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The problem of dissipative fuzzy control for singular Markovian jump systems is studied with generally uncertain transition rates. Firstly, a new Lyapunov-Krasovskii functional is established to develop the new bounded real lemma（BRL） which guarantee the system to be stochastically admissible with given dissipative performance α. Delay decomposition approach and new inequality to deal with functional are used, which can reduce the conservatism to a certain extent. Secondly, based on these ingredients, the explicit expression of the desired controller is obtained by solving a set of strict linear matrix inequalities（LMIs）. In the design process of the controller, the generally uncertain transition rates are divided into two cases, and then obtain the LMIs in two different cases. Finally, some numerical examples reflect the less conservatism and effectiveness of the method in this article. [ABSTRACT FROM AUTHOR]

The fixed-time synchronization problems are solved for fractional-order memristive neural networks. According to the voltage and current characteristics of memristors, the model of fractional-order memristive neural networks with time-varying delays is established. Different from the traditional calculation method of memristive synaptic weights based on the maximum absolute value, by introducing some transformations, using differential inclusion theory and set-valued maps, the fractional-order memristive neural networks are transformed into a type of fractional-order systems with uncertain parameters in the framework of Filippov solution. Based on the fixed-time stability theory and the theory of measurable selection, the sufficient conditions of fixed-time synchronization are given by constructing Lyapunov function and using inequality techniques, and the calculation formula of the upper bound for the synchronization time is given. By designing an appropriate state feedback controller, the master-slave systems can reach fixed-time synchronization, and the upper bound for the synchronization time is independent of the initial state for the systems. The simulation example shows that the designed controller makes the systems achieve synchronization quickly. [ABSTRACT FROM AUTHOR]

The projective synchronization of fractional quaternion neural networks with time-varying delays was studied. Instead of transforming the fractional quaternion neural network system into 2 complex-valued systems or 4 real-valued systems, the means of treating the quaternion network system directly as a whole was applied. Under a rational controller, through the construction of a suitable Lyapunov function and with some inequality techniques, the sufficient criteria for the projective synchronization of fractional quaternion neural networks with time-varying delays were obtained. The numerical simulation example shows the validity and feasibility of the conclusions. [ABSTRACT FROM AUTHOR]

The non-fragile decentralized H∞ control problems for uncertain singular fractional-order interconnected systems with commensurate order 0<α<1 are studied. The existing criteria for admissibility and H∞ performance of singular fractional-order linear systems are extended. And the new criteria are given in the form of strict linear matrix inequality. Based on those conclusions, through analysis of the special structure of interconnected systems, under additive and multiplicative disturbances of controller gains, sufficient conditions for the existence of non-fragile decentralized H∞ controllers and their design methods are given by using linear matrix inequalities and matrix decomposition technology. In the design process of controllers, the interconnected matrices are not limited and strict linear matrix inequality criteria are obtained, which reduce conservatism of the systems to a certain extent. The effectiveness of the proposed methods is verified by LMI toolbox and Simulink numerical simulation. [ABSTRACT FROM AUTHOR]

An improved robust predictive control method is proposed for a class of multicellular descriptive LPV systems with bounded state disturbances, and an output feedback controller is designed to ensure the asymptotic stability of the systems. To offset the bounded state disturbance, the controller considered the undisturbed LPV system, and based on the off-line state observer, the linear matrix inequality is used to solve the minimum-maximum optimization problem in the infinite time domain of predictive control. Then the off-line state observer is adopted to obtain the difference between the estimated values of the disturbed LPV system and the undisturbed LPV system, and the feedback gain of the guaranteed performance is determined, so as to obtain the optimal offset that makes the disturbed LPV system asymptotically stable, which is combined with the undisturbed system control law as the optimal control law and applied to the actual system. The experimental results show that the improved robust predictive control method can obtain better control performance, and improve the stability of the system and the efficiency of solving optimization problems. The simulation experiments verifies the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

An observer-based fault estimation strategy is proposed to solve the fault problem of yaw rate sensor. Firstly， considering the uncertainty caused by tire cornering stiffness characteristics and nonlinear disturbance in the system， the mathematical model of vehicle four-wheel steering system is established. Then， an observer-based sensor fault estimation strategy is designed， and the observer gain is solved by Lyapunov function and linear matrix inequality method. Finally， the effectiveness of the sensor fault estimation strategy is verified by Carsim and Simulink simulation. The results show that the proposed strategy can estimate the system state and sensor fault well when the sensor fault occurs. It can provide key information for vehicle safety and stability system， and provide technical support for the next step of sensor fault-tolerant control [ABSTRACT FROM AUTHOR]

