Basis Of Linear Matrix Inequalities Research Articles

Synchronization of coupled switched neural networks subject to hybrid stochastic disturbances

In this paper, the theoretical analysis on exponential synchronization of a class of coupled switched neural networks suffering from stochastic disturbances and impulses is presented. A control law is developed and two sets of sufficient conditions are derived for the synchronization of coupled switched neural networks. First, for desynchronizing stochastic impulses, the synchronization of coupled switched neural networks is analyzed by Lyapunov function method, the comparison principle and a impulsive delay differential inequality. Then, for general stochastic impulses, by partitioning impulse interval and using the convex combination technique, a set of sufficient condition on the basis of linear matrix inequalities (LMIs) is derived for the synchronization of coupled switched neural networks. Eventually, two numerical examples and a practical application are elaborated to illustrate the effectiveness of the theoretical results.

Robust finite-time PID control for discrete-time large-scale interconnected uncertain system with discrete-delay

In this paper, we investigate the decentralized proportional–integral–derivative (PID) output-feedback control problem for a class of discrete-time uncertain large-scale systems with delayed interconnections. The robust finite time stabilization of the addressed uncertain large-scale system is attained via the feedback control with the prescribed extended passive performance index. Specifically, by using an appropriate Lyapunov–Krasovskii functional, a new set of sufficient conditions is derived on the basis of linear matrix inequality which ensures the finite-time boundedness of the augmented closed-loop uncertain large-scale systems. Furthermore, cone complementarity linearization (CCL) algorithm is developed to obtain the control gain parameters. Finally, a numerical example is provided to illustrate the effectiveness of proposed control design.

Analysis of Controllability, Observability and Stabilization for a Class of Systems Described by Takagi-Sugeno Fuzzy Models by means of Fuzzy Pole Assignment

The present work is concerned to solve the problem of nonlinear robotic control systems on the basis of Takagi- Sugeno (T-S) fuzzy models. In addition, controllability and observability studies for T-S fuzzy model systems are considered for Single-Input Single-Output (SISO) and Multiple-Input Multiple-Output (MIMO) systems. In particular, the robust pole assignment approach is extended to the fuzzy field. This approach is used to design fuzzy stabilizers and fuzzy observers directly on the overall T-S fuzzy system. The latter one is the representation of the nonlinear robotic system, which is linearized around certain operation regions. The suggested method is considered for either SISO or MIMO systems. Furthermore, the method allows inducing an arbitrary behavior into the fuzzy plant in a relatively easy way. Two examples are used to verify the effectiveness of the proposed approach. The results are compared with the well-known Parallel Distributed Compensation (PDC) method, which is designed on the basis of Linear Matrix Inequalities (LMIs).

Delay-dependent Robust Dissipative Control for Singular LPV Systems with Multiple Input Delays

This paper addresses the robust dissipative control problem for the singular linear parameter-varying (LPV) systems with multiple input time-delays. First, by constructing the parameter-dependent Lyapunov functional, a delay-dependent robust dissipativity criterion for singular LPV systems with multiple state time-delays is proposed. Second, on the basis of linear matrix inequalities (LMIs) technique, a novel delay-dependent robust dissipativity-based controller for the singular LPV delay systems is designed. Furthermore, it is proved that the resultant closed-loop system via state feedback controller is admissible and strictly robustly (Q,S,R)-dissipative. Finally, the effectiveness of the proposed method is demonstrated by three numerical examples.

Robust Stabilization and H∞ Control of Cooperative Driving System with Time Delay in Variable Speed‐Limited Area from Cyber‐Physical Perspective

AbstractIn order to suppress traffic congestion and reduce traffic accidents, a cooperative driving systems with time‐varying delay and nonlinearity under uncertain external disturbances in a variable speed‐limited area is proposed from a cyber‐physical perspective. Robust stabilization of the cooperative driving system is investigated by using Lyapunov‐Krasovskii functional stability theory. Robust H∞ control is designed to guarantee that the proposed system is robustly stable. Meanwhile, sufficient conditions for the state feedback controller are proposed to attenuate the external disturbances on the basis of linear matrix inequality. Finally, some useful results are obtained from the comparisons between without control scheme, existing ACC (adaptive cruise control) scheme, and the proposed control scheme, which could suppress traffic congestion and reduce traffic accidents.

