H/sub /spl infin// fuzzy output feedback control design for nonlinear systems: an LMI approach

Addresses the problem of stabilizing a class of nonlinear systems by using an H/sub /spl infin// fuzzy output feedback controller. First, a class of nonlinear systems is approximated by a Takagi-Sugeno (TS) fuzzy model. Then, based on a well-known Lyapunov functional approach, we develop a technique for designing an H/sub /spl infin// fuzzy output feedback control law which guarantees the L/sub 2/ gain from an exogenous input to a regulated output is less or equal to a prescribed value. A design algorithm for constructing an H/sub /spl infin// fuzzy output feedback controller is given. In contrast to the existing results, the premise variables of the H/sub /spl infin// fuzzy output feedback controller are not necessarily to be the same as the premise variables of the TS fuzzy model of the plant. A numerical simulation example is presented to illustrate the theory development.     

Relationship between availability of states and pole/zerocancellations in H∞-control

This note compares servo systems designed with three methods of H _∞-control, that is, output feedback control, state feedback control and partial state feedback control. The three kinds of control use different information of the plant to generate the control input. We show that if more states are used, then the number of the pole/zero cancellations can be reduced     

Sufficient LMI conditions for H/sub /spl infin// output feedback stabilization of linear discrete-time systems

In this note, sufficient conditions for H/sub /spl infin// output feedback stabilization of linear discrete-time systems are proposed via linear matrix inequalities (LMIs). In order to reduce conservatism existing in earlier LMI methods, auxiliary slack variables with structure are employed. It is shown that degree of freedoms by the introduction of auxiliary slack variables lead to more flexibility in obtaining an approximate solution of H/sub /spl infin// output feedback stabilization problems. Consequently, the proposed method can yield a less conservative result than earlier LMI methods. In particular, typical output feedback control problems, such as decentralized H/sub /spl infin// output feedback control and simultaneous H/sub /spl infin// output feedback control, can be more efficiently solved. Numerical examples are included to illustrate the advantages of the proposed LMI method.     

State feedback performance recovery via an observer in H∞ robust control

The paper is concerned with H_∞ robust suboptimal control problem for linear time-invariant systems with structural uncertainties. The main result shows that if there exists a state feedback gain matrix which ensures H_∞robust suboptimally of the closed-loop system, then the robust performance achieved by the state feedback can be asymptotically recovered by a controller with high-gain observer.     

l/sup /spl infin//-bounded robustness for nonlinear systems: analysis and synthesis

The purpose of this paper is to describe systematic analysis and design tools for robust control problems with l/sup /spl infin// criteria. We first generalize the Hill-Moylan-Willems framework for dissipative systems to accommodate l/sup /spl infin// criteria, and then derive state feedback and measurement feedback synthesis procedures for l/sup /spl infin// robust control problems. The information state framework is used for the measurement feedback robust control problem. Necessary and sufficient conditions are proved, and new synthesis procedures using dynamic programming are presented.     

H∞-control of discrete-time nonlinear systems

This paper presents an explicit solution to the problem of disturbance attenuation with internal stability via full information feedback, state feedback, and dynamic output feedback, respectively, for discrete-time nonlinear systems. The H_∞-control theory is first developed for affine systems and then extended to general nonlinear systems based on the concepts of dissipation inequality, differential game, and LaSalle's invariance principle in discrete time. A substantial difficulty that V(A(x)+B(x)u+E(x)w) [respectively, V(f(x,u,w))] is no longer quadratic in [_w^u] arising in the case of discrete-time nonlinear systems has been surmounted in the paper. In the case of a linear system, we show how the results reduce to the well-known ones recently proposed in the literature     

$H_infty$Output Feedback Control of Discrete-Time Fuzzy Systems With Application to Chaos Control

This paper presents an observer based$H_infty$output feedback synthesis method for discrete time fuzzy dynamic systems based on a piecewise Lyapunov function. The basic idea of the approach is to design an observer based piecewise linear output feedback control law to guarantee the global stability with$H_infty$performance of the resulting closed-loop fuzzy control systems. It is shown that the controller parameters can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible with commercially available software. Application to control chaotic systems is given to illustrate the effectiveness and advantages of the proposed method.     

Robust H/sub /spl infin// control for uncertain discrete-time-delay fuzzy systems via output feedback controllers

This work investigates the problem of robust output feedback H/sub /spl infin// control for a class of uncertain discrete-time fuzzy systems with time delays. The state-space Takagi-Sugeno fuzzy model with time delays and norm-bounded parameter uncertainties is adopted. The purpose is the design of a full-order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed-loop system and guarantees an H/sub /spl infin// norm bound constraint on disturbance attenuation for all admissible uncertainties. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of this problem is presented. Explicit expressions of a desired output feedback controller are proposed when the given LMIs are feasible. The effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust H/sub /spl infin// control for a class of uncertain nonlinear discrete delay systems.     

Quasi-ISS/ISDS observers for interconnected systems and applications

This paper considers interconnected nonlinear dynamical systems and studies observers for such systems. For single systems the notion of quasi-input-to-state dynamical stability (quasi-ISDS) for reduced-order observers is introduced and observers are investigated using error Lyapunov functions. It combines the main advantage of ISDS over input-to-state stability (ISS), namely the memory fading effect, with reduced-order observers to obtain quantitative information about the state estimate error. Considering interconnections quasi-ISS/ISDS reduced-order observers for each subsystem are derived, where suitable error Lyapunov functions for the subsystems are used. Furthermore, a quasi-ISS/ISDS reduced-order observer for the whole system is designed under a small-gain condition, where the observers for the subsystems are used. As an application, we prove that quantized output feedback stabilization for each subsystem and the overall system is achievable, when the systems possess a quasi-ISS/ISDS reduced-order observer and a state feedback law that yields ISS/ISDS for each subsystem and therefor the overall system with respect to measurement errors. Using dynamic quantizers it is shown that under the mentioned conditions asymptotic stability can be achieved for each subsystem and for the whole system.     

