating complex-valued neural networks into two real-valued systems, the state estimation of fractional-order complex-valued neural networks (FCNNs) with uncertain parameters and time delay is investigated in this paper. Based on Lyapunov-Krasovskii functional approach, a new linear matrix inequality (LMI) criterion is derived for asymptotic stability of the estimation error system. A numerical example with simulations is given to confirm the feasibility and availability of the raised result.

Design of Robust PID Controller using Static Output Feedback framework

This paper considers the design of a robust PID controller for higher order MIMO plants. The design problem is first recast into a Static Output Feedback (SOF) controller design problem and then the transformed SOF problem is solved within the framework of Linear Matrix Inequalities (LMIs) through a decomposition of the Lyapunov matrix variable. Sufficient LMI criteria are derived that ensure H∞ performance of the underlying system. By means of a numerical example, it is shown that the designed controller yields less conservative results. Also, a comparative study is done with the existing techniques to demonstrate the efficacy of the proposed method.

Stabilization of Discrete-Time Delayed Systems in Presence of Actuator Saturation Based on Wirtinger Inequality

This paper examines the stability analysis of discrete-time control systems particularly during the event of actuator saturation and time-varying state delay. With the help of Wirtinger inequality along with Lyapunov-Krasovskii functional gain of state feedback controller is determined for stabilization of above system. The saturation nonlinearity is represented in the terms of convex hull. A new linear matrix inequality (LMI) criterion is settled with reciprocally convex combination based inequality which is dependent on delay. The proposed criterion is less conservative in concern to increase the delay bound and a controller is also simulated for real time problem of missile control system in this paper. It is also attained that projected stability criterion is less conservative compared to other outcomes. Furthermore, an optimization procedure together with LMI constraints has been proposed to maximize the attraction of domain.

Improved Results on Reachable Set Estimation of Linear Systems

In this study, we investigate the reachable set estimation for linear systems with discrete delay and distributed delay as well as disturbances. Based on the reciprocally convex combination lemma, free-weighting matrix approach and convex analysis technique, improved delay-dependent linear matrix inequalities (LMIs) criteria are derived for finding an ellipsoid to bound the reachable sets of such systems. Moreover, this result is extended to the one for linear systems with discrete delay, distributed delay and disturbances as well as polytopic-type uncertainties. In addition, the proposed results include some existing ones as special cases since the initial conditions of the systems are not required to be zero. Finally, two numerical examples are provided to show that our results have less conservative.

New results on restricted static output feedback controller design with regional pole placement

This study addresses the design of static output feedback (SOF) controller for continuous time linear systems. New sufficient conditions are derived for designing SOF controllers. The development involves suitable decomposition of Lyapunov matrices and deriving linear matrix inequality (LMI) criterion that ensures H ∞ performance. LMI criteria for pole placement in the LMI region are also derived. The proposed criteria can be used for restricted SOF controller design effectively. Several numerical examples are presented to demonstrate the effectiveness of the proposed results.