Linear Matrix Inequality Control Research Articles

Sampled-data controller scheme for multi-agent systems and its Application to circuit network

The objective of this study is to investigate the synchronization criteria under the sampled-data control method for multi-agent systems (MASs) with state quantization and time-varying delay. Currently, a looped Lyapunov–Krasovskii Functional (LKF) has been developed, which integrates information from the sampling interval to ensure that the leader system synchronizes with the follower system, resulting in a specific condition in the form of Linear Matrix Inequalities (LMIs). The LMIs can be easily solved using the LMI Control toolbox in Matlab. Finally, the proposed approach’s feasibility and effectiveness are demonstrated through numerical simulations and comparative results.

A delay-dependent dissipativity and passivity-based synchronization analysis for Markovian jumping complex dynamical network models with distributed coupling delays

This paper studies the issue of delay-dependent dissipativity and passivity-based synchronization analysis for Markovian jumping complex dynamical network (MJCDN) models with distributed coupling delays. The state feedback control scheme is designed for the synchronization of the MJCDN closed-loop error model. By constraining the appropriate Lyapunov functional along with the properties of the Kronecker product and using integral inequality techniques,several new delay dependent sufficient conditions are derived in terms of linear matrix inequalities (LMIs), which ensure that the dissipativity and passivity performance of the considered MJCDN model. The results of this analysis are verified using the MATLAB LMI control toolbox. Illustrative examples are provided to demonstrate the feasibility of the results

Event-triggered state and fault simultaneous estimation for nonlinear systems with time delays

This paper addresses the problem of event-triggered robust state and fault simultaneous estimation for nonlinear time-delay systems subject to actuator and sensor unknown disturbances. Based on a fault decomposition technique and some basic mathematical transformations, we obtain an augmented system where the state vector consists of the variable of the original system and the fault. Then a novel event-triggered state observer for the augmented system is proposed to robustly estimate the variable of the original system and the fault. We next established a sufficient condition for the existence of such an observer. We translated it into a linear matrix inequality (LMI), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, an illustrative example is applied to test the proposed method.

Stabilization of DFIG-based wind turbine with active and reactive power: A coupling memory state-feedback control scheme

In this paper, we examine a stabilization problem for the active and reactive power of doubly fed induction generator (DFIG)-based wind turbine (WT) through fuzzy coupling memory state-feedback control (CMSFC). In order to narrate the nonlinear terms in the proposed system, a more efficacious Takagi–Sugeno (T-S) fuzzy theory is utilized. The effective T-S fuzzy model describes the behavior of the nonlinear model into linear sub-models based on IF-THEN fuzzy membership functions and the corresponding fuzzy CMSFC is proposed. The main intention of this paper is to stabilize the active and reactive power constant, control the stator and rotor voltages of α−β frames when enhancing the system stable output power. To do this, a fuzzy CMSFC strategy is designed. By constructing a Lyapunov-Krasovskii functional (LKFs) with the effect of constant time-delay, the delay-dependent sufficient criteria are derived in the form of linear matrix inequalities (LMIs), which can be easily assessed by MATLAB LMI Control toolbox. Based on the delay-dependent sufficient criteria, the mean-square asymptotic stability of the DFIG-based WT system under the proposed controller is also achieved. Finally, we demonstrate the feasibility and efficacy of the proposed method through numerical simulations and comparative results.

Control of Switched Affine Systems with Bounded Sampling Time Rate on the Switching Function: Application to Buck DC-DC Converter

The paper addresses the problem of designing a stabilizing control for switched affine and its experimental verification based on Linear Matrix Inequalities (LMIs). The main contribution is on the determination of a switching function that exploits the potential of LMI control approaches and which assures global stability and minimizes a guaranteed quadratic cost. Slack variables are introduced to reduce the design conservatism and new sufficient LMI conditions for the synthesis of the controllers are presented. Thus, it is showed that the performance of the control system is superior with a smaller guaranteed cost upper bound of that afforded by recent results. In addition, a theorem with sufficient conditions for the control of switched affine systems that allows a way to garantee a bounded sample time rate on the switching function is proposed. The implementation of the switching function taking into account a bounded sampling time is analysed and discussed with particular interest. Finally, the theoretical results are applied to Buck DC-DC converter. Several simulations show the usefulness of the methodology and experimental results obtained from a prototype validate this approach.

