Class Of Linear Matrix Inequalities Research Articles

A robust [formula omitted] fault-tolerant control approach for time-delay LPV systems with uncertain parameters and unknown disturbances

The article proposes a H∞ fault-tolerant control approach for a series of uncertain linear parameter-varying (LPV) time-delay models to obtain disturbance suppressions. Specifically, by applying the Lyapunov functions, a series of feedback controllers are provided to ensure the robust performance of LPV models with actuator faults. Meanwhile, a convex optimization strategy is developed for resolving optimization problems in the presence of bilinear matrix inequalities (BMIs), where the robustness conditions are improved to guarantee the stability of LPV model under uncertain factors. By resolving a class of linear matrix inequalities (LMIs), the gain matrices for LPV systems can be obtained. Furthermore, the less conservative conditions are developed and supported by strict theoretical derivation. Ultimately, the validity of proposed approach is confirmed by simulation analyses of truck–trailer systems.

Diagonal solutions for a class of linear matrix inequality

<p>In this paper, we present a characterization of diagonal solutions for a class of linear matrix inequalities. We consider linear hybrid time-delay systems and explore the conditions under which these systems are positive and asymptotically stable. Specifically, we investigate the existence of positive diagonal solutions for a linear inequality when the system matrices are Metzler and nonnegative. Using various mathematical tools, including the Schur complement and separation theorems, we derive necessary and sufficient conditions for the stability of these systems. Our results extend existing stability criteria and provide new insights into the stability analysis of positive time-delay systems.</p>

Resilient control for T-S fuzzy systems with multiple transmission channels under asynchronous denial-of-Service attacks

This paper investigates the resilient control problem of the T-S fuzzy system with multiple transmission channels under asynchronous denial-of-service (DoS) attacks. A part of the transmission channels are chosen as ones corresponding to the premise variables of the T-S fuzzy system. The considered asynchronous DoS attacks occur on the sensor-to-controller transmission channels, which may DoS attacks cause the system state to be unstable. The stability of the T-S fuzzy system under random DoS attack mode is considered, including the influence of the premise variables attacked. A class of parallel distributed compensation controllers are proposed, which adopts the strategy of discarding the attacked channels information. By using a piecewise Lyapunov function method and a class of linear matrix inequalities, the system stability sufficient conditions related to the duration and frequency of DoS attacks on the transmission channels are presented. Compared with the existing method, the more general relationship between premise variables and transmission channels are considered in this paper. Finally, a numerical example is used to illustrate the effectiveness of the proposed scheme.

Decomposition of Additive LMIs with Applications in Distributed Analysis of Interconnected LTI Systems

In this paper we present a simple technique which can be systematically used to obtain non-conservative decomposition for a class of linear matrix inequalities (LMIs) with an additive structure. By non-conservative decomposition we mean a suitable replacement of an additive LMI with a set of equivalent inequalities which are coupled by common variables. The results are applied on several stability/dissipativity analysis problems to produce analysis LMIs suitable for distributed computation.

Expected power bound and stability of two-dimensional digital filters with multiplicative noise in the FMLSS model

This paper studies the two-dimensional (2-D) expected power bound (EPB) for 2-D digital filters with multiplicative noise in the Fornasini-Marchesini local state-space (FMLSS) model. By virtue of a class of linear matrix inequalities (LMIs), the novel existence criterion of 2-D EPB for 2-D digital filters in the considered model is obtained. The corresponding stabilization controller design method is presented based on the above criterion. Finally, two examples are presented to verify the effectiveness of our results.

Interval Estimation for Discrete Sequential Systems Under Round-robin Protocol

In this paper, an interval estimator is designed for discrete sequence systems (DSSs) with delayed measurements. In order to reduce network transmission burden and prevent data collision, the round-robin (RR) protocol is employed to schedule the transmission order of the nodes. The purpose of the problem addressed is to design a novel interval estimator consisting of two coupled sub-estimators for DSSs with the bounded noises, such that 1) the error dynamics of the estimation upper bound and estimation lower bound are asymptotically stable, 2) the effect from the bounded noises on the estimation accuracy is attenuated at a given level by means of an H∞ norm. Based on the positive system theory combined with the Lyapunov stability theory, the real state is ensured in the interval, whose bounded is determined by the estimation upper bound and estimation lower bound. Moreover, the desired gains are obtained by solving a class of linear matrix inequalities. Finally, the effectiveness of the proposed interval estimator is verified by two numerical examples.