For singularly perturbed bilinear systems with input constraints and time-varying delays， a design method of state feedback passive controller is proposed to eliminate the effects of delay factors and input saturation on the closed-loop system. Firstly， in the framework of Lyapunov stability theory and passivity theory， using linear matrix inequality technology and convex combination technology， the design of the system state feedback controller is reduced to solve a set of linear matrix inequalities independent of the upper bound of time delay. The obtained controller makes the closed-loop system asymptotically stable and passive， and constructs the estimation of the elliptic domain of attraction related to singular perturbation parameters. The above method is extended to the system without time delay and external input. Then， a convex optimization problem is proposed to obtain the maximum estimation of the domain of attraction of the closed-loop system， and the stability bound of singular perturbation parameter is also one of the design objectives. Finally， numerical simulation examples illustrate the effectiveness of the proposed theoretical method. [ABSTRACT FROM AUTHOR]

Based on the Lyapunov stability theory, the matrix analysis method and the linear matrix inequality method, etc, the generalized H2 control of singularly perturbed uncertain-control time-varying delay systems with control input and disturbance input, was studied. A memory state generalized H2 controller was designed, and the decision theorem for the specific design method was given. With a new lemma for delay-dependent and delay-independent cases, the relatively less conservative stability criterion was derived. The obtained results were linearized, the selected numerical examples were used to verify the effectiveness and feasibility of the derived conclusions. The results show that, the closed-loop system is asymptotically stable in the whole range from zero to the singular perturbation upper bound, which expands the generalized H2 stability space and reduces the L2-L∞ performance index. The comparison of the stability state parameter index with the related literatures indicate that, the proposed method has certain advantages and less conservatism, and is suitable for standard and non-standard cases. [ABSTRACT FROM AUTHOR]

In order to improve the stability of vehicles under complex operating conditions when the actuator fails, a fault reconstruction strategy based on observer was designed for the electronic stability control system of uncertain vehicles. Considering the uncertain factors in the four-wheel steering system, a dual-input and dual-output mathematical model was established. An augmented system is constructed and the observer gain matrix is obtained by Lyapunov function and linear matrix inequality techniques. The effectiveness of the proposed method is verified by MATLAB/ Simulink and Carsim joint simulation. The results indicate that there is some certain deviation between the observer state estimated value and the real value when the fault occurs. However, the estimated value can quickly track the real value to realize fault diagnosis. Compared with the front-wheel steering system, the four-wheel steering system can significantly enhance the stability and safety of the vehicle at high speed. [ABSTRACT FROM AUTHOR]

The research of gene regulatory networks (GRNs) and their dynamic models is important in the post-genome era. Qualitative analysis of GRNs and their dynamics is of great significance to the understanding of organisms from a systematic perspective. A stochastic GRN model with time-varying delay and Markovian switching was proposed to study the properties of mean-square synchronization and stochastically passive synchronization. Through the design of an appropriate Lyapunov-Krasovskii functional (LKF), the sufficient conditions for mean-square synchronization and stochastically passive synchronization were obtained by means of the Lyapunov stability theory, the linear matrix inequality method and the random analysis techniques. In addition, the comparison between the results of this paper and some other literatures shows that, the present results have markable theoretical meaning. The numerical simulation illustrates the validity of the obtained sufficient conditions. [ABSTRACT FROM AUTHOR]

A new design method of the static output feedback control for singular systems is proposed. Firstly, by using the matrix trace inequality, the admissibility issue of singular systems is introduced and the algebraic criteria of admissibility for this kind of systems is established. Secondly, based on the admissibility analysis result, the sufficient condition for static output feedback controller design is obtained to ensure the admissibility for closed-loop systems. Meanwhile, the solving method of matrix trace inequality is given to obtain the gain matrix. Different from the design method of static output feedback controller via linear matrix inequalities, the proposed method does not need the special requirement setting of output matrix. Finally, three numerical examples illustrate the feasibility and effectiveness of the proposed theoretical method, which also applies for the output feedback controller design of normal systems. [ABSTRACT FROM AUTHOR]

Based on the intermediate estimator, the fault estimation problem was studied for the nonlinear systems with time delays and multiple faults. Intermediate variables and intermediate estimators were designed to realize fault estimation and avoid the limitation of observer matching conditions. According to the Lyapunov stability theory and the linear matrix inequality method, the error systems are asymptotically stable. At last, through the MATLAB simulation, the effectiveness of the proposed method was verified. [ABSTRACT FROM AUTHOR]