Finite-time boundedness and finite-time stabilization boundedness for nonlinear interconnected systems with Atangana–Baleanu–Caputo fractional derivative

In this paper, we consider the finite-time boundedness (FTB) and finite-time stabilization boundedness (FTSB) problems for a class of nonlinear interconnected systems with Atangana–Baleanu–Caputo (ABC) fractional derivative. By employing the FTB theory and some properties of ABC fractional derivative, and some basic mathematical transformations, we derive new conditions for the FTB and FTSB problems of ABC fractional-order nonlinear interconnected systems. These conditions are formed in linear matrix inequalities (LMIs), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, two numerical examples with simulations are provided to illustrate the efficiency of the proposed method.

Robust stability and passivity analysis for discrete-time neural networks with mixed time-varying delays via a new summation inequality

<abstract><p>The summation inequality is essential in creating delay-dependent criteria for discrete-time systems with time-varying delays and developing other delay-dependent standards. This paper uses our rebuilt summation inequality to investigate the robust stability analysis issue for discrete-time neural networks that incorporate interval time-varying leakage and discrete and distributed delays. It is a novelty of this study to consider a new inequality, which makes it less conservative than the well-known Jensen inequality, and use it in the context of discrete-time delay systems. Further stability and passivity criteria are obtained in terms of linear matrix inequalities (LMIs) using the Lyapunov-Krasovskii stability theory, coefficient matrix decomposition technique, mobilization of zero equation, mixed model transformation, and reciprocally convex combination. With the assistance of the LMI Control toolbox in Matlab, numerical examples are provided to demonstrate the validity and efficiency of the theoretical findings of this research.</p></abstract>

Maritime Autonomous Surface Ships in Use with LMI and Overriding Trajectory Controller

Concepts in maritime issues such as Maritime Autonomous Surface Ships (MASS) have been known for several years. At present, it is difficult to define clear rules for the cooperation of multiple systems for autonomous control, i.e., unmanned operation, which is written in the MASS requirements for the various degrees of control (four degrees). The paper proposes a multidimensional control of a ship on a certain determined trajectory, where a model of a training ship sails autonomously in restricted waters in a port. The control algorithm is based on the synthesis of a Linear Matrix Inequalities (LMI) controller and an overriding trajectory controller. The automation is divided into two parts. The master trajectory controller converts the ship’s position and course into small velocities, which, with the help of the LMI controller through an allocation system, control the operation of the ship’s propellers. The setpoints are specific twelve trajectory points given in the form of x, y coordinates and the ship’s course. The tests were carried out under real conditions and showed a silhouette of the ship performing the maneuver and a reading of the individual speeds, wind parameters and GPS mode. The solution presented is used to address MASS 3 level control.

The Passivity of Uncertain Fractional-Order Neural Networks with Time-Varying Delays

In this paper, we study the passive problem of uncertain fractional-order neural networks (UFONNs) with time-varying delays. First, we give a sufficient condition for the asymptotic stability of UFONNs with bounded time-varying delays by using the fractional-order Razumikhin theorem. Secondly, according to the above stability criteria and some properties of fractional-order calculus, a delay-dependent condition that can guarantee the passivity of UFONNs with time-varying delays is given in the form of a linear matrix inequality (LMI) that can be reasonably solved in polynomial time using the LMI Control Toolbox. These conditions are not only delay-dependent but also order-dependent, and less conservative than some existing work. Finally, the rationality of the research results is proved by simulation.

Convex reformulations for self-optimizing control optimization problem: Linear Matrix Inequality approach

The purpose of self-optimizing control (SOC) is minimizing the steady-state economic loss of chemical processes in the presence of disturbances and measurement noises by keeping selected controlled variables (CVs) at constant set-points. In self-optimizing control, by defining a desired objective/loss function and selecting the appropriate combination of process measurements, the average loss, the worst-case loss, or both can be minimized. In general, the optimization problem of self-optimizing control is a non-convex problem and there exist some approaches to change it to a convex form by adding another constraint to the optimization problem, using branch and bound algorithm or mixed integer quadratic programming method to solve the SOC problem. Linear Matrix Inequalities (LMIs) are one of the popular and powerful tools to solve convex optimization problems and changing the optimization problems to the LMI form is gaining popularity. In parallel, for some problems that are non-convex and cannot be transformed to the LMI form, Bilinear Matrix Inequalities (BMI) have been developed. In this paper, we present; first a method to change the convex form of SOC problem to the LMI form and second, reformulate the main and non-convex SOC problem to a BMI form and then change it to the LMI form. The proposed methods are then evaluated on three benchmark processes: a binary distillation column, an evaporator, and a Kaibel column. The LMI/BMI methods are implemented using LMI Control Toolbox and PENBMI of YALMIP toolbox of MATLAB ® software. Results show that the proposed algorithm outperforms other methods in the case of structured measurement matrix H. The main benefit of LMI approach is that the desired structure of matrix H can be directly implemented in the optimization method.