Nonlinear H∞-control of time-varying systems: aunified distribution-based formalism for continuous and sampled-datameasurement feedback design

Nonlinear H_∞-controller synthesis is presented for time-varying systems via sampled-data measurement feedback. The H _∞-control problem for a nonlinear system with a sampled-data measurement output is shown to be equivalent to the H_∞-control problem for a certain nonlinear system with a time-continuous measurement output. Special mathematical tools are developed to straightforwardly derive a local solution of the sampled-data measurement feedback (SMF) H_∞-control problem from that of the time-continuous measurement feedback (CMF) H _∞-control problem     

Finite gain l/sub p/ stabilization of discrete-time LinearSystems subject to actuator Saturation: The case of p=1

It has been established by Bao, Lin, and Sontag (2000) that, for neutrally stable discrete-time linear systems subject to actuator saturation, finite gain l/sub p/ stabilization can be achieved by linear output feedback, for every p/spl isin/(1,/spl infin/] except p=1. An explicit construction of the corresponding feedback laws was given. The feedback laws constructed also resulted in a closed-loop system that is globally asymptotically stable. This note complements the results of Bao, Lin, and Sontag (2000) by showing that they also hold for the case of p=1. In establishing our results for p=1, we also allow the presence of certain additional external disturbance.     

H∞ analysis and synthesis ofdiscrete-time systems with time-varying uncertainty

The problems of H_∞ analysis and synthesis of discrete-time systems with block-diagonal real time-varying uncertainty are considered. It is shown that these problems can be converted into scaled H_∞ analysis and synthesis problems. The problems of quadratic stability analysis and quadratic stabilization of these types of systems are dealt with as a special case. The results on synthesis are established for general linear dynamic output feedback control     

TCP/IP闭环拥塞控制系统的一般研究

当前,Internet拥塞控制问题已成为Internet应用中的热点课题。系统地研究了TCP/IP闭环拥塞控制系统,包括：TCP层和IP层上拥塞检测和拥塞控制的方法、TCP/IP闭环拥塞控制系统的一般结构、发送端窗口控制动力学模型、链接节点队列动力学模型、AQM模型等,最后研究了上述模型的各种简化方法。     

On $l_2$ Stabilization of Linear Systems With Quantized Control

This paper extends results from [D. Liberzon and D. NeŠiĆ, “Input-to-state stabilization of linear systems with quantized feedback,” IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 767--781, May 2007], where input-to-state stabilization (ISS) of linear systems with quantized feedback was considered. In this paper, we show that, by using the same scheme and under the same conditions as in D. Liberzon and D. NeŠiĆ, “Input-to-state stabilization of linear systems with quantized feedback,” IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 767--781, May 2007, it is also possible to achieve (nonlinear gain) $l_2$ stabilization for linear systems. We also prove a new lemma on $cal K_{infty}$ functions that is interesting in its own right.      

H∞ tuning for task-space feedback control of robotwith uncertain Jacobian matrix

The H_∞ tuning problem for task-space feedback control of a robot with uncertain kinematics and Jacobian matrix from joint space to task space is formulated and solved. H_∞ tuning methods are presented for two task-space feedback controllers when the systems are subject to external disturbance. It is shown that the conditions for the establishment of H_∞ tuning can be obtained in simple forms without solving the Hamilton-Jacobi inequalities even in the presence of kinematics uncertainty     

Reduced-complexity nonlinear H/sup /spl infin// control of discrete-time systems

In this note, we describe a reduced-complexity solution to the nonlinear H/sup /spl infin// control problem. This reduction applies to systems where some of the states are perfectly known, and is an intermediate problem between full state feedback and the standard measurement feedback problem. The reduction of computational complexity is significant and of practical importance. Online implementation is feasible with 2003 computer technology for a range of practical engineering design problems.     

离散线性切换系统的一致有限时间稳定分析和反馈控制及其在网络控制系统中的应用

研究了一类离散线性切换系统的一致有限时间稳定性分析和反馈镇定．基于线性矩阵不等式技术,给出了在任意切换信号作用下,离散线性切换系统有限时间稳定和有限时间有界的充分条件,并给出了离散线性切换控制系统一致有限时间状态反馈控制器的设计方法．将上述分析结果应用于一类丢包有界的网络控制系统,得到了保证其有限时间稳定的反馈控制器．最后,通过两个数值仿真例子验证了所提方法的有效性．     

Robust nonlinear H∞-output feedback control

This paper investigates the problem of robust H_∞-output feedback control for nonlinear systems with time-varying parameter uncertainty satisfying some integral functional constraints. We address the problem of designing a compensator such that the L₂-gain of the mapping from the exogenous input noise to the penalty output is minimized or guaranteed to be less than or equal to a prescribed value. We establish the interconnection between the robust nonlinear H_∞-control problem and the nonlinear H _∞-control problem, Based on this connection, a sufficient condition for the existence of a solution to the robust nonlinear H_∞-output feedback control problem is derived in terms of a “scaled” Hamilton-Jacobi inequality