H∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay

In this paper, H∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H∞ performance indices is induced, and then a strategy for H1 state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach.     

H_∞ Synchronization of Chaotic Systems via Delayed Feedback Control

The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality (LMI). A numerical simulation is also presented to validate the effectiveness of the developed theoretical results...     

Robust H_∞ Controller Design for Uncertain Neutral Systems via Dynamic Observer Based Output Feedback

In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.     

H∞ Synchronization of Chaotic Systems via Delayed Feedback Control

The H∞ synchronization problem for a class of delayed chaotic systems with external disturbance is investigated. A novel delayed feedback controller is established under which the chaotic master and slave systems are synchronized with a guaranteed H∞ performance. Based on the Lyapunov stability theory, a delay-dependent condition is derived and formulated in the form of linear matrix inequality (LMI). A numerical simulation is also presented to validate the effectiveness of the developed theoretical results.     

H_∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay

In this paper, H∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H∞ performance indices is induced, and then a strategy for H∞ state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach.     

Improved Parameter-dependent H_∞ Filtering for Polytopic Delta Operator Systems

The problem of H∞ filtering for polytopic Delta operator linear systems is investigated. An improved H∞ performance criterion is presented based on the bounded real lemma. Upon the improved performance criterion, a sufficient condition for the existence of parameter-dependent H∞ filtering is derived in terms of linear matrix inequalities. The designed filter can be obtained from the solution of a convex optimization problem. The filter design makes full use of the parameter-dependent approach, which leads t...     

Improved Results on Robust H∞ Control of Uncertain Discrete-time Systems with Time-varying Delay

In this paper,the robust H∞ control problem for uncertain discrete-time systems with time-varying state delay is considered.Based on the Lyapunov functional method,and by resorting to the new technique for estimating the upper bound of the difference of the Lyapunov functional,a new less conservative sufficient condition for the existence of a robust H∞ controller is obtained.Moreover,the cone complementary linearisation procedure is employed to solve the nonconvex feasibility problem.Finally,several numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.     

Adaptive H_∞ Control for Nonlinear Hamiltonian Systems with Time Delay and Parametric Uncertainties

This paper addresses the adaptive H∞ control problem for a class of nonlinear Hamiltonian systems with time delay and parametric uncertainties. The uncertainties under consideration are some small parameter perturbations involved in the structure of the Hamiltonian system. Both delay-independent and delay-dependent criteria are established based on the dissipative structural properties of the Hamiltonian systems and the Lyapunov-Krasovskii functional approach. In order to construct the adaptive H∞controller, the situation that the parameter perturbation is inexistent in the system is also studied and the controller is designed.The adaptive H∞ control problem is solved under some sufficient conditions which ensure the asymptotic stability and the L2 gain performance of the resulted closed-loop system. Numerical example is given to illustrate the applicability of the theoretical results.     

Fuzzy H_∞ Filter Design for a Class of Nonlinear Systems with Time Delays via LMI

This paper develops fuzzy H_∞filter for state estimation approach for nonlinear discrete- time systems with multiple time delays and unknown bounded disturbances.We design a stable fuzzy H_∞filter based on the Takagi-Sugeno (T-S) fuzzy model,which assures asymptotic stability and a prescribed H_∞index for the filtering error system.Sufficient condition for the existence of such a filter is established by solving the linear matrix inequality (LMI) problem.The LMI problem can be efficiently solved with global convergence using the interior point algorithm.Simulation examples are provided to illustrate the design procedure of the proposed method.     

H∞ Design for Sampled-Data Systems via Lifting Technique： Conditions and Limitation

The initial motivation of the lifting technique is to solve the H∞ control problems. However, the conventional weighted H∞ design does not meet the conditions required by lifting, so the result often leads to a misjudgement of the design. Two conditions required by using the lifting technique are presented based on the basic formulae of the lifting. It is pointed out that only the H∞ disturbance attenuation problem with no weighting functions can meet these conditions, hence, the application of the lifting technique is quite limited.     

Improved Results on Robust H_∞ Control of Uncertain Discrete-time Systems with Time-varying Delay

In this paper, the robust H∞ control problem for uncertain discrete-time systems with time-varying state delay is con- sidered. Based on the Lyapunov functional method, and by resorting to the new technique for estimating the upper bound of the difference of the Lyapunov functional, a new less conservative sufficient condition for the existence of a robust H∞ controller is obtained. Moreover, the cone complementary linearisation procedure is employed to solve the nonconvex feasibility problem. Finally, several numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.     