Decentralized state estimation for a large-scale spatially interconnected system

A decentralized state estimator is derived for the spatially interconnected systems composed of many subsystems with arbitrary connection relations. An optimization problem on the basis of linear matrix inequality (LMI) is constructed for the computations of improved subsystem parameter matrices. Several computationally effective approaches are derived which efficiently utilize the block-diagonal characteristic of system parameter matrices and the sparseness of subsystem connection matrix. Moreover, this decentralized state estimator is proved to converge to a stable system and obtain a bounded covariance matrix of estimation errors under certain conditions. Numerical simulations show that the obtained decentralized state estimator is attractive in the synthesis of a large-scale networked system.

Робастные регуляторы электроэнергетической системы на основе линейных матричных неравенств

Робастные регуляторы электроэнергетической системы на основе линейных матричных неравенств

Fault detection and diagnosis for delay-range-dependent stochastic systems using output PDFs

This paper investigates a new fault detection and diagnosis(FDD) scheme for delay-range-dependent stochastic systems. Compared with classical FDD problem, the measurable information in this paper is supposed to be the output probability density function(PDF), rather than the output itself. By using the square root B-spline approximation technique, the dynamic weight model of the output PDFs is established and the considered problem is converted into a nonlinear FDD problem for stochastic systems with delays. The main objective of this paper is to construct a filter based residual generator such that the fault can be detected and estimated. The FDD criteria is provided on the basis of linear matrix inequalities(LMIs). Besides, to improve the FDD performance, the tuning parameters, slack variables as well as the free-weighting matrices are applied to optimize the FDD criteria. Finally, the simulations are given to demonstrate the effectiveness of the proposed method.

Exponential Synchronization of Memristive Chaotic Recurrent Neural Networks Via Alternate Output Feedback Control

AbstractThis paper considers the global exponential synchronization problem of two memristive chaotic recurrent neural networks with time‐varying delays using periodically alternate output feedback control. First, the periodically alternate output feedback control rule is designed for the global exponential synchronization of two memristive chaotic recurrent neural networks. Then, according to the Lyapunov stability theory, we construct an appropriate Lyapunov‐Krasovskii functional to derive several new sufficient conditions guaranteeing exponential synchronization of two memristive chaotic recurrent neural networks under periodically alternate output feedback control. Compared with existing results on synchronization conditions on the basis of linear matrix inequalities of memristive chaotic recurrent neural networks, the derived results complement, extend earlier related results, and are also easy to validate in this paper. An illustrative example is provided to illustrate the effectiveness of the synchronization criteria.

Dynamics and Robust Control of an Underactuated Torsional Vibratory Gyroscope Actuated by Electrostatic Actuator

It has been shown that the underactuated MEMS gyroscopes provide inherent robustness against structural and environmental parameter variations. To further improve the performance of the systems, the electrical and mechanical coupling dynamics of the underactuated torsional gyroscopes with double oscillators actuated by a single electrostatic actuator is investigated in this paper. It is shown that the highly nonlinear coupling dynamics of the underactuated gyroscope systems can be transformed into the fifth-order linear systems even though the electrical uncertainties of the systems are considered. For the purpose of simplifying the structures of the underactuated torsional MEMS gyroscopes, an observer-based robust controller with considering structural uncertainties is presented on the basis of linear matrix inequalities (LMIs). The robust stability of the presented controller is also demonstrated by some numerical simulations on a three-degree-of-freedom underactuated MEMS gyroscope. It is shown that the LMI-based robust controller can accommodate both large initial errors in the system state and bounded uncertainties in the structural parameters of the system.

