Global finite-time stabilization by output feedback for planar systems without observable linearization

This note considers the problem of global finite-time stabilization by output feedback for a class of planar systems without controllable/observable linearization. A sufficient condition for the solvability of the problem is established. By developing a nonsmooth observer and modifying the adding a power integrator technique, we show that an output feedback controller can be explicitly constructed to globally stabilize the systems in finite time. As a direct application of the main result, global output feedback finite-time stabilization is achieved for the double linear integrator systems perturbed by some nonlinear functions which are not necessarily homogeneous.     

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 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.     

On stabilization of decentralized dynamic output feedback systems

A dynamic output feedback law is presented for large scale interconnected systems. If the coupling terms between the subsystems are neglected, the control scheme can be interpreted as decentralized reconstruction of the state variables from the output of the subsystems. A class of systems stabilizable by decentralized state feedback is investigated. A sufficient condition is determined for systems to be stabilizable with local state feedback and reconstruction with observers of full order. The resulting closed-loop systems are connectively stable. Moreover, any prescribed degree of stability can be achieved and the closed-loop systems are robust with respect to bounded nonlinearities in the couplings between the subsystems.     

Hankel/Toeplitz matrices and the static output feedback stabilization problem

The static output feedback (SOF) stabilization problem for general linear, continuous-time and discrete-time systems is discussed. A few novel necessary and sufficient conditions are proposed, and a modified SOF stabilization problem with performance is studied. For multiple-input single-output (or single-input multiple-output) systems the relation with a class of Hankel matrices, and their inverses, in the continuous-time case and with a class of Toeplitz matrices, in the discrete-time case, is established. These relationships are used to construct conceptual numerical algorithms. Finally, it is shown that, in the continuous-time case, the problem can be recast as a concave–convex programming problem. A few worked out examples illustrate the underlying theory.     

On the output feedback stabilization for distributed semilinear systems

The output stabilization for a class of distributed semilinear system is obtained with stabilizing controls that depend on the output operator. Then, we give sufficient conditions for exponential, strong and weak stabilization. The obtained results are illustrated by examples and simulations.     

On passivity-based output feedback global stabilization of euler-lagrange systems

It is well known that in systems described by Euler-Lagrange equations the stability of the equilibria is determined by the potential energy function. Further, these equilibria are asymptotically stable if suitable damping is present in the system. These properties motivated the development of a passivity-based controller design methodology which aims at modifying the potential energy of the closed loop and the addition of the required dissipation. To achieve the latter objective measurement of the generalized velocities is typically required. Our main contribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extension provided the system satisfies a dissipation propggation condition. This allows us to determine a class of Euler-Lagrange systems that can be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of set-point control of elastic joints robots. Our research contributes, if modestly, to the development of a theory for stabilization of nonlinear systems with physical structures which effectively exploits its energy dissipation properties.     

On the stabilization of controllable and observable systems by an output feedback law

For control systems which can be locally stabilized in small time by means of a dynamic periodic time-varyingstate feedback law, we give a sufficient condition on Lie derivatives of the output for local stabilization in small time by means of a dynamic periodic time-varyingoutput feedback law. If the system is analytic our sufficient condition is also necessary.     

基于事件触发策略的输出受限磁悬浮系统的有限时间镇定

研究输出受限磁悬浮系统基于事件触发机制的有限时间稳定控制问题.借助具有时变阈值的有限时间触发策略和正切型障碍函数,设计一个新的事件触发控制器,不仅确保磁悬浮系统的悬浮气隙被限制在一个指定范围,其状态还在有限时间内收敛到原点.创新之处在于实现有输出约束和无输出约束控制设计与理论分析的统一,最后通过仿真表明控制策略的有效性.     

Output-feedback finite-time stabilization of disturbed feedback linearizable nonlinear systems

A novel methodology for designing multivariable High-Order Sliding-Mode (HOSM) controllers for disturbed feedback linearizable nonlinear systems is introduced. It provides for the finite-time stabilization of the origin of the state-space by using output feedback. Only the additional assumptions of algebraic strong observability and smooth enough matched disturbances are required. The control problem is solved in two consecutive steps: firstly, designing an observer based on the measured output and, secondly, designing of a full-state controller computed from a new virtual output with vector relative degree. The introduced notion of algebraic strong observability allows recovering the state of the system using the measured output and its derivatives. By estimating the required derivatives through the HOSM differentiator, a finite-time convergent observer is constructed.     

