Robust H_∞ control for uncertain descriptor systems with state and control delay

1 .INTRODUCTIONTi me delayis commonly encounteredin various en-gineering systems ,which often occursinthe trans-mission of information or material between differ-ent parts of a systemand is frequently a source ofinstability and poor performance[1]. Transporta-tion systems , communications systems , chemicalprocess , power systems are typical examples ofti me-delay systems . In the recent years , muchwork has been devoted to the analysis and synthe-sis of controller for state-delayed system…     

基于T-S模糊模型的网络控制系统鲁棒H∝容错控制

针对同时存在网络时延和数据包丢失的网络环境,研究了执行器故障下一类非线性网络控制系统的鲁棒H_∞容错控制问题。基于不确定T-S模糊模型描述的非线性网络控制系统模型,考虑了更实际、更常见的执行器部分失效情况。通过引入一个积分不等式,获得了此类系统的时滞相关鲁棒稳定性条件,且采用锥补线性化算法给出了此类系统的鲁棒H_∞容错控制器设计方法。仿真算例表明,对于任意容许的不确定性以及执行器故障,所设计的控制器能使系统鲁棒渐近稳定,且具有H_∞范数界。       

Fault-tolerant control of linear uncertain systems using H∞ robust predictive control

The robust fault-tolerant control problem of linear uncertain systems is studied. It is shown that a solution for this problem can be obtained from a H∞ robust predictive controller （RMPC） by the method of linear matrix inequality （LMI）. This approach has the advantages of both H∞ control and MPC： the robustness and ability to handle constraints explicitly. The robust closed-loop stability of the linear uncertain system with input and output constraints is proven under an actuator and sensor faults condition. Finally, satisfactory results of simulation experiments verify the validity of this algorithm.     

不确定广义系统的镇定

针对输出反馈下不确定广义系统的可镇定问题,从状态反馈下闭环广义系统的稳定性问题入手,利用矩阵不等式,依次给出不确定广义系统可镇定、关联不确定广义大系统的分散可镇定、以及关联不确定广义大系统在执行器故障、传感器故障下分散可镇定的充分条件。由此推广到输出反馈,给出了输出反馈意义下的广义系统可镇定、关联不确定广义大系统的分散可镇定、以及关联不确定广义大系统在执行器故障、传感器故障下分散可镇定的充分条件(即完整性设计)。其中反馈控制器的设计方法简明而又统一,便于应用。最后用数值例子来验证所给结果的有效性。     

Sliding mode H∞ control for a class of uncertain nonlinear state-delayed systems

A new proportional-integral (PI) sliding surface is designed for a class of uncertain nonlinear state-delayed systems. Based on this, an adaptive sliding mode controller (ASMC) is synthesized, which guarantees the occurrence of sliding mode even when the system is undergoing parameter uncertainties and external disturbance. The resulting sliding mode has the same order as the original system, so that it becomes easy to solve the H_∞ control problem by designing a memoryless H_∞ state feedback controller. A delay-dependent sufficient condition is proposed in terms of linear matrix inequalities (LMIs), which guarantees the sliding mode robust asymptotically stable and has a noise attenuation level γ in an H_∞ sense. The admissible state feedback controller can be found by solving a sequential minimization problem subject to LMI constraints by applying the cone complementary linearization method. This design scheme combines the strong robustness of the sliding mode control with the H_∞ norm performance. A numerical example is given to illustrate the effectiveness of the proposed scheme.     

Robust H∞ control for networked control systems

The robust H∞ control for networked control systems with both stochastic network-induced delay and data packet dropout is studied. When data are transmitted over network, the stochastic data packet dropout process can be described by a two-state Markov chain. The networked control systems with stochastic network-induced delay and data packet dropout are modeled as a discrete time Markov jump linear system with two operation modes. The sufficient condition of robust H∞ control for networked control systems stabilized by state feedback controller is presented in terms of linear matrix inequality. The state feedback controller can be constructed via the solution of a set of linear matrix inequalities. An example is given to verify the effectiveness of the method proposed.     

Robust H∞ controller design for a class of nonlinear fuzzy time-delay systems

The problem of fuzzy modeling for state and input time-delays systems with a class of nonlinear uncertainties by fuzzy T-S model is addressed. By using the linear matrix inequality (LMI) method, the problem of fuzzy robust H∞ controller design for the system is studied. Assuming that the nonlinear uncertain functions in the model considered are gain-bounded, a sufficient condition for the robustly asymptotic stability of the closed-loop system is obtained via Lyapunov stability theory. By solving the LMI, a feedback control law which guarantees the robustly asymptotic stability of the closed-loop system is constructed and the effect of the disturbance input on the controlled output is ruduced to a prescribed level.     

Robust predictive control of polytopic uncertain systems with both state and input delays

A robust model predictive control algorithm for discrete linear systems with both state and input delays subjected to constrained input control is presented,where the polytopic uncertainties exist in both state matrices and input matrices.The algorithm optimizes an upper bound with respect to a state feedback control law.The feedback control law is presented based on the construction of a parameter-dependent Lyapunov function.The above optimization problem can be formulated as a LMI-based optimization.The feasibility of the optimization problem guarantees that the algorithm is robustly stable.The simulation results verify the effectiveness of the proposed algorithm.     

