一类非线性不确定系统的鲁棒H∞控制

利用Hamilton-Jacobi不等式讨论了一类含不确定项的非线性控制系统的鲁棒H∞控制问题,分别得到了状态反馈控制器和动态输出反馈控制器,使得相应的闭环系统具有鲁棒H∞特性的充分条件,并且给出了它们的具体设计.     

Global output regulation and disturbance attenuation with globalstability via measurement feedback for a class of nonlinear systems

Considers the problem of global stabilization via output feedback for a class of nonlinear systems which have been previously considered by many authors and are characterized by having nonlinear terms depending only on the output y. The author's result incorporates many previous results. When static output feedback is considered, it is shown that the existence of an output control Lyapunov function, satisfying a suitable continuity property, is sufficient for constructing a continuous output feedback law u=k(y) which globally (or semiglobally) stabilizes the above class of systems. When dynamic output feedback is allowed, it is shown that the stabilization problem can be split into two independent stabilization subproblems: one is the corresponding problem via state feedback, and the other is the problem via output injection. From solving the two subproblems, one obtains two Lyapunov functions which, combined, give a candidate Lyapunov function for solving the output feedback stabilization problem. The proofs of the author's results give systematic procedures for constructing output feedback controllers, once two such Lyapunov functions are known. One can also consider the problem of output regulation and disturbance attenuation with global stability via measurement feedback and show that a similar “separation” condition holds     

Output feedback stabilization of a class of uncertain internally delayed systems

This paper is concerned with the problem of output feedback stabilization of a class of uncertain internally (i.e. in the state) delayed systems, in which only the upper bounds of nonlinear uncertainties are given. The designs of both static and dynamic output feedback controllers are considered. Some sufficient conditions for the stabilization of closed-loop systems are proposed, based upon the use of Lyapunov's stability criteria     

ROBUST STABILIZATION OF A CLASS OF UNCERTAIN TIME DELAY SYSTEMS IN SLIDING MODE

This paper addresses the problem of robust stabilization of a class of uncertain systems subject to internal (i.e., in the state) point delays, external (i.e., in the input) point delays and nonlinear disturbances by using sliding mode control. Methods for the design of sliding mode controllers based on state feedback, static output feedback and dynamic output feedback, respectively, are proposed. Sufficient conditions for the asymptotic stability and robustnesss of the closed–loop systems are given under a wide class of admissible nonlinear disturbances. © 1997 by John Wiley & Sons, Ltd.     

模糊不确定时滞系统的静态输出的反馈镇定:迭代线性矩阵不等式方法

对一类不确定非线性时滞系统利用模糊T＿S模型进行建模,研究了静态输出反馈镇定问题.用矩阵不等式的形式给出了模糊T＿S不确定时滞系统可通过静态输出反馈镇定的充分条件.并将矩阵不等式的条件转化为迭代线性矩阵不等式(ILMI),并给出相应的算法.     

Feedback realization of nonsingular precompensators for linearsystems with delays

The problem of realization of dynamic precompensators for linear systems with delays by static or dynamic state feedback, and static output feedback, is considered. Necessary and sufficient conditions for the solutions are given     

GLOBAL ROBUST SERVOMECHANISM OF A CLASS OF NONLINEAR SYSTEMS USING OUTPUT FEEDBACK

The robust servomechanism problem (alternatively, output regulation problem) of the class of nonlinear systems in lower triangular form has been extensively studied in recent years. The semi‐global solution was first given by either state feedback or output feedback. The global solution by state feedback was given very recently. However, the global solution by output feedback has long been an open problem. In this paper, we present a set of solvability conditions of the global robust servomechanism problem for this class of nonlinear systems by output feedback.     

Noninteracting control with stability for Hamiltonian systems

The problem of noninteraction with stability via dynamic state feedback is addressed and solved for a class of nonlinear Hamiltonian systems. A simple way to check necessary and sufficient conditions is proposed. It is well known that to decide if the problem is solvable, and which class of state feedback has to be used, the stability properties of some special dynamics are to be investigated. For this reason, on the way to the main result, it is shown that such dynamics are not necessarily Hamiltonian. Several examples, clarifying the role of different classes of state-feedback control laws (either static or dynamic) in the solution of the problem, are proposed     

Nonlinear output regulation for invertible nonlinear MIMO systems

In this paper, we address the problem of output regulation for a broad class of multi‐input multi‐output (MIMO) nonlinear systems. Specifically, we consider input–affine systems, which are invertible and input–output linearizable. This class includes, as a trivial special case, the class of MIMO systems which possess a well‐defined vector relative degree. It is shown that if a system in this class is strongly minimum phase, in a sense specified in the paper, the problem of output regulation can be solved via partial‐state feedback or via (dynamic) output feedback. The result substantially broadens the class of nonlinear MIMO systems for which the problem in question is known to be possible. Copyright © 2015 John Wiley & Sons, Ltd.     

Control for discrete singular hybrid systems

The problems of stability, state feedback control and static output feedback control for a class of discrete-time singular hybrid systems are investigated in this paper. A new sufficient and necessary condition for a class of discrete-time singular hybrid systems to be regular, causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict LMIs, respectively. Finally, two illustrative examples are provided to demonstrate the applicability of the proposed approach.     