The concept of passivity is extended to T-S fuzzy generalized switched systems, and then the passivity problem for asynchronous situation between a class of subsystem switching and observer-based controller switching is studied. Firstly, by using piecewise Lyapunov function and model dependent average dwell time, the sub-systems with excess passivity can compensate for the sub-system with insufficient passivity, so as to ensure the overall passivity of the switched system.Afterwards, the sufficient conditions for globally uniformly exponential stability and strictly exponential passivity of T-S fuzzy generalized switched systems with time delay are obtained by using the linear matrix inequality method, and the corresponding observers and controllers are designed. Finally, numerical examples are provided to validate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This study aims at estimating the sensor fault interval of attitude control system of quadrotor UAV based on zonotopes. The UAV’s nonlinear system is linearized by Taylor series expansion and the original system is transformed into an equivalent generalized system by considering the sensor fault as an augmented state. A robust augmented state observer is design by using H∞ technique. By solving the linear matrix inequalities, the fault estimation of sensor in quadrotor UAV attitude control system is obtained. The fault interval and algorithm design can be obtained by the analysis of zonotopes. Based on the MATLAB simulation platform, taking the quadrotor UAV attitude control sensor failure system as the object, the feasibility and effectiveness of the interval estimation proposed in the study are verified. [ABSTRACT FROM AUTHOR]

For the asymplotic synchronization problem of neutral coupled complex networks with unknown control nodes, an adaptive pinning controller which is more suitable to engineering applications is designed, and the design basis of the adaptive update law is provided in the present study. According to the generalized Ito formula, linear matrix inequality and Lyapunov stability theory, the sufficient conditions for asymptotic synchronization of neutral coupled complex networks are given. Through a numerical simulation, the minimum number of pinned nodes required for synchronization is calculated, which further verifies the validity of the obtained results. [ABSTRACT FROM AUTHOR]

The problem of strictly asynchronous dissipative control for a class of continuous time nonlinear generalized Markov jump systems under Takagi-Sugeno fuzzy rules is studied. Firstly, by constructing a less conservative mode independent Lyapunov function, the sufficient conditions for stochastic stability and strict dissipation of generalized system are discussed. Then, the hidden Markov model that is widely used in practice is introduced. By combining the state transition probability with the conditional probability of the hidden Markov process, and through Schur transformation, a fuzzy state feedback controller is designed, which can operate asynchronously with the original system, so as to ensure the stochastic stability and strict dissipation of the closed-loop system. Finally, numerical simulation using Matlab linear matrix inequality(LMI) toolbox is applied to verify the effectiveness of the conclusion. [ABSTRACT FROM AUTHOR]

Exponential stability and L2gain control of singular nonlinear switching systems with pulses are studied. The pulse and nonlinear control are added to the system to make it of more practical significance. First, an effective design method of state feedback controller with L2 - gain control is proposed by constructing the Lyapunov function, and the state feedback controller in the system is improved to make the closed-loop system exponentially stable. Secondly, by using the linear matrix inequality and the model dependent average dwell time method, the sufficient conditions for exponential stability and L2- gain performance are given. Finally, numerical examples and image simulation are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

The passivity for a class of fractional-order delayed complex-valued neural networks with uncertainties was studied. The complex-valued neural network was not divided into 2 real-valued neural networks, but treated as a whole. Through construction of the appropriate Lyapunov function and application of the inequality technique, the sufficient criterion in the form of the linear matrix inequality was established to ensure the passivity of the considered neural networks. Numerical examples and simulations verify the feasibility and effectiveness of the obtained conclusion. [ABSTRACT FROM AUTHOR]

The stabilization problem for a class of networked control systems with aperiodic sampling and stochastic packet dropouts was studied. Other than the traditional view that a time delay was often a negative factor of system stability, the positive effect was considered and a novel active time-delay control method was proposed to stabilize the systems. To analyze the positive effects of the time delay control and to obtain some less conservative conclusions, the aperiodic sampled-data system with stochastic packet dropouts was firstly modeled as a stochastic impulsive switched system with a fixed switching law. Then a new separation lemma was presented in a mean square sense to analyze the stability of the stochastic impulsive switched system. Based on the loop-functional method and the proposed separation lemma, the mean square stability criterion for the stochastic impulsive switched system was obtained in terms of linear matrix inequalities. Furthermore, the refined mean square stability criterion was given with an interval segmentation technique. Finally, a classical numerical example illustrates the validity of the obtained stability criteria and the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

