The guaranteed cost control for uncertain nonlinear large-scale stochastic systems via state and static output feedback

The guaranteed cost control (GCC) problem involved in decentralized robust control of a class of uncertain nonlinear large-scale stochastic systems with high-order interconnections is considered. After determining the appropriate conditions for the stochastic GCC controller, a class of decentralized local state feedback controllers is derived using the linear matrix inequality (LMI). The extension of the result of the study to the static output feedback control problem is discussed by considering the Karush-Kuhn-Tucker (KKT) conditions. The efficiency of the proposed design method is demonstrated on the basis of simulation results.     

Guaranteed cost control of time-delay chaotic systems via memoryless state feedback

This paper studies the problem of guaranteed cost control for a class of time-delay chaotic systems via memoryless state feedback. A design procedure is proposed to construct a memoryless state feedback controller, which guarantees that the resulting closed-loop system is asymptotically stable and achieves an adequate level of performance. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

Robust exponential stabilization for large-scale uncertain impulsive systems with coupling time-delays

In this paper, we aim to study robust exponential stabilization for a large-scale uncertain impulsive system with coupling time-delays. Furthermore, we also provide an estimation of the rate of convergence of exponential stabilization. By utilizing the Lyapunov method and Razumikhin technique, we shall design the feedback hybrid controllers in terms of linear matrix inequalities under which the robust exponential stability is achieved for a closed-loop large-scale uncertain impulsive system with coupling time-delays. Moreover, we shall also use the results obtained to design impulsive controllers for a large-scale uncertain continuous system under which the closed-loop continuous system achieves robust and exponential stability. To illustrate our results, one example is solved.     

Robust decentralized adaptive control for uncertain large-scale delayed systems with input nonlinearities

The paper is concerned with the problem of robust stabilization for uncertain large-scale time-varying delayed systems with input nonlinearities. Based on the sliding mode control, a memoryless decentralized adaptive sliding mode controller (DASMC) is developed. The proposed controller ensures the occurrence of the sliding manifold of the composite system even subjected to input nonlinearity. It shows that the uncertain nonlinear large-scale system also possesses the property of insensitivity to uncertainties and disturbances as a linear system does. A numerical example is given to verify the validity of the developed memoryless DASMC.     

Delay-dependent robust control for uncertain discrete-time singular systems with time-delays

The robust memoryless state feedback H_∞ control problem for uncertain time-delay discrete-time singular systems is discussed. Under a series of equivalent transformation, the equivalence of this problem and the robust state feedback H_∞ control problem for standard state-space uncertain time-delay discrete-time systems is presented. In terms of matrix inequality, the delay-dependent sufficient condition for the solution of this problem is given, the design method of the memoryless state feedback controller and the controller are also given.     

Non-fragile guaranteed cost control of uncertain large-scale systems with time-varying delays

The robust non-fragile guaranteed cost control problem is studied in this paper for a class of uncertain linear large-scale systems with time-varying delays in subsystem interconnections and given quadratic cost functions. The uncertainty in the system is assumed to be norm-bounded and time-varying. Also, the state-feedback gains for subsystems of the large-scale system are assumed to have norm-bounded controller gain variations. The problem is to design state feedback control laws such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Sufficient conditions for the existence of such controllers are derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the robust non-fragile guaranteed cost controllers is given in terms of the feasible solutions to a certain LMI. Finally, in order to show the application of the proposed method, a numerical example is included.     

Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control

In this paper, the problem of guaranteed cost synchronization for a complex network is investigated. In order to achieve the synchronization, two types of guaranteed cost dynamic feedback controller are designed. Based on Lyapunov stability theory, a linear matrix inequality (LMI) convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function. Finally, a numerical example is given to illustrate the proposed method.     

一类具有闭环极点约束的不确定线性系统的保性能控制

主要研究了闭环系统的极点约束在一个给定圆盘中的保性能控制问题,基于线性矩阵不等式处理方法给出了状态反馈控制器存在的充要条件,并利用线性矩阵不等式的解给出了保性能控制器的设计方法,得到一个状态反馈控制器,使得对所有允许的不确定性闭环系统稳定,并且闭环性能指标值不超过某个确定的上界.最后以数值例子验证了结果的正确性.     

Robust memory state feedback model predictive control for discrete-time uncertain state delayed systems

In this paper, we propose a memory state feedback model predictive control (MPC) law for a discrete-time uncertain state delayed system with input constraints. The model uncertainty is assumed to be polytopic, and the delay is assumed to be unknown, but with a known upper bound. We derive a sufficient condition for cost monotonicity in terms of LMI, which can be easily solved by an efficient convex optimization algorithm. A delayed state dependent quadratic function with an estimated delay index is considered for incorporating MPC problem formulation. The MPC problem is formulated to minimize the upper bound of infinite horizon cost that satisfies the sufficient conditions. Therefore, a less conservative sufficient conditions in terms of linear matrix inequality (LMI) can be derived to design a more robust MPC algorithm. A numerical example is included to illustrate the effectiveness of the proposed method.     