Finite‐Time H∞ Filtering for Discrete‐Time Singular Markovian Jump Systems with Time Delay and Input Saturation

The paper is discussed with the problem of finite‐time H∞ filtering for discrete‐time singular Markovian jump systems (SMJSs). The systems under consideration consist of time‐varying delay, actuator saturation and partly unknown transition probabilities. We pay attention to the design of a H∞ filtering which ensures the filtering error systems to be singular stochastic finite‐time boundedness. By employing an adequate stochastic Lyapunov functional together with a class of linear matrix inequalities (LMIs), a sufficient condition is firstly established, which guarantees the systems to achieve our goal and satisfy a prescribed H∞ attenuation level in the given finite‐time interval. Considering the above conditions, a distinct presentation for the requested H∞ filter is given. Finally, two numerical examples add to a dynamical Leontief model of economic systems are presented to illustrate the validity of the developed theoretical results.

Input-to-State Stabilizing Control for Cyber-Physical Systems With Multiple Transmission Channels Under Denial of Service

This paper is concerned with the input-to-state stabilizing control problem for cyber-physical systems (CPSs) with multiple transmission channels under denial-of-service (DoS) attacks. Under the data update policy with bounded update interval, a new control scheme that discards the outdated information is proposed, and the stability analysis of CPSs under DoS attacks is transformed into analyzing the stability of the system under a switched controller with the help of a class of linear matrix inequalities (LMIs). Then, inspired by the techniques for switched systems, sufficient conditions on the duration and frequency of the DoS attacks, under which the stability of the closed-loop systems is still guaranteed, are proposed. Compared with the existing method for the single-channel case, the considered multiple-channel case is more challenging, and the proposed LMI-based method is more flexible.

Distributed consensus control for multi-agent systems under denial-of-service

This paper investigates the problem of distributed consensus control for multi-agent systems under denial-of-service (DoS) attacks. Different from the existing results where DoS attacks on all the channels are same, in this paper, the adversaries compromise each channel independently. The objective is to design distributed controllers such that the consensus is still achieved in the presence of DoS attacks. Both state-feedback and observer-based controllers are considered. First, the decay rates under different attack modes are obtained by solving a class of linear matrix inequalities. Second, sufficient conditions on the duration of the DoS attacks, under which the consensus is still achieved, are proposed. The difficulty that there is no one-to-one match between the obtained decay rates and DoS duration limitations, is overcome by introducing the equivalent decay rates corresponding to channels. Moreover, the computational complexity is reduced greatly by introducing a novel scaling method. Finally, two examples are presented to illustrate the effectiveness of the proposed approaches.

Robust Constrained Model Predictive Control for Discrete‐Time Uncertain System in Takagi‐Sugeno's Form

AbstractIn this paper, we investigate a robust constrained model predictive control synthesis approach for discrete‐time Takagi‐Sugeno's (T‐S) fuzzy system with structured uncertainty. The key idea is to determine, at each sampling time, a state feedback fuzzy predictive controller that minimizes the performance objective function in the infinite time horizon by solving a class of linear matrix inequalities (LMIs) optimization problem. To do this, the fuzzy predictive controller is designed on the basis of non‐parallel distributed compensation (non‐PDC) control law, relaxed stability conditions of the closed‐loop fuzzy system are developed by employing an extended nonquadratic Lyapunov function and introducing additional slack and collection matrices. In addition, the presented approach is capable of ensuring the robust asymptotic stability as well as the recursive feasibility of the closed‐loop fuzzy system. Simulations on a highly nonlinear continuous stirred tank reactor (CSTR) are eventually presented to demonstrate the effectiveness of the developed theoretical approach.

Linear Threshold Discrete-Time Recurrent Neural Networks: Stability and Globally Attractive Sets

The stability of linear threshold dynamic neural networks is studied, and a series of methods to obtain globally attractive sets is proposed. A sufficient condition to judge whether an invariant set is a globally attractive set is also proposed. This method requires only the solution to a class of linear matrix inequalities. Also, two direct methods to obtain globally attractive sets are given. The stability criteria presented are based on the proposed globally attractive sets. Some numerical examples are given to illustrate the effectiveness of the obtained results.

An improved method of ultimate bound computation for linear switched systems with bounded disturbances

In this note, an improved method of ultimate bound computation for a linear switched system under arbitrary switching is presented. An ultimate bound for a linear switched system can be computed by solving a class of linear matrix inequalities. The effectiveness of the obtained results is illustrated by numerical examples.