The admissibility issue of discrete singular systems was mainly studied. Applying restricted equivalent transformations of the discrete singular system， a new necessary and sufficient condition was proposed to ensure discrete singular system admissible. By introducing an intermediate matrix to configure partial poles of system matrix such that the closed-loop system is regular， a state feedback controller was designed to make the closed-loop system admissible. Using similar methods， the controller design problem of uncertain discrete singular systems was discussed as well， a sufficient condition of robust stabilization for uncertain discrete singular systems was obtained. All the methods proposed in this article are strictly linear matrix inequalities(LMI). Two numerical examples verify the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The control problem for a class of nonlinear generalized delay Markov jump systems with generally uncertain transition rate is studied. First, a hybrid controller composed of a linear controller and an adaptive controller is designed for the unknown nonlinear parameters in the system, and a Lyapunov functional is constructed to make the trajectory of the system approach to the state space surface and the closed-loop system is admissible, satisfying H∞ criteria -. Furthermore, considering the characteristics of the generally uncertain transition rates matrices, a strict linear matrix inequality is constructed to make the conclusion more general. Finally, the effectiveness and feasibility of this control method are verified by numerical examples and image simulation. [ABSTRACT FROM AUTHOR]

In order to make active air suspension have a better vibration control effect while driving, dynamic equation of parameter uncertainty two-degree-of-freedom quarter-vehicle suspension model and non-stationary pavement excitation model are established, analyzing and optimizing active suspension control under linear matrix inequalities with robust H∞ control theory. Under the time domain hard constraints, H∞ state feedback control strategy is proposed and used in the design of the active suspension control system of the quarter vehicle model. The stability of the controller is obtained through time domain analysis and robust parameter stability analysis. For non-steady running roads, the use of a robust H∞ control strategy can effectively improve the riding comfort under the given constraint control force, reduce the body acceleration by about 40% and meet the requirements of limit suspension dynamic deflection of 0.08 m and tire dynamics load of 1 500 N, which improves the vehicle’s handling stability and ride comfort. [ABSTRACT FROM AUTHOR]

For the problem of finite time delay-dependent state feedback stabilization of networked control systems with bilateral stochastic time-delay and bilateral packet loss, the basic idea was to transform packet loss into time delay by introducing a time offset and transformed time-delay into state delay. It gave the probability formula of continuous packet loss based on the full probability formula, and used the Markov chain to characterize the variation law of time-delay. It gave the improved finite time delay correlation stability criterion in the form of linear matrix inequality, and verified the effectiveness of the proposed method by numerical simulation. [ABSTRACT FROM AUTHOR]

The finite-time stability of fractional-order linear differential systems with time delays was studied. Firstly, with a new Lyapunov function and the linear matrix inequality, some sufficient conditions for the finite-time stability of fractional linear differential systems with time delays were derived. Then, under the action of a state feedback controller, some conditions for the finite-time stability of fractional differential closed-loop systems with time delays were given, and the design method for the controller was given. In the end, the effectiveness of the theoretical results was illustrated with two examples. [ABSTRACT FROM AUTHOR]

With the Lyapunov stability theory, the linear matrix inequality method, the time delay piecewise analysis method, the matrix analysis method and the free weight matrix method, the stability of singularly perturbed filter error dynamic systems with time-varying delays and uncertain structures was studied on the basis of the previous filter design theory. Through construction of a new Lyapunov function, with a new cross-term definition method and according to the system characteristics, a new criterion for stability of filter error dynamic systems in 2 cases of time delay dependence and time delay independence was derived. Finally, the selected numerical example illustrates the effectiveness and feasibility of the obtained results. [ABSTRACT FROM AUTHOR]

This paper proposed a novel robust controller to ensure the security and stability for a class of cyber-physical systems subject to the effects including actuator attacks, external disturbances, and encoder/decoder mismatches. An optimized H2 performance in the form of linear matrix inequality solved the linear gain of the constructed controller. The nonlinear structure of the control included two parts: one aimed to eliminate the influence of external disturbance and quantization error, and the other part compensa ted the actuator attack by means of adaptive estimations of unknown actuator attack parameters. Finally, the simulation results show that the controller guarantees uniform ultimate boundedness of the closed-loop dynamical system, which shows the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposed two containment control algorithms for first-order/second-order multi-agent systems for discrete-time flocking motion problems. By using modern control theory, algebraic graph theory and linear matrix inequalities to analyze the proposed control algorithm, this paper obtained convergence conditions in a finite time for flocking motion of multiagent systems with interference under discrete-time conditions. Finally, by using the LMI toolbox in numerical simulation, it determined the range of positive definite matrices. The simulations illustrate the correctness of the conclusion. [ABSTRACT FROM AUTHOR]