线性时滞系统的耗散控制

研究了一类线性时滞系统的二次耗散控制问题,基于线性矩阵不等式（LMI）方法导出了耗散控制器存在的充分条件,通过线性矩阵不等式的可行解构造出耗散态状态反馈和动态输出反馈控制律,相应的闭环系统是二次稳定和严格（Q,S,R）耗散的,本文的主要贡献是统一了线性时滞系统现有的H∞控制和无源控制结果。     

Output transformations and separation results for feedback linearisable delay systems

The class of strict-feedback systems enjoys special properties that make it similar to linear systems. This paper proves that such a class is equivalent, under a change of coordinates, to the wider class of feedback linearisable systems with multiplicative input, when the multiplicative terms are functions of the measured variables only. We apply this result to the control problem of feedback linearisable nonlinear MIMO systems with input and/or output delays. In this way, we provide sufficient conditions under which a separation result holds for output feedback control and moreover a predictor-based controller exists. When these conditions are satisfied, we obtain that the existence of stabilising controllers for arbitrarily large delays in the input and/or the output can be proved for a wider class of systems than previously known.     

Decentralised memory static output feedback control for the nonlinear time-delay similar interconnected systems

In this paper, the problem of decentralised memory static output feedback control for a class of nonlinear time-delayed interconnected systems with similar structure is investigated, where both the linear and nonlinear state vectors involve time delay. The contributions of the paper include the following: (1) a new similar structure is presented via memory static output feedback; (2) by exploiting the structure of interconnected systems, the new integral inequalities, constrained Lyapunov equations and LMI method, the decentralised memory static output derivative feedback controllers with similar structure are designed, which is dependent of time delays, to stabilise the interconnected systems uniformly asymptotically; and (3) the stability domain is estimated. The conservatism of the results obtained is reduced by full using the system output information. Finally, the numerical examples are given to demonstrate the effectiveness of the results obtained in this paper.     

广义系统输出反馈严格正实控制器设计

研究连续广义系统的正实控制问题。目的是设计静态输出反馈和动态输出反馈严格正实控制器使得闭环系统容许且扩展严格正实。基于广义系统严格正实引理，利用线性矩阵不等式和广义代数Riccati不等式，给出了广义系统静态输出反馈和动态输出反馈严格正实控制器存在的充要条件及设计方法。对动态输出反馈情形，给出了一个数值算例说明控制器设计方法的有效性及可行性。     

线性时滞系统的耗散控制

从全新的二次型供给率的耗散角度,研究了线性时滞系统的二次稳定性和耗散控制问题,给出了线性矩阵不等式(LMI)形式的充分条件。而且,考虑了时滞系统在状态反馈控制器和动态输出反馈控制器作用下的闭环系统的二次稳定和耗散性问题,同样给出了LMI形式的充分条件,并通过线性矩阵不等式的可行解构造出耗散状态反馈控制律和动态输出反馈控制律。     

An LMI approach to stabilization of linear discrete-time periodic systems

The problem of stabilization of linear discrete-time periodic systems is considered. LMI based conditions for stabilization via static periodic state feedback as well as via static periodic output feedback are presented. In the case of state feedback, the conditions are necessary and sufficient whereas for output feedback the result is only sufficient as it depends on the particular state-space representation used to describe the system. The problem of quadratic stabilization in the presence of either norm-bounded or polytopic parameter uncertainty is also treated. As an application of the output feedback stabilization technique, we consider the problem of designing a stabilizing (respectively, quadratically stabilizing) static periodic output feedback controller for linear time-invariant discrete-time systems which are not stabilizable (respectively, quadratically stabilizable) by static constant output feedback.     

Global stabilization of a class of delay discrete-time nonlinear systems via state and output feedback

This paper deals with stabilization of a class of delay discrete-time nonlinear systems through state and output feedback. We provide an explicit bounded state feedback law as an extension of the Jurdjevic-Quinn method, from nonlinear theory, to this class of systems. Next, we present a useful and systematic approach to design an observer for the same class of systems. Then, we show how the global stabilization problem via dynamic output feedback can be solved by using the two previous results. Finally, numerical examples are given to illustrate the effectiveness of the proposed design method.     

一类非线性奇异控制系统的块解耦

讨论了在正则状态下反馈作用下，一类非线性奇异控制系统的输入输出块解耦问题，首先给一种算法，然后利用该算法导出系统输入块解耦问题可解的充分必要条件。     

一类线性不可观非线性系统的动态输出反馈镇定

本文研究一类不可观非线性系统的动态输出反馈镇定,基于逼近渐近稳定性的概念,给出了动态输出反馈可镇定的充分条件,本文主要结果的直接推论是零动太逼近渐近稳定的最小相位系统能用动态输出反馈镇定,本文的方法也能处理非最小相位系统。     

Dynamic self‐triggered output‐feedback control for nonlinear stochastic systems with time delays

In this paper, the dynamic self‐triggered output‐feedback control problem is investigated for a class of nonlinear stochastic systems with time delays. To reduce the network resource consumption, the dynamic event‐triggered mechanism is implemented in the sensor‐to‐controller channel. Criteria are first established for the closed‐loop system to be stochastically input‐to‐state stable under the event‐triggered mechanism. Furthermore, sufficient conditions are given under which the closed‐loop system with dynamic event‐triggered mechanism is almost surely stable, and the output‐feedback controller as well as the dynamic event‐triggered mechanism are co‐designed. Moreover, a dynamic self‐triggered mechanism is proposed such that the nonlinear stochastic system with the designed output‐feedback controller is stochastically input‐to‐state stable and the Zeno phenomenon is excluded. Finally, a numerical example is provided to illustrate the effectiveness of proposed dynamic self‐triggered output‐feedback control scheme.