Global finite-time stabilization for a class of switched nonlinear systems via output feedback

This paper addresses the problem of global finite-time stabilization for a class of uncertain switched nonlinear systems via output feedback under arbitrary switchings. Based on the adding a power integrator approach, we design a homogeneous observer and controller for the nominal switched system without the perturbing nonlinearities. Then, a scaling gain is introduced into the proposed output feedback stabilizer to implement global finite-time stability of the closed-loop system. In addition, the proposed approach can be also extended to a class of switched nonlinear systems with upper-triangular growth condition. Two examples are given to illustrate the effectiveness of the proposed method.     

Global exponential stabilization of a class of nonlinear systems by output feedback

This work extends the existing output feedback stabilization schemes for the systems in a "perturbed chain-of-integrator" form. In particular, we further relax the triangular-type conditions imposed on the perturbed terms and analyze the robust property of the linear output feedback control law using the newly proposed condition.     

Global output feedback stabilization for a class of nonlinear systems with quantized input and output

In this paper, we aim at addressing the problem of global output feedback stabilization for a class of uncertain nonlinear systems with quantized input and output. The nonlinear functions of the system are assumed to satisfy high‐order growth condition on the unmeasurable states. Based on the homogeneous domination approach and sector bound approach, a homogeneous quantized controller computed from quantized output is constructed, and a guideline is derived to select the parameters of the quantizers. Further, it is proved that, with the proposed scheme, the closed‐loop system is globally asymptotically stable. Copyright © 2016 John Wiley & Sons, Ltd.     

基于状态反馈的一类非线性系统动态输出反馈镇定

针对一类具有线性不可测量状态的非线性系统,基于状态反馈稳定控制器,利用不变流形和滑模变结构控制技术设计了动态输出反馈镇定控制器.这类控制器的结构类似于系统的状态反馈稳定控制器,在较简单的假定条件下,能够保证被控系统的状态得到渐近镇定.仿真算例表明该动态输出反馈控制器具有较强的镇定能力.     

Stability and static output feedback stabilization for a class of nonlinear discrete-time singular switched systems

In this paper, the stability and static output feedback stabilization problems for a class of nonlinear discrete-time singular switched systems are discussed. First, based on Lyapunov theory and the implicit function theorem, linear matrix inequalities sufficient conditions are developed which guarantee that the nonlinear discrete-time singular switched systems are regular, causal, have unique solution in a neighborhood of the origin, and are uniformly asymptotically stable. Then, with these conditions, and based on singular value decomposition approach, the design method of static output feedback controllers is given. Last, numerical examples are provided to illustrate the effectiveness of the proposed methods.     

一类非线性系统的自适应抗测量噪声的输出反馈镇定

本文研究一类非线性系统的自适应抗测量噪声的输出反馈镇定问题. 所研究的非线性系统输出中存在正的且 有界的乘性噪声. 非线性项的增长率为一个未知常数乘以输出的幂函数加上带有时滞输出的幂函数. 首先, 证明一个矩 阵不等式. 其次, 设计含有3个时变增益的输出反馈控制器, 并给出增益的自适应律, 然后, 构造适当的Lyapunov-Krasovskii 泛函, 给出确保闭环系统渐近稳定的充分条件. 最后, 仿真实验验证该方法的可行性和有效性.     

Global finite-time stabilization by dynamic output feedback for a class of continuous nonlinear systems

This note studies the problem of global finite-time stabilization by dynamic output feedback for a class of continuous but nonsmooth nonlinear systems. By extending the adding-a-power-integrator technique and a special continuous observer design, a dynamic output feedback controller is explicitly constructed to render the systems globally finite-time stable. The novelty of the note is the development of a recursive design procedure, which takes full advantage of the continuous structure of the systems in constructing the state feedback stabilizer and the continuous observer with rigorously selected gains.     

Global output feedback stabilization of upper-triangular nonlinear time-delay systems

In this paper,the problem of global output feedback stabilization for a class of upper-triangular nonlinear systems with time-varying time-delay in the state is considered.The uncertain nonlinearities are assumed to be higher-order in the unmeasurable states.Based on the extended homogeneous domination approach,using a low gain observer in combination with controller,the delay-independent output feedback controller makes closed-loop system globally asymptotically stable under a homogeneous growth condition.     

Global stabilization of uncertain stochastic nonlinear time‐delay systems by output feedback

Constructive control techniques have been proposed for controlling strict feedback (lower triangular form) stochastic nonlinear systems with a time‐varying time delay in the state. The uncertain nonlinearities are assumed to be bounded by polynomial functions of the outputs multiplied by unmeasured states or delayed states. The delay‐independent output feedback controller making the closed‐loop system globally asymptotically stable is explicitly constructed by using a linear dynamic high‐gain observer in combination with a linear dynamic high‐gain controller. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. Copyright © 2007 John Wiley & Sons, Ltd.     