The consensus control method is studied for consensus tracking of leader in multi-agent system under directed switching topology. The consensus tracking problem of leader is transformed into the stability problem of low-dimensional system by using Laplacian matrix with leader. The sufficient con¬ditions satisfying the transient response index are given. Lyapunov function and linear matrix inequality are used to analyze the stability of the system, and the design method of distributed controller and the average dwell time condition are obtained. The proposed method can be used to make the states of the system tend to be identical rapidly with smaller oscillation when the system is affected by random external disturbance. The multi-UAV system was simulated with considering the transient response, and without considering the transient response and external disturbance. The results show that the Hx consensus con¬troller considering the transient response can attain the consensus faster and more smoothly than the con¬troller without considering the transient response, which meets the transient response performance index [ABSTRACT FROM AUTHOR]

Aim at the problem of the delay dependent robust dissipative problem of uncertain neural networks with additive time-varying delays, this paper studied a generalized activation functions. Different from previous studies, it considered some sufficient information on neuron activation function and additive time-varying delays. It constructed a suitable LKF with some new integral terms, and estimated their derivative by using newly developed single integral inequality that included Jensen's inequality and Wirtinger-based integral inequality as a special case. It established a new delay-dependent less conservative global asymptotic stability and dissipative criteria in the form of linear matrix inequalities ( LMI ) technique. Finally, this paper verified the validity of the proposed theory by calculation and numerical simulation. [ABSTRACT FROM AUTHOR]

The fault detection problem is investigated for a class of networked systems with sensor saturation and communication constraint. A novel event - triggered mechanism is introduced to save limited network resource in the sensor - to - filter channel. After properly augmenting the states of the original system and the fault detection filter，the addressed fault detection problem is converted into an auxiliary H∞ filtering problem. By utilizing Lyapunov stability theory and free - weighting matrix technique，the sufficient conditions for the existence of the fault detection filter is established in terms of linear matrix inequalities，and the corresponding optimal filter parameters can be easily derived by solving a convex optimization problem via a semi - definite program method. Finally，a numerical example is provided to illustrate the validity of the event-triggered fault detection scheme. [ABSTRACT FROM AUTHOR]

In order to study the problem of H∞ control for a class of neutral time-delay interconnected systems, the decentralized memory feedback controller is designed when the delay time has little influence on the system and the stability of the system is analyzed by using Lyapunov function theory, free weighted matrix and Newton-Leibniz formula. Sufficient conditions are given for the system to remain stable and satisfy the H∞ performance index in the presence of external disturbances by using linear matrix inequalities. Finally, the numerical simulation results show that the proposed control method not only guarantees the stability of the controlled system, but also ensures H∞ performance index when there external interference. [ABSTRACT FROM AUTHOR]

For a class of networked nonlinear parameter-varying systems with time-varying delays and global Lipschitz nonlinearities, this paper studied the fault-tolerant problem when external disturbances, random actuator and sensor faults existed simultaneously. It modeled the randomly occurring faults as Bernoulli distributed white sequences with known conditional probability distributions, and handled time-varying delays by the free weight matrix method. Based on Lyapunov-Krasovskii stability theory and LMI methods, the paper derived sufficient conditions for the existence of the H∞ fault-tolerant controller. It used the approximate basis function and the grid technique to turn the problem of solving an infinite-dimensional linear matrix inequalities into the problem of solving a finite-dimensional linear matrix inequalities. Then it obtained the corresponding fault-tolerant controller gains. Finally, numerical simulation verified the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The synchronization problem of master-slave systems with multiple time-varying delays based on the event-triggered mechanism was studied. The proposed event-triggered mechanism can effectively reduce data transmission and mitigate the pressure of network bandwidth during the synchronization process of master-slave systems. With the Lyapunov stability theory and the linear matrix inequality method, the sufficient conditions for the synchronization of master-slave systems with multiple time-varying delays were obtained. Finally, the effectiveness of the proposed synchronization criterion was verified through the MATLAB simulation. [ABSTRACT FROM AUTHOR]

The state estimation of complex-valued neural networks with leakage delay and both discrete and distributed additive time-varying delays was studied. In the case where the activation function of the network was not required to be separated, through construction of the appropriate Lyapunov-Krasovskii functionals, and with the free weight matrix, the matrix inequality and the reciprocal convex combination method, the state of the neuron was estimated by means of observable output measurements. In addition, complex-valued linear matrix inequalities related to time delays were given to ensure the global asymptotic stability of the error-state model. Finally, numerical simulation examples verify the validity of the theoretical analysis. [ABSTRACT FROM AUTHOR]