Study of the TP transformation via the inverted pendulum example

This study decribes the Tensor Product (TP) based model construction through the nonlinear dynamic system of the inverted pendulum. It presents the steps of TP modeling, various weighting functions and the Linear Matrix Inequality (LMI) based approach. LMI control has been used to stabilize the nonlinear system. This study shows the quasi-Linear Parameter-Varying (qLPV) state-space modeling and the Higher-Order Singular Value Decomposition (HOSVD) based TP model transformation. Some research in this issue already exists, but only the furuta, rotary, single and parallel-type double pendulum have been examined. In this paper the TP model transformation of the inverted pendulum is analyzed in terms of stability.

Extended Dissipativity and Non-Fragile Synchronization for Recurrent Neural Networks With Multiple Time-Varying Delays via Sampled-Data Control

This paper deals with the extended dissipativity and non-fragile synchronization of delayed recurrent neural networks (RNNs) with multiple time-varying delays and sampled-data control. A suitable Lyapunov-Krasovskii Functional (LKF) is built up to prove the quadratically stable and extended dissipativity condition of delayed RNNs using Jensen inequality and limited Bessel-Legendre inequality approaches. A non-fragile sampled-data approach is applied to investigate the problem of neural networks with multiple time-varying delays, which ensures that the master system synchronizes with the slave system and is designed with respect to the solutions of Linear Matrix Inequalities (LMIs). The effectiveness of the suggested approach is established by providing suitable simulations using MATLAB LMI control toolbox. Finally, numerical examples and comparative results are provided to illustrate the adequacy of the planned control scheme.

Robust stability analysis for fuzzy stochastic Hopfield neural networks with time–varying delays

This paper investigates the delay-dependent robust stability problem of fuzzy stochastic Hopfield neural networks with random timevarying delays. Moreover, in this paper, the stochastic delay is assumed to satisfy a certain probability distribution. By introducing a stochastic variable with Bernoulli distribution, the neural networks with random time delays is transformed into one with deterministic delays and stochastic parameters. Based on a LyapunovKrasovskii functional and stochastic analysis approach, delay-probability-distribution-dependent stability criteria have been derived in terms of linear matrix inequalities (LMIs), which can be checked easily by the LMI control toolbox. Finally two numerical examples are given to illustrate the effectiveness of the theoretical results.

Comparative analysis of observer-based LQR and LMI controllers of an inverted pendulum

An inverted pendulum is a multivariable, unstable, nonlinear system that is used as a yardstick in control engineering laboratories to study, verify and confirm innovative control techniques. To implement a simple control algorithm, achieve upright stabilization and precise tracking control under external disturbances constitutes a serious challenge. Observer-based linear quadratic regulator (LQR) controller and linear matrix inequality (LMI) are proposed for the upright stabilization of the system. Simulation studies are performed using step input magnitude, and the results are analyzed. Time response specifications, integral square error (ISE), integral absolute error (IAE) and mean absolute error (MAE) were employed to investigate the performances of the proposed controllers. Based on the comparative analysis, the upright stabilization of the pendulum was achieved within the shortest possible time with both controllers however, the LMI controller exhibits better performances in both stabilization and robustness. Moreover, the LMI control scheme is effective and simple.

Robust Control for Helicopters Performance Improvement: an LMI Approach

This paper presents an LMI (Linear Matrix Inequalities) application for the design of robust controllers for multivariate systems that have multiple points of operation. Some systems change their parameters along time, then, it is necessary to switch the control for different operational points. The purpose of this controller is to ensure the stability and performance requirements of the system for different operating points with the same controller. The method uses the following concepts of predefined structures controller, LMI region, and polytopic systems. To validate the controller a linearized model of a helicopter was used. These helicopters belong to a system class of MIMO (Multiple-Input Multiple Outputs) type and present a complex dynamic in their flight modes, therefore, due to these features, this type of helicopter is a good model to implement and test the efficiency of the described method in this work. The results were satisfactory. Some limitations in its implementation were found and discussed. An LQG (Linear-Quadratic-Gaussian) controller was also designed for the same model of the helicopter just for comparison. Analyzing the settling time properties, the LMI controller presented a better response than the LQG controller.