Synchronization stability in complex interconnected neural networks with nonsymmetric coupling

Some global stability criteria for arrays of linearly coupled delayed neural networks with nonsymmetric coupling are established on the basis of linear matrix inequality (LMI) method, in which the coupling configuration matrix may be arbitrary matrix with appropriate dimensions. Meanwhile, the relations of coupling matrix to stability and synchronization are discussed in detail, and some analysis methods to the synchronization stability of complex networks are also argued. The difficulty arising from the nonsymmetry of the coupling matrix has been overcome in this work. Numerical simulation is also given to verify the effectiveness of the theoretical results.

Robust residual generator design for Takagi-Sugeno fuzzy bilinear system subject to unknown inputs

In this paper, a method to design a residual generator for Takagi-Sugeno fuzzy bilinear system subject to unknown inputs and unmeasurable disturbances is proposed. The aim of this approach is to detect and isolate actuator faults despite the presence of disturbances. Such residual generator is determined on the basis of Linear Matrix Inequalities (LMIs) conditions. An example illustrates the effectiveness of the designed residual generator with unknown inputs and unmeasurable disturbances.

LMI-Based Approach for Global Asymptotic Stability Analysis of Recurrent Neural Networks with Various Delays and Structures

Global asymptotic stability problem is studied for a class of recurrent neural networks with distributed delays satisfying Lebesgue-Stieljies measures on the basis of linear matrix inequality. The concerned network model includes many neural network models with various delays and structures as its special cases, such as the delays covering the discrete delays and distributed delays, and the network structures containing the neutral-type networks and high-order networks. Therefore, many new stability criteria for the above neural network models have also been derived from the present stability analysis method. All the obtained stability results have similar matrix inequality structures and can be easily checked. Three numerical examples are used to show the effectiveness of the obtained results.

Guaranteed cost PID control for uncertain discrete-time stochastic systems with additive gain perturbations

This paper investigates a novel design method for robust nonfragile proportional-integral-derivative (PID) control that is based on the guaranteed cost control (GCC) problem for a class of uncertain discrete-time stochastic systems with additive gain perturbations. On the basis of linear matrix inequality (LMI), a class of fixed PID controller parameters is obtained, and some sufficient conditions for the existence of the GCC are derived. Although the additive gain perturbations are included in the feedback systems, both the stability of closed-loop systems and adequate cost bound are attained. As a sequel, decentralized GCC PID for a class of discrete-time uncertain large-scale stochastic systems is also considered. Finally, the numerical results demonstrate the efficiency of the proposed controller synthesis. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Synthesis of linear quadratic control laws on basis of linear matrix inequalities

Classic problems of control law construction for a linear dynamic object that is optimal by the quadratic criterion in the determinate and stochastic cases are reduced, as is known, to solving nonlinear matrix Riccati equations. It is shown that the notion of H 2-norm of a system transfer matrix makes it possible to formulate and solve the stated problems in terms of linear matrix inequalities.

Synthesis of nonfragile controllers on the basis of linear matrix inequalities

The notion of a nonfragile controller is introduced that affords the fulfillment of the aim of control at variations of its parameters from a definite class. Synthesis of nonfragile stabilizing controllers in the state and the output is carried out on the basis of linear matrix inequalities and an algorithm for the search of mutually inverse matrices.

H∞ state feedback control for generalized continuous/discrete time-delay system

In this paper, we consider the problem of designing H ∞ state feedback controller for the generalized time-delay systems with delayed states and control inputs in continuous and discrete time cases, respectively. The generalized time-delay system problems are solved on the basis of linear matrix inequality (LMI) technique considering time delays. The sufficient condition for the existence of controller and H ∞ state feedback controller design methods are presented. Also, using some changes of variables and Schur complements, the obtained sufficient condition can be rewritten as an LMI form in terms of transformed variables. The proposed controller design method can be extended into the problem of robust H ∞ state feedback controller design method easily.