A robust multi-objective linear parameter-varying (LPV) control method based on pole assignment in specified region is proposed for longitudinal flight control of air-breathing hypersonic vehicle with wave-rider configuration. A longitudinal nonlinear mechanism model of air-breathing hypersonic vehicle is presented, which is used for obtaining its rigid LPV model. A design method of LPV state feedback control system based on pole assignment in specified region is proposed. The robust stability, disturbance rejection and tracking performance of the system are constrained to realize the multi-objective robust tracking control of LPV system by extended linear matrix inequality. The conservatism of this method is reduced by introducing the slack variables to decouple the Lyapunov function matrix and system matrix. The designed controller is applied to the nonlinear mechanism model of hypersonic vehicle for simulation proof. The simulated results show that the designed controller can be used to make the closed-loop feedback control system effectively track the change of command signals, and the system has good dynamic performance and strong anti-interference ability. [ABSTRACT FROM AUTHOR]

Dynamic stability of a fixed canard dual-spin projectile under the condition of arbitrary timevarying roll angle input is investigated. Force equations and moment equations are presented in body fixed plane frame for fixed canard dual-spin projectile, and a state space model for angular motion is established. Dynamic stability is addressed by using Lyapunov method. The dynamic stability of projectile can be determined by solving a Riccati-type linear matrix inequality. The stability factor equation is derived by using complex square root calculation method, and the H_∞ norm of absolute stability is defined based on the bounded real lemma. Absolute stability criteria for fixed canard dual-spin projectile is proposed, including stability factor constraint and H_∞ norm constraint of absolute stability, and the correctness of stability criteria is validated by using exterior ballistic simulation results. [ABSTRACT FROM AUTHOR]

By means of the differential geometry method and the robust H○∞ control theory， a robust H○∞ control strategy for active seat suspension and vehicle active suspension based on differential geometry method is proposed. On the basis of establishing the three-degree-of-freedom model of the "car-chair" vehicle， considering the nonlinear characteristics of the elastic force and damping force of seat suspension and vehicle suspension， the differential geometry method and the nonlinear state feedback transformation method are applied to precisely linearize the active suspension nonlinear system. Then， the vertical accelerations of the chassis and the seat are taken as the control targets， and the robust suspension H○∞ controller of seat suspension and vehicle suspension is designed with the wheel dynamic displacement and the vehicle suspension deflection range less than the specified value as the constraint conditions. The simulation experiment with Matlab/Simulink is carried out to verify the effectiveness and feasibility of the integrated variable gain LQR control method. [ABSTRACT FROM AUTHOR]

The observer for the uncertain fractional-order system with sensor fault and system measurement noise is developed. By using the method of augmented matrix and the invariant property of matrix rank， the uncertain fractional-order system is augmented into the singular fractional-order uncertain system. Based on the linear matrix inequality approach of stability criterion for fractional-order systems， an asymptotic stability criterion of the error dynamic system with fractional-order satisfying 1 [ABSTRACT FROM AUTHOR]

The robust fault diagnosis of THPFSY-2double-tank under disturbance and fault was studied in this paper. According to the physical model of the double-tank system, a T-S fuzzy model of the system was established by local linear method. Then by introducing a reference model, a generalized residual error equation was established. At the same time, the problem of fault diagnosis was converted into a typical system robust control problem. Linear matrix inequalities (LMI) conditions for the optical solutions were given according to the bounded real lemma (BRL). Finally, effectiveness of the proposed algorithm was verified by Matlab simulation. [ABSTRACT FROM AUTHOR]

The stabilization problem was studied for a class of Markov jump linear systems subject to actuator saturation， whose transition rates are piecewise homogeneous. Firstly， by using appropriate Lyapunov functional and ellipsoidal invariant set theory， the attraction domain of system in mean square sense was estimated to get the sufficient conditions with constraints of linear matrix inequalities for the closed-loop systems. Then， a convex optimization problem was solved to get the maximum domain of attraction in mean square sense and the state feedback controller gain. Finally， the effectiveness of the results was verified by a numerical example. [ABSTRACT FROM AUTHOR]