Research on Robust Control of Gas Tungsten arc Welding System with the LMI Approach

By using the Lyapunov second method, the robust control and robust optimal control for the gas tungsten arc welding dynamic process whose underlying continuous-time systems are subjected to structured uncertainties are discussed in time-domain. As results, some sufficient conditions of robust stability and the corresponding robust control laws are derived. All these results are designed by solving a class of linear matrix inequalities (LMIs) and a class of dynamic optimization problem with LMIs constraints respectively. An example adapted under some experimental conditions in the dynamic process of gas tungsten arc welding system in which the controlled variable is the backside width and controlling variable welding speed, is worked out to illustrate the proposed results. It is shown in the paper that the sampling period is the crucial design parameter

Constrained PI Tracking Control for Output Probability Distributions Based on Two-Step Neural Networks

In this paper, a new method for the control of the shape of the conditional output probability density function (pdf) for general nonlinear dynamic stochastic systems is presented using two-step neural networks (NNs). Following the square-root B-spline NN approximation to the measured output pdf, the problem is transferred into the tracking of dynamic weights. Different from the previous related works, time-delay dynamic NNs with undetermined parameters are employed to identify the nonlinear relationships between the control input and the weighting vectors. In order to achieve the required control objective and satisfy the state constraints due to the property of output pdfs, a constrained PI tracking controller is designed by solving a class of linear matrix inequalities and algebraic equations. With the proposed tracking controller and adaptive projection algorithms, both identification and tracking errors can be made to converge to zero, and the state constraints can also be simultaneously guaranteed. Finally, two simulated examples are given, which effectively demonstrate the use of the proposed control algorithm.

New stability and stabilization for switched neutral control systems

This paper concerns stability and stabilization issues for switched neutral systems and presents new classes of piecewise Lyapunov functionals and multiple Lyapunov functionals, based on which, two new switching rules are introduced to stabilize the neutral systems. One switching rule is designed from the solution of the so-called Lyapunov–Metzler linear matrix inequalities. The other is based on the determination of average dwell time computed from a new class of linear matrix inequalities (LMIs). And then, state-feedback control is derived for the switched neutral control system mainly based on the state switching rules. Finally, three examples are given to demonstrate the effectiveness of the proposed method.

Robust control of gas tungsten arc welding system

The robust control law for gas tungsten arc welding dynamic process,which is a typical sampled-data system and full of uncertainties,is presented.By using the Lyapunov second method, the robust control and robust optimal control for a class of sampled-data systems whose underlying continuous-time systems are subjected to structured uncertainties are discussed in time-domain.As a result,some sufficient conditions of robust stability and the corresponding robust control laws are derived.All these results are designed by solving a class of linear matrix inequalities(LMIs)and a class of dynamic optimization problem with LMIs constraints respectively.An example adapted under some experimental conditions in the dynamic process of gas tungsten arc welding system in which the controlled variable is the backside width of weld pool and controlling variable pulse duty ratio,is worked out to illustrate the proposed results,it is shown that the sampling period is the crucial design parameter.

A neural network for linear matrix inequality problems

Gradient-type Hopfield networks have been widely used in optimization problems solving. This paper presents a novel application by developing a matrix oriented gradient approach to solve a class of linear matrix inequalities (LMIs), which are commonly encountered in the robust control system analysis and design. The solution process is parallel and distributed in neural computation. The proposed networks are proven to be stable in the large. Representative LMIs such as generalized Lyapunov matrix inequalities, simultaneous Lyapunov matrix inequalities, and algebraic Riccati matrix inequalities are considered. Several examples are provided to demonstrate the proposed results. To verify the proposed control scheme in real-time applications, a high-speed digital signal processor is used to emulate the neural-net-based control scheme.

A Novel Approach Solving for Linear Matrix Inequalities UsingNeural Networks

Linear matrix inequalities (LMIs) play a very important role in postmodern control by providing a framework that unifies many concepts. While numerous papers have appeared cataloging applications of LMIs to control system analysis and design, there have been few publications in the literature describing the numerical solution of these problems. Specially, neural network processing has rarely been used to solve those problems. This paper attempts to propose a new approach to solving a class of LMIs using recurrent neural networks. The nature of parallel and distributed processing renders these networks, which possess the computational advantages over the traditional sequential algorithms in real-time applications. The proposed networks are proven to be largely asymptotical and capable of solving LMIs. Some illustrative examples are provided to demonstrate the proposed results.