Robust sampled-data control

Robust stabilization of a class of linear systems using sampled-data feedback control is studied. It is shown that a linear, time-invariant system subject to additive perturbations can be stabilized using high-gain periodic feedback from sampled values of the state, provided that the perturbations satisfy certain structural conditions. This result is also extended to decentralized sampled-data control of interconnected systems     

Local stabilization of semilinear parabolic system by boundary control

This paper addresses local stabilization of a semilinear parabolic system by boundary control. Under a certain assumption on the nonlinearity of the parabolic equation, a linear boundary feedback control law is applied to control the semilinear system. Based on the operator theories and relations of different norms, locally exponential stabilization of the closed loop system is established. Simulations support the established stability result.     

Passivity, feedback equivalence, and the global stabilization ofminimum phase nonlinear systems

Conditions under which a nonlinear system can be rendered passive via smooth state feedback are derived. It is shown that, as in the case of linear systems, this is possible if and only if the system in question has relative degree one and is weakly minimum phase. It is proven that weakly minimum phase nonlinear systems with relative degree one can be globally asymptotically stabilized by smooth state feedback, provided that suitable controllability-like rank conditions are satisfied. This result incorporates and extends a number of stabilization schemes recently proposed for global asymptotic stabilization of certain classes of nonlinear systems     

Semi-global stabilization with guaranteed regional performance of linear systems subject to actuator saturation

For a linear system under a given saturated linear feedback, we propose feedback laws that achieve semi-global stabilization on the null controllable region while preserving the performance of the original feedback law in a fixed region. Here by semi-global stabilization on the null controllable region we mean the design of feedback laws that result in a domain of attraction that includes any a priori given compact subset of the null controllable region. Our design guarantees that the region on which the original performance is preserved would not shrink as the domain of attraction is enlarged by appropriately adjusting the feedback laws. Both continuous-time and discrete-time systems will be considered.     

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.     

有界区域上Petrowsky系统的能控性和能稳性

利用D.L.Russel关于“能稳性导致能控性”的论断,研究Petrow sky系统的能控性,首先取线性反馈控制,得到线性反馈Petrow sky系统的能量的指数衰减,从而由D.L.Russel的“能稳性导致能控性”的论断得到能控性.其次取非线性反馈控制,得到Petrow sky系统的一些能量估计,但是不能得到指数能稳.     

A delay‐independent output feedback for linear systems with time‐varying input delay

It is well known that a delay‐dependent or delay‐independent truncated predictor feedback law stabilizes a general linear system in the presence of a certain amount of input delay. Results also exist on estimating the maximum delay bound that guarantees stability. In the face of a time‐varying or unknown delay, delay‐independent feedback laws are preferable over delay‐dependent feedback laws as the former provide robustness to the uncertainties in the delay. In the light of few results on the construction of delay‐independent output feedback laws for general linear systems with input delay, we present in this paper a delay‐independent observer–based output feedback law that stabilizes the system. Our design is based on the truncated predictor feedback design. We establish an estimate of the maximum allowable delay bound through the Razumikhin‐type stability analysis. An implication of the delay bound result reveals the capability of the proposed output feedback law in handling an arbitrarily large input delay in linear systems with all open‐loop poles at the origin or in the open left‐half plane. Compared with that of the delay‐dependent output feedback laws in the literature, this same level of stabilization result is not sacrificed by the absence of the prior knowledge of the delay.     