Ｔｈｅ ｒｏｂｕｓｔ ｆｉｎｉｔｅ-ｔｉｍｅ ｃｏｎｔｒｏｌ ｐｒｏｂｌｅｍ ｕｎｄｅｒ ｔｈｅ ｃｏｎｓｔｒａｉｎｔ ｏｆ ｅｎｅｒｇｙ-ｔｏ-ｐｅａｋ ｐｅｒｆｏｒｍａｎｃｅ ｉｎｄｅｘ ｗａｓ ｉｎｖｅｓｔｉｇａｔｅｄ ｆｏｒ ｌｉｎｅａｒ ｓｙｓｔｅｍｓ ｗｉｔｈ ｄｅｌａｙｓ. Ｎｏｒｍ-ｂｏｕｎｄｅｄ ｕｎｃｅｒｔａｉｎｔｉｅｓ ｗａｓ ｉｎｃｌｕｄｅｄ ｉｎ ｔｈｅ ｃｏｅｆｆｉｃｉｅｎｔ ｍａｔｒｉｃｅｓ ｏｆ ｓｙｓｔｅｍｓ ａｎｄ ｄｉｓｃｒｅｔｅ ａｎｄ ｄｉｓｔｒｉｂｕｔｅｄ ｄｅｌａｙｓ ｗｅｒｅ ｉｎｃｌｕｄｅｄ ｉｎ ｔｈｅ ｓｔａｔｅｓ. Ａ Ｌｙａｐｕｎｏｖ ｆｕｎｃｔｉｏｎａｌ ｉｎｖｏｌｖｉｎｇ ａ ｐａｒａｍｅｔｅｒ ｗａｓ ｉｎｔｒｏｄｕｃｅｄ. Ｉｔｓ ｅｘｐｏｎｅｎｔｉａｌ ｇｒｏｗｔｈ ｗａｓ ｃｈｅｃｋｅｄ ｆｏｒ ｂｏｕｎｄｉｎｇ ｔｈｅ ｓｔａｔｅｓ ａｎｄ ｏｕｔｐｕｔｓ. Ｔｈｅｎ, ｓｕｆｆｉｃｉｅｎｔ ｃｏｎｄｉｔｉｏｎｓ ｗｅｒｅ ｄｅｒｉｖｅｄ ｇｕａｒａｎｔｅｅｉｎｇ ｔｈａｔ ｔｈｅ ｃｌｏｓｅｄ-ｌｏｏｐ ｓｙｓｔｅｍｓ ａｒｅ ｆｉｎｉｔｅ-ｔｉｍｅ ｂｏｕｎｄｅｄ ａｎｄ ｓａｔｉｓｆｙ ｐｒｅｓｃｒｉｂｅｄ ｅｎｅｒｇｙ-ｔｏ-ｐｅａｋ ｐｅｒｆｏｒｍａｎｃｅ ｉｎｄｅｘ ｆｏｒ ａｌｌ ａｄｍｉｓｓｉｂｌｅ ｕｎｃｅｒｔａｉｎｔｉｅｓ. Ｗｈａｔ'ｓ ｍｏｒｅ, ｔｈｅ ｃｏｎｔｒｏｌ ｌａｗ ｗａｓ ｏｂｔａｉｎｅｄ ｓｉｍｕｌｔａｎｅｏｕｓｌｙ. Ｔｈｅｓｅ ｃｏｎｄｉｔｉｏｎｓ ｗｅｒｅ ｆｏｒｍｕｌａｔｅｄ ｉｎ ｔｅｒｍｓ ｏｆ ｌｉｎｅａｒ ｍａｔｒｉｘ ｉｎｅｑｕａｌｉｔｉｅｓ ｗｉｔｈ ａｎ ｅｉｇｅｎｖａｌｕｅ ｃｏｎｓｔｒａｉｎｔ. Ｔｈｒｏｕｇｈ ｔｒａｎｓｆｏｒｍｉｎｇ ｔｈｅ ｃｏｎｓｔｒａｉｎｔ ｔｏ ｎｏｎｌｉｎｅａｒ ｍａｔｒｉｘ ｉｎｅｑｕａｌｉｔｉｅｓ, ａ ｃｏｎｅ ｃｏｍｐｌｅｍｅｎｔａｒｉｔｙ ｌｉｎｅａｒｉｚａｔｉｏｎ ａｌｇｏｒｉｔｈｍ ｗａｓ ｄｅｓｉｇｎｅｄ ｔｏ ｓｏｌｖｅ ｓｕｃｈ ｍａｔｒｉｘ ｉｎｅｑｕａｌｉｔｉｅｓ. Ａｎ ｅｘａｍｐｌｅ ｗａｓ ｐｒｅｓｅｎｔｅｄ ｔｏ ｓｈｏｗ ｔｈｅ ｅｆｆｅｃｔｉｖｅｎｅｓｓ ｏｆ ｔｈｅ ｐｒｏｐｏｓｅｄ ｍｅｔｈｏｄ. [ABSTRACT FROM AUTHOR]