Decentralized model-reference adaptive control for a class of uncertain large-scale time-varying delayed systems with series nonlinearities

In this paper, the problem of model-reference adaptive control for large-scale time-varying delayed systems with series nonlinearities is investigated. By applying the theory of variable structure control, we propose an adaptive controller, which is both memoryless and decentralized, to derive the error subsystem between the local model state and plant state to zero. The proposed variable structure control is able to ensure the stability of a sliding manifold of the composite system even though the control input is nonlinear. The main difficulty for handling the effects of interconnected terms is well solved by a new proposed adaptation mechanism. Finally, a numerical example is illustrated to demonstrate the validity of the derived controller.     

Output feedback guaranteed cost control of uncertain linear discrete systems with interval time-varying delays

This paper deals with output feedback guaranteed cost control problem for a general class of uncertain linear discrete delay systems, where the state and the observation output are subjected to interval time-varying delay. The proposed output feedback controller uses the observation measurement to exponentially stabilize the closed-loop system and guarantee an adequate level of system performance. By constructing a set of augmented Lyapunov–Krasovskii functionals, a delay-dependent condition for the robust output feedback guaranteed cost control is established in terms of linear matrix inequalities (LMIs). Three numerical examples are provided to demonstrate the efficiency of the proposed method.     

Guaranteed cost control of time-delay chaotic systems

This article studies a guaranteed cost control problem for a class of time-delay chaotic systems. Attention is focused on the design of memory state feedback controllers such that the resulting closed-loop system is asymptotically stable and an adequate level of performance is also guaranteed. Using the Lyapunov method and LMI (linear matrix inequality) framework, two criteria for the existence of the controller are derived in terms of LMIs. A numerical example is given to illustrate the proposed method.     

Synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control

In this paper, we investigate the synchronization of non-autonomous chaotic systems with time-varying delay via delayed feedback control. Using a combination of Riccati differential equation approach, Lyapunov-Krasovskii functional, inequality techniques, some sufficient conditions for exponentially stability of the error system are formulated in form of a solution to the standard Riccati differential equation. The designed controller ensures that the synchronization of non-autonomous chaotic systems are proposed via delayed feedback control and intermittent linear state delayed feedback control. Numerical simulations are presented to illustrate the effectiveness of these synchronization criteria.     

Robust stabilization of internally delayed uncertain systems via sliding mode control

Summary The problem of robust stabilization of internally delayed uncertain systems via sliding mode controllers (SMC's) is studied in this paper. The robustness property and assymptotic stability of the system are discussed. Some sufficient conditions for the design of SMC and the switching hyperplane are given. Further generalization results, which lead to a simple design and implementation, are made for the system being described in companion form. A method is suggested for the elimination of limit cycles in systems being regulated by a relay SMC while allowing the generation of sliding motion and thus ensuring the closed-loop asymptotic stability.     

Positive real control for 2-D discrete delayed systems via output feedback controllers

This paper considers the problem of positive real control for two-dimensional (2-D) discrete delayed systems in the Fornasini–Marchesini second local state-space model. Attention is focused on the design of dynamic output feedback controllers, which guarantee that the closed-loop system is asymptotically stable and the closed-loop transfer function is extended strictly positive real. We first present a sufficient condition for extended strictly positive realness of 2-D discrete delayed systems. Based on this, a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality (LMI). When the LMI is feasible, an explicit parametrization of a desired output feedback controller is presented. Finally, we provide a numerical example to demonstrate the application of the proposed method.     

Chaos control in AFM systems using nonlinear delayed feedback via sliding mode control

In this paper a nonlinear delayed feedback control is proposed to control chaos in an Atomic Force Microscope (AFM) system. The chaotic behavior of the system is suppressed by stabilizing one of its first-order Unstable Periodic Orbits (UPOs). At first, it is assumed that the system parameters are known, and a nonlinear delayed feedback control is designed to stabilize the UPO of the system. Then, in the presence of model parameter uncertainties, the proposed delayed feedback control law is modified via sliding mode scheme. The effectiveness of the presented methods is numerically investigated by stabilizing the unstable first-order periodic orbit of the AFM system. Simulation results show the high performance of the methods for chaos elimination in AFM systems.     

Output-feedback guaranteed cost control for uncertain time-delay systems with Markov jumps

This paper considers the guaranteed cost control problem ofthe jump linear system with uncertain parameters and constanttime delay. The sufficient and necessary condition for the systemto be mean square quadratically stable (MSQS) is obtained. Usingthe LMI technique, an algorithm to design an output-feedbackguaranteed controller which stabilizes the system in the MSQSsense is developed.     

具外部扰动的变时滞不确定奇异系统的滑动模态控制

研究了含有多个变时滞的不确定奇异系统的滑动模态问题.该系统相比文献中已研究的系统更为复杂,具有多个变时滞,且分别含有匹配和不匹配的外部扰动项.通过对系统进行等价分解化为两个子系统,对分解后的系统进行切换函数的设计,再通过定义Lyapunov函数得到使得系统的滑模运动渐近稳定的充分条件.由此证明了所设计的滑模控制率能够保证状态轨迹在优先时间内被驱动到指定的切换面上且保持运动.设计过程简单,且结果以线性矩阵不等式呈现,相比文献中已有的结论更易于实现.最后通过例子验证结论的正确性.