Event-triggered H∞ synchronization for switched discrete time delayed recurrent neural networks with actuator constraints and nonlinear perturbations

In this paper, event-triggered H∞ synchronization problem is investigated for robust discrete time delayed recurrent neural networks with switching parameters, actuator constraints and non-linear perturbations. An event-triggered communication transmission scheme is adopted and an event generator is presented between the controller and sensor. Meanwhile, average dwell time approach together with the unreliable communication links are considered between the switched recurrent neural networks. Our aim is to design a controller such that, the unavoidable phenomenon of network-induced delays is fully considered, the resulting closed-loop system is exponentially stable with the disturbance attenuation level γ^>0. By utilizing techniques like improved summation inequality together with Jensen’s inequality and Lyapunov- Krasovskii functional, results are derived and formulated in terms of linear matrix inequalities (LMIs) which can be easily verified by the MATLAB LMI control toolbox. Finally, numerical examples are given to demonstrate the effectiveness and benefits of the developed stability criteria.

Synchronization of Fractional Order Fuzzy BAM Neural Networks With Time Varying Delays and Reaction Diffusion Terms

In this article synchronization of fractional order fuzzy BAM neural networks with time varying delays and reaction diffusion terms is studied. The time varying delays consist of discrete delays and distributed delays are considered. Then, some sufficient conditions black are presented to guarantee the global asymptotic stability of the error system by using Lyapunov-Krasovskii functional having the double integral terms, we utilized Jensens inequality techniques and LMI approach. Accordingly, we accomplished synchronization of master-slave fuzzy BAMNNs. The delay dependent stability conditions are set up in terms of linear matrix inequalities(LMIs), which can be productively understood utilizing Matlab LMI control tool box. At last, illustrative numerical results have been provided to verify the correctness and effectiveness of the obtained results.

Improved stability analysis for Markovian Jump Static Neural Networks with Mode-Dependent Time-Varying Delays

This paper investigates the problem of delay-dependent stability analysis for Markovian jump static neural networks (MJSNNs) with mode-dependent time-varying delays. The fundamental objective of this paper is to create novel stability criterion for the considered MJSNNs with less conservatism. A suitable Lyapunov-Krasovskii functional (LKF) is constructed with more system information. By employing integral inequality, a novel delay-dependent sufficient condition is obtained to ensure the asymptotically stability of the equilibrium point. The obtained stability condition is derived and entrenched in terms of linear matrix inequality (LMI) which can be clearly checked by MATLAB LMI control toolbox. At long last, two benchmark illustrative case are given to show the effectiveness of the theoretical result.

Improved Delay-Derivative-Dependent Stability Analysis for Generalized Recurrent Neural Networks with Interval Time-Varying Delays

In this paper, the problem of delay-derivative-dependent stability analysis for generalized neural networks with interval time-varying delays is considered. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov–Krasovskii functional (LKF) for each subinterval of delay, where the information on the lower and upper bounds of time delay and its derivative are fully exploited. Second, a new delay-derivative-dependent stability condition for time-varying delay systems with interval time-varying delays, which expressed in terms of quadratic forms of linear matrix inequalities (LMIs), and has been derived by constructing the LKF from the delayed-decomposition approach and integral inequality approach. Third, all the conditions are presented in terms of LMIs can be easily calculated by using Matlab LMI control toolbox. Fourth, the computational complexity of newly obtained stability conditions is reduced because fewer variables are involved. Finally, four numerical examples are provided to verify the effectiveness of the proposed criteria.

Stability and Dissipativity Analysis for Neutral Type Stochastic Markovian Jump Static Neural Networks with Time Delays

Abstract This paper studies the global asymptotic stability and dissipativity problem for a class of neutral type stochastic Markovian Jump Static Neural Networks (NTSMJSNNs) with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii Functional (LKF) with some augmented delay-dependent terms and by using integral inequalities to bound the derivative of the integral terms, some new sufficient conditions have been obtained, which ensure that the global asymptotic stability in the mean square. The results obtained in this paper are expressed in terms of Strict Linear Matrix Inequalities (LMIs), whose feasible solutions can be verified by effective MATLAB LMI control toolbox. Finally, examples and simulations are given to show the validity and advantages of the proposed results.