Stabilization of exponentially unstable discrete-time linear systems by truncated predictor feedback

Predictor state feedback solves the problem of stabilizing a discrete-time linear system with input delay by predicting the future state with the solution of the state equation and thus rendering the closed-loop system free of delay. The solution of the state equation contains a term that is the convolution of the past control input with the state transition matrix. Thus, the implementation of the resulting predictor state feedback law involves iterative calculation of the control signal. A truncated predictor feedback law results when the convolution term in the state prediction is discarded. When the feedback gain is constructed from the solution of a certain parameterized Lyapunov equation, the truncated predictor feedback law has been shown to achieve asymptotic stabilization of a system that is not exponentially unstable in the presence of an arbitrarily large delay by tuning the value of the parameter small enough. In this paper, we extend this result to exponentially unstable systems. Stability analysis leads to a bound on the delay and a range of the values of the parameter for which the closed-loop system is asymptotically stable as long as the delay is within the bound. The corresponding output feedback result is also derived.     

Non-uniform in time stabilization for linear systems and tracking control for non-holonomic systems in chained form

The paper contains certain results concerning non-uniform in time stabilization for linear time-varying systems by means of a linear time-varying feedback controller. These results enable us to present an explicit solution for the state feedback tracking control problem of non-holonomic systems in chained form under weaker hypotheses than those imposed in earlier existing works.     

Stabilization of Markov jump linear systems using quantized state feedback

This paper addresses the stabilization problem for single-input Markov jump linear systems via mode-dependent quantized state feedback. Given a measure of quantization coarseness, a mode-dependent logarithmic quantizer and a mode-dependent linear state feedback law can achieve optimal coarseness for mean square quadratic stabilization of a Markov jump linear system, similar to existing results for linear time-invariant systems. The sector bound approach is shown to be non-conservative in investigating the corresponding quantized state feedback problem, and then a method of optimal quantizer/controller design in terms of linear matrix inequalities is presented. Moreover, when the mode process is not observed by the controller and quantizer, a mode estimation algorithm obtained by maximizing a certain probability criterion is given. Finally, an application to networked control systems further demonstrates the usefulness of the results.     

On interconnections, control, and feedback

The purpose of this paper is to study interconnections and control of dynamical systems in a behavioral context. We start with an extensive physical example which serves to illustrate that the familiar input-output feedback loop structure is not as universal as we have been taught to believe. This leads to a formulation of control problems in terms of interconnections. Subsequently, we study interconnections of linear time-invariant systems from this vantage point. Let us mention two of the results obtained. The first one states that any polynomial can be achieved as the characteristic polynomial of the interconnection with a given plant, provided the plant is not autonomous. The second result states that any subsystem of a controllable system can be implemented by means of a singular feedback control law. These results yield pole placement and stabilization of controllable plants as a special case. These ideas are finally applied to the stabilization of a nonlinear system around an operating point     

Feedback stabilization of rotating Timoshenko beam with adaptive gain

The problem of boundary feedback stabilization of rotating Timoshenko beam, arising from control of flexible robot arms, is studied in this paper. First, under gain adaptive direct strain feedback controls, a counterexample is given to show that the corresponding closed loop system is not asymptotically stable, which is contrary to traditional conjecture. The counterexample given in this paper also exemplifies an interesting result: certain two two-order linear partial differential equations with five homogeneous boundary conditions have non-trivial solutions. Then, with an additional boundary feedback control, the related energy of the closed loop system is proved to be strongly stable, or more precisely, the configuration of the beam can be exponentially stabilized with some suitable non-linear boundary feedback controls with adaptive gain.     

Global stabilization of linear discrete-time systems with bounded feedback

This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections (“single hidden layer neural networks”) of simple saturation functions.     

基于观测器的时滞系统鲁棒控制器的设计

研究了一类不确定时滞系统基于观测器的鲁棒镇定问题,系统的不确定性时变未知且范数有界,目的是设计状态观测器和线性无记忆观测状态反馈控制器,使其能够镇定一类状态和控制输入不确定性时滞系统。基于Lyapunov稳定性理论,采用线形矩阵不等式这一有效工具,给出了系统基于观测状态反馈鲁棒镇定的充分条件,并且利用线形矩阵不等式的解构造了使得系统鲁棒稳定的基于观测状态反馈控制器,所得结果与时滞相关,从而相对减弱了控制器设计的保守性。数值算例表明了所提出的设计方法的有效性。     

Stabilization via dynamic output feedback for systems with output nonlinearities

The problem of asmptotically stabilizing a class of systems by means of continuous output feedback is considered. These systems are characterized by nonlinear terms, depending only on the ouputs. It is shown that for these systems stabilization via continuous state-feedback plus stabilization via output injection imply stabilization via continuous dynamic output-feedback. This generalizes a well-knwon result for linear systems.     