Asymptotic stabilization via output feedback for nonlinear systems with delayed output

We propose a novel and simple design scheme of output feedback controller for a class of nonlinear systems with delayed output. The nonlinear systems considered here are more general than feedforward systems (upper triangular systems). By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and solving linear matrix inequalities (LMIs), the delay-dependent controller making the closed-loop system globally asymptotically stable (GAS) is explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Stabilization of a class of discrete-time switched systems via observer-based output feedback

In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lyapunov function (SLF) method with Finsler’s Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.     

一类非线性系统输出反馈的半全局实用镇定

研究了一类含有未知参数的非线性系统的半全局实用镇定问题,通过系统线性部分和零动态部分的Lyapunov函数构造了整个系统的Lyapunov函数,据此设计了使系统半全局实用稳定的状态反馈和动态输出反馈,且证明了只要未知参数不改变系统的相对阶,那么控制器是鲁棒的.仿真实例说明了所提出方法的有效性.     

Robust output feedback stabilization of discrete-time uncertaindynamical systems

The authors address the problem of stabilizing a certain class of discrete-time uncertain dynamical systems. The approach used requires no prior statistical information about such uncertainties, except that closed and bounded sets that they belong to. An output feedback controller that guarantees uniform boundedness and uniform ultimate boundedness of the solution of the system in question is derived     

Global stabilization of high-order nonlinear time-delay systems by state feedback

We consider the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-delay. By developing a novel dynamic gain-based backstepping approach, a state feedback controller independent of the time-delay is explicitly constructed with the help of appropriate Lyapunov–Krasovskii functionals. The precise knowledge (even the upper bound) of the time-delay is not required. It is proved that the states of the nonlinear time-delay systems can be regulated to the origin while all the closed loop signals are globally bounded. Finally, both physical and academic examples are given to illustrate the applications of the proposed scheme.     

Global output regulation of a class of lower triangular nonlinear systems with unknown control direction via output feedback

In this paper, we study the global output regulation problem of a class of lower triangular systems under measurement output feedback. A novel high-gain filter is proposed to estimate the unmeasured states of the systems. Furthermore, we integrate the robust stabilisation technique and Nussbaumgain technique to achieve asymptotic regulation when the control direction is unknown. The simulation results illustrate the effectiveness of the proposed method.     

Global practical tracking of a class of nonlinear systems by output feedback

In this paper we address the practical tracking problem for a class of nonlinear systems by dynamic output feedback control. Unlike most of the existing results where the unmeasurable states in the nonlinear vector field can only grow linearly, we allow higher-order growth of unmeasurable states. The proposed controller makes the tracking error arbitrarily small and demonstrates nice properties such as robustness to disturbances and universal property to reference signals.     

Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems

This paper studies sampled-data output feedback control of a class of nonlinear systems. It is shown that the performance of a stabilizing continuous-time state feedback controller can be recovered by a sampled-data output feedback controller when the sampling period is sufficiently small. The output feedback controller uses a deadbeat discrete-time observer to estimate the unmeasured states. Two schemes are proposed to overcome large initial transients when the controller is switched on.     

Global sampled-data output feedback control for a class of feedforward nonlinear systems

This paper investigates the problem of global output feedback stabilization for a class of feedforward nonlinear systems via linear sampled-data control. To solve the problem, we first construct a linear sampled-data observer and controller. Then, a scaling gain is introduced into the proposed observer and controller. Finally, we use the sampled-data output feedback domination approach to find the explicit formula for choosing the scaling gain and the sampling period which renders the closed-loop system globally asymptotically stable. A simulation example is given to demonstrate the effectiveness of the proposed design procedure.     

Global finite-time control for a class of switched nonlinear systems with different powers via output feedback

This paper is concerned with the problem of global finite-time control for switched nonlinear systems whose nonlinear terms satisfy homogenous growth conditions. At first, we design homogenous output feedback controllers for nominal switched nonlinear systems by adding a power integrator method. Then, we employ the homogeneous domination approach to scale homogeneous observers and controllers to render switched nonlinear systems with lower-triangular homogenous growth condition globally finite-time stable. Finally, the proposed control method can be extended to switched nonlinear systems satisfying with upper-triangular homogeneous growth condition. Two examples are provided to demonstrate the effectiveness of the proposed control scheme.