Robust Stabilization for Uncertain Control Systems Using Piecewise Quadratic Lyapunov Functions

The sufficient condition based on piecewise quadratic simultaneous Lyapunov functions for robust stabilization of uncertain control systems via a constant linear state feedback control law is obtained. The objective is to use a robust stability criterion that is less conservative than the usual quadratic stability criterion. Numerical example is given, showing the advanteges of the proposed method.     

Discrete sliding mode prediction control of uncertain switched systems

The robust stabilization problem for a class of uncertain discrete-time switched systems is presented. A predictive sliding mode control strategy is proposed, and a discrete-time reaching law is improved. By applying a predictive sliding surface and a reference trajectory, combining with the state feedback correction and rolling optimization method in the predictive control strategy, a predictive sliding mode controller is synthesized, which guarantees the asymptotic stability for the closed-loop systems. The designed control strategy has stronger robustness and chattering reduction property to conquer with the system uncertainties. In addition, a unique nonswitched sliding surface is designed. The reason is to avoid the repetitive jump of the trajectories of the state components of the closed-loop system between sliding surfaces because it might cause the possible instability. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory.     

Robust H∞ control for neutral stochastic uncertain systems with time-varying delay

The problem of robust H∞ control for uncertain neutral stochastic systems with time-varying delay is discussed. The parameter uncertaintie is assumed to be time varying norm-bounded. First, the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method. Then, a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality (BMI), which ensures a prescribed stochastic robust H∞ performance level for the resulting closed loop system with nonzero disturbance input and for all admissible uncertainties. An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.     

不确定切换组合大系统的鲁棒分散控制

考虑了一类不确定切换组合大系统的鲁棒分散状态反馈镇定问题。利用单李雅普诺夫函数方法,得到了不确定切换组合大系统鲁棒可稳的充分条件。在互相关联的低维子系统的状态矩阵和控制输入矩阵同时带有未知、时变但有界的不确定性、各自的单个子系统均不能被镇定的情况下,基于凸组合技术和线性矩阵不等式方法,设计出分散状态反馈控制器及相应的分散切换策略,使得闭环系统渐近稳定。仿真结果表明所设计方法的正确有效性。     

Robust Feedback Controller for Exponential Stability of Nonlinear Systems with Mismatched Uncertainties

The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.     

一类切换系统的鲁棒状态反馈控制

考虑了一类非线性不确定切换系统的鲁棒状态反馈稳定问题，不确定项包含了系统矩阵的摄动以及满足匹配条件和不满足匹配条件三部分．对于给定的不确定切换系统，研究了其二次稳定和渐近稳定问题．基于公共李雅普诺夫函数方法，以矩阵不等式的形式给出了非线性切换系统鲁棒状态反馈稳定的若干充分条件．仿真结果验证了文中结论的正确有效性。     

Delta算子系统基于输出反馈的鲁棒协方差控制

研究Delta算子描述的线性不确定系统基于输出反馈的鲁棒协方差控制问题,即设计输出反馈控制器,使Delta算子不确定系统鲁棒稳定,且稳态输出协方差矩阵具有给定上界。利用线性矩阵不等式(LMI)方法,给出Delta算子不确定系统输出反馈鲁棒协方差控制器存在的充分条件,并在此基础上,提出Delta算子不确定系统输出反馈鲁棒协方差控制器设计算法。数值算例表明设计方法的可行性。     

Robust output-feedback stabilization of a class of nonlinear systems with the nonlinearities of varied form

1 .INTRODUCTIONThe problem of global stabilization of nonlinearsystems by output feedback has received much at-tention. Unlike in the case of linear systems ,theseparation principle generally does not hold fornonlinear systems . This is one of the reasons whythe problemis more difficult . As investigated byRef .[1] ,some extra growth conditions onthe un-measurable states of the systemare usually neces-sary for the global stabilization of nonlinear sys-tems via output feedback. For exampl…     

Delay-dependent robust H∞ control for uncertain discrete time-delay fuzzy systems

The robust H∞ control problem of norm bounded uncertain discrete Takagi-Sugeno (T-S) fuzzy systems with state delay is addressed. First, by constructing an appropriate basis-dependent Lyapunov-Krasovskii function, a new delay-dependent sufficient condition on robust H∞-disturbance attenuation is presented, in which both robust stability and prescribed H∞ performance are guaranteed to be achieved. Then based on the condition, a delay-dependent robust H∞ controller design scheme is developed in term of a convex algorithm. Finally, examples are given to illustrate the effectiveness of the proposed method.     

不确定离散广义时滞系统的静态输出反馈控制

针对一类不确定离散时滞广义系统,给出了静态输出反馈控制器的设计方法.首先基于标称离散广义时滞系统的稳定条件,以受限线性矩阵不等式形式,得到闭环离散广义时滞系统正则、因果且渐近稳定的充分条件,同时利用受限矩阵不等式的可行解给出静态输出反馈控制器的设计方法;然后采用矩阵的正交补,把求受限线性矩阵不等式的可行解问题转化为求严格线性矩阵不等式的可行解;最后的数值实例说明了所给方法的有效性和正确性.