Partial‐state stabilization and optimal feedback control

In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for partial stability and partial‐state stabilization. Partial asymptotic stability of the closed‐loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state, which can clearly be seen to be the solution to the steady‐state form of the Hamilton–Jacobi–Bellman equation and hence guaranteeing both partial stability and optimality. The overall framework provides the foundation for extending optimal linear‐quadratic controller synthesis to nonlinear nonquadratic optimal partial‐state stabilization. Connections to optimal linear and nonlinear regulation for linear and nonlinear time‐varying systems with quadratic and nonlinear nonquadratic cost functionals are also provided. Finally, we also develop optimal feedback controllers for affine nonlinear systems using an inverse optimality framework tailored to the partial‐state stabilization problem and use this result to address polynomial and multilinear forms in the performance criterion. Copyright © 2015 John Wiley & Sons, Ltd.     

具有边界控制的线性Timoshenko型系统的指数稳定性

本文研究多孔弹性材料在实际应用中的镇定问题.多孔物体的动力学行为由线性Timoshenko型方程描述,这样的系统一般只是渐近稳定但不指数稳定.假定系统两端都是自由的,在自由端对系统施加边界速度反馈控制,本文讨论闭环系统的适定性和指数稳定性.首先,利用有界线性算子半群理论得到了系统的适定性.进一步对系统算子的本征值的渐近值估计,得到算子谱分布在一个带域,相互分离的,模充分大的本征值都是简单本征值.通过引入一个辅助算子,利用它的谱性质以及有界线性算子的扰动理论,得到系统的广义本征向量的完整性以及Riesz基性质.最后利用Riesz基性质和谱分布得到闭环系统的指数稳定性.     

Output feedback stabilization

The stabilization of control systems using output feedback is addressed. Necessary and sufficient Lyapunov conditions are established, generalizing the Artstein's stabilization theorem. For linear control systems, a necessary and sufficient Lyapunov condition is provided for stabilization by means of a linear output feedback law     

基于线性矩阵不等式的不确定关联系统的分散鲁棒镇定

应用线性矩阵不等式（LMI）方法研究不确定性关联大系统的分散便棒镇定问题。系统中不稳定项具有数值界,可不满足匹配条件。基于不确定项的表达形式,给出了其可分散状态反馈镇定的充分条件,即一组LMIs有解。在此基础上,通过求第一凸优化问题,提出了具有较小反馈增益的分散稳定化状态反馈控制律的设计方法。仿真示例说明了该方法的有效性和优越性。     

Stabilization of perturbed systems via linear optimal regulator

Linear quadratic state feedback regulators make the resulting closed-loop systems stable enough, i.e. they realize robust stabilization. Many attempts at robust stabilization using linear quadratic regulators have been reported. One of the major trends of formulating uncertainty in systems is to express perturbed parameters as the sum of two terms, i.e. nominal values and the deviation from them. In this paper, it is assumed that the upper and lower bounds for each uncertain parameter can somehow be estimated. This enables us to dispense with nominal values. The main aim is to contrive a robust feedback stabilization law for systems with parameters falling into certain ranges via a linear quadratic regulator based only upon information on their bounds. The systems under consideration are therefore those having interval system matrices (in which each element has the above-mentioned two-sided bounds). A certain feedback law is a stabilizing law for a system with an interval system matrix if and only if the same feedback law remains so for systems with system matrices whose entries are all possible combinations of the endpoints of their variation range.