The fuzzy H∞ controller design problem was studied for steam valve opening of multi-machine power systems which consisting of turbo-generators with mixed time-varying delays. The mixed time-varying delays include the interval retarded-type discrete delay， the neutral-type discrete delay and the time-varying distributed delays. Fuzzy models were established， and the controllers of the systems were designed. Linear matrix inequalities (LMIs)-based H∞ stability conditions were derived. Moreover， the results were expanded to different conditions of time-delay， including H∞ stability condition with the fast time-varying distributed delays (i.e. the derivatives of distributed delay is larger than 1). Therefore， the obtained results are new and less conservative. Finally， simulation results for the steam value opening of three-machine infinite bus systems were provided to verify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Based on the integrated models of ‘vehicle-seat-people'， an integrated vehicle seat and suspension robust H∞ integrated control strategy was proposed by using linear matrix inequalities (LMI) technique. An H∞ state feedback controller of integrated vehicle seat and suspension was designed， with the PSD of vertical body acceleration chosen as the controlled outputs and the limits of dynamic suspension deflection， relative dynamic tire load， and integrated control force chosen as the constrained outputs. The MATLAB simulation was employed in the paper， and the simulation results confirm the feasibility and effectiveness. The analysis results provide a fundamental basis for the study of active control suspension system. [ABSTRACT FROM AUTHOR]

For the networked control systems with uncertain time delay, the unknown disturbances and the modeling error were transformed into the matrix which met the given constraint condition, this paper set up the model of parameter uncertainty networked control systems. Based on Lyapunov stability theory, it proved the asymptotic stability for the system, and designed the robust H∞ controller by using LMI. In the simulation experiment, it compared the state response under diverse time delay conditions, and the results show that the robust H∞ controller has the robustness and can solve the uncertainties of modeling error, disturbance and time delay for the control systems. [ABSTRACT FROM AUTHOR]

The global asymptotical stability analysis for genetic regulatory networks with time delays is concerned. By using Lyapunov functional theorem, employing some free-weighting matrices, this paper presented some new delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) to guarantee the delayed genetic regulatory networks to be asymptotically stable. By using the auxiliary matrix E and defining a more general regulatory function, it obtained the less conservative stability criterion which had more wider application range. The results can provide some reference for the design of gene chip. Experimental results demonstrate the usefulness of the main results and less conservativeness of the proposed method. [ABSTRACT FROM AUTHOR]

An optimizing design method for NCSs is presented to solve this kind of problems in the design of common NCSs controller with clock-driven sensors, event-driven controllers and actuators. In the design of networked control systems (NCSs) based on Lyapunov stability theory and linear matrix inequality (LMI), the number of variables in LMI often exceeds the number of LMI constraints, which may present the difficulty in solving the parameters of controller. The optimal controller parameters can be found on the basis of the gradient optimization. The simulation results show the effectiveness of the present method for UUV heading control system. [ABSTRACT FROM AUTHOR]

An observer-based H∞, controller; design method for discrete-time piecewise affine systems is presented. The basic idea is to construct dissipation inequality with piecewise-quadratic Lyapunov function to guarantee the stability and H∞ performance of the closed-loop systems. By approximating polytopic operating regions with ellipsoids and using the singular value decomposition technique to treat the constraint of matrix equality, the minimum problem of the H∞ performance index is transformed as a convex optimization problem involving linear matrix inequalities (LMIs), which are numerically feasible with commercially available LMI software. A numerical example is also given to verify the proposed theoretical results. [ABSTRACT FROM AUTHOR]

Aiming at the problem of uncertainty and state time delay disturbances in vehicle lane keeping control, a self-tuning sliding mode control method is proposed. With the method firstly the sufficient condition for the existence of integral sliding surface is given by applying linear matrix inequality theory, so that the system has complete invariance to uncertainty and state time delay disturbances under sliding mode. Then bipolar Sigmoid function is introduced to replace signum function and a sliding mode controller with self-tuning capability is designed based on Lyapunov stability theory so that the switching gain and the boundary layer thickness of Sigmoid function can be adaptively adjusted to mitigate the phenomena of the excessive quantity and chattering of sliding mode controller output. Finally, the simulation results of vehicle lane keeping control on curved road verify the feasibility and effectiveness of the control method. [ABSTRACT FROM AUTHOR]