H∞ output feedback control for large-scale nonlinear systems with time delay in both state and input

The H∞ output feedback control problem for a class of large-scale nonlinear systems with time delay in both state and input is considered in this paper. It is assumed that the interconnected nonlinearities are limited by constant multiplied by unmeasured states, delayed states and external disturbances. Different from existing methods to study the H∞ control of large-scale nonlinear systems, the static gain control technique is utilized to obtain an observer-based output feedback control strategy, which makes the closed-loop system globally asymptotically stable and attenuates the effect of external disturbances. An example is finally carried out to show the feasibility of the proposed control strategy.     

Adaptive H_∞ Synchronization of Master-slave Systems with Mixed Time-varying Delays and Nonlinear Perturbations: An LMI Approach

This paper proposes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays comprising different discrete and distributed time delays. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and an adaptation law including the master-slave parame- ters are established for designing a delayed synchronization law in terms of linear matrix inequalities(LMIs). The time-varying cont...     

H_∞ Filter Design for Discrete-time Systems with Missing Measurements

For packet-based transmission of data over a network, or temporary sensor failure, etc., data samples may be missing in the measured signals. This paper deals with the problem of H∞ filter design for linear discrete-time systems with missing measurements. The missing measurements will happen at any sample time, and the probability of the occurrence of missing data is assumed to be known. The main purpose is to obtain both full-and reduced-order filters such that the filter error systems are exponentially mean-square stable and guarantee a prescribed H∞ performance in terms of linear matrix inequality (LMI). A numerical example is provided to demonstrate the validity of the proposed design approach.     

Distributed H_∞ PID Feedback for Improving Consensus Performance of Arbitrary-delayed Multi-agent System

The H∞ proportional-integral-differential(PID) feedback for arbitrary-order delayed multi-agent system is investigated to improve the system performance. The closed-loop multi-input multi-output(MIMO) control framework with the distributed PID controller is firstly described for the multi-agent system in a unified way. Then, by using the matrix theory, the prescribed H∞performance criterion of the multi-agent system is shown to be equivalent to several independent H∞ performance constraints of the single-input single-output(SISO) subsystem with respect to the eigenvalues of the Laplacian matrix. Subsequently, for each subsystem,the set of the PID controllers satisfying the required H∞ performance constraint is analytically characterized based on the extended Hermite-Biehler theorem. Finally, the three-dimensional set of the decentralized H∞ PID control parameters is derived by finding the intersection of the H∞ PID regions for all the decomposed subsystems. The simulation results reveal the effectiveness of the proposed method.     

H∞最优性能指标的连续性问题

对Gahinet提出的H∞最优性能指标的不连续性进行了分析,指出这不连续性是由 于H∞控制器的存在条件不同和可能的零极点对消造成的.还指出,方法不同并不能改变设 计中存在的问题,对奇异H∞问题,还需要采用另外的措施才能解决.     

Robust H_∞ Filtering for a Class of Uncertain Lurie Time-delay Singular Systems

This paper deals with the problem of the robust H∞filtering for a class of Lurie singular systems with state time-delays, parameter uncertainties and unknown statistics characteristics but with limited power disturbance,aiming to design a robustly stable filter such that the uncertain Lurie time-delay singular systems are not only regular,impulse free and stable,but also have a prescribed level of H∞performance for the filtering error dynamics for all admissible uncertainties．A sufficient condition for the existence of such a filter is proposed in terms of linear matrix inequalities (LMIs)．When a solution to this set of LMIs exists,the parametric matrices of a desired filter can be easily obtained using LMI toolbox．     

H_∞ Control for 2-D Discrete State Delayed Systems in the Second FM Model

This paper is concerned with the problem of H_∞control for two-dimensional (2-D) discrete state delay systems described by the second Fornasini and Marchesini (FM) state- space model.A sufficient condition to have an H_∞noise atten- uation for this 2-D system is given in terms of a certain linear matrix inequality (LMI).The optimal H_∞controller is obtained by solving a convex optimization problem.Finally,a simulation example is given to illustrate the effectiveness of the proposed result.