线性系统的事件触发输出反馈有限时间有界控制

本文研究了线性系统的事件触发输出反馈有限时间有界控制问题. 与渐近稳定只定性地要求系统在采样间隔 有界不同, 有限时间有界需要估计系统轨迹的上界以保证满足动态系统的定量要求. 本文基于类李雅普诺夫函数给出了 保证闭环系统的有限时间有界性和避免芝诺现象的充分条件. 这些充分条件可以转化为线性矩阵不等式, 便于验证和实 际应用. 此外, 为了节约资源, 提出了一种可变参数的事件触发规则, 提高了设计灵活性. 仿真结果验证了本文的主要结 论.     

On output feedback stabilization of Euler-Lagrange systems with nondissipative forces

This paper provides a solution to the problem of output feedback stabilization of systems described by Euler-Lagrange equations perturbed by nondissipative forces. This class of forces appears in some applications where we must take into account the interaction of the system with its environment. The nonlinear dependence on the unmeasurable part of the state and the loss of the fundamental passivity property render most of the existing results on stabilization of nonlinear systems unapplicable to this problem. The technique we use consists of finding a dynamic output feedback controller and a nonlinear change of coordinates such that the closed loop can be decomposed as a cascade of an asymptotically stable system and an input-to-state stable system. This should be contrasted with the well-known passivity-based technique that aims at a feedback interconnection of passive systems. We believe this design methodology to be of potential applicability to other stabilization problems where passivity arguments are unapplicable.     

Optimal controllers and output feedback stabilization

In this paper the output feedback stabilizability problem is explored in terms of control Lyapunov functions. Sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem. Our main results extends those developed in [31] and generalize a theorem due to Sontag [23].     

Finite-time stabilization via dynamic output feedback

In this paper the finite-time stabilization of continuous-time linear systems is considered; this problem has been previously solved in the state feedback case. In this work the assumption that the state is available for feedback is removed and the output feedback problem is investigated. The main result provided is a sufficient condition for the design of a dynamic output feedback controller which makes the closed loop system finite-time stable. Such sufficient condition is given in terms of an LMI optimization problem; this gives the opportunity of fitting the finite-time control problem in the general framework of the LMI approach to the multi-objective synthesis. In this context an example illustrates the design of a controller which guarantees, at the same time, finite-time stability together with some pole placement requirements.     

On multiple‐delay output feedback stabilization of LTI plants

We develop a control methodology for linear time‐invariant plants that uses multiple delayed observations in feedback. Using the special coordinate basis, we show that multiple‐delay controllers can always be designed to stabilize minimum‐phase plants, and identify a class of non‐minimum‐phase plants that can be stabilized using these controllers. Copyright © 2009 John Wiley & Sons, Ltd.     

一种简化的自适应神经网络输出反馈镇定

针对一类输出反馈非线性时滞系统,提出一种简化的自适应神经网络镇定算法.所设计的状态观测器和控制器不依赖于时滞.不同于现有的结果,系统的时滞项假定完全未知,仅采用一个神经网络补偿所有未知非线性函数,因此控制器设计更加简单,而且最终的闭环系统被证明是半全局渐近稳定的.仿真结果进一步验证了该控制方案的有效性.     

Robust output feedback stabilization via risk-sensitive control

We consider a problem of robust linear quadratic Gaussian (LQG) control for discrete-time stochastic uncertain systems with partial state measurements. For a finite-horizon case, the problem was recently introduced by Petersen et al. (IEEE Trans. Automat. Control 45 (2000) 398). In this paper, an infinite horizon extension of the results of Petersen et al. (IEEE Trans. Automat. Control 45 (2000) 398) is discussed. We show that for a broad class of uncertain systems under consideration, a controller constructed in terms of the solution to a specially parameterized risk-sensitive stochastic control problem absolutely stabilizes the stochastic uncertain system.     

Dynamic output feedback linearization and global stabilization

We present a class of single-input single-output nonlinear systems which are globally transformable by a dynamic output feedback control and a time-varying state space transformation into a linear, observable and minimum phase system. We then show how those systems can be globally stabilized by a dynamic output feedback nonlinear control and how global output tracking can be achieved as well.     

On an output‐feedback stabilization problem with uncertainty in the relative degree

This paper deals with an output‐feedback finite‐time control problem for a class of nonlinear uncertain systems whose relative degree is affected by an uncertain system parameter and is therefore unknown at the stage of control design. We show that an existing second‐order sliding mode control algorithm can address successfully the control task of a finite‐time output‐feedback stabilization when the uncertain relative degree is equal to 1 or 2. We derive constructive tuning rules for the control parameters and show its effectiveness by using computer simulations. Copyright © 2007 John Wiley & Sons, Ltd.