A partial parameterization of nonlinear output feedback controllers for saturated linear systems

This paper addresses the stabilization problem of linear systems subject to input saturation. The major purpose is to introduce nonlinearity into control laws so as to expand the design freedom for performance enhancement. To this end, a new approach is developed which involves a partial differential matrix inequality (PDMI). A class of stabilizing feedback laws is explicitly obtained by solving this PDMI analytically and the feedback laws are parameterized by a nonlinear function. Further, it is revealed that any linear observer can be used to realize the output feedback stabilization. Numerical examples, including the seek control of a hard disk drive, show that the introduced nonlinearity does contribute to the improvement of system performance. The application to integral control is also discussed.     

A passive output feedback controller with wave filter for marine vehicles

An output feedback controller with a wave filter for regulation of nonlinear marine vehicles is derived. Only measurements of position and attitude are needed. Asymptotic stability for the position and attitude around the desired values, and the velocity about zero is proven by applying Lyapunov stability analysis. Even though the wave filter in this paper has a notch filter structure, it is incorporated in the controller such that the system from the vehicle's velocity to the control input is passive. This is opposed to conventional notch filters which are usually designed separately from the controller itself, possibly complicating the stability analysis. Finally, a simulation study of a ship illustrates the design procedure of the controller. © 1998 John Wiley & Sons, Ltd.     

Observers and output feedback stabilising controllers for nonlinear strict-feedback systems with sampled observation

The design of observers and output feedback stabilising controllers for continuous-time strict-feedback systems with sampled observation is considered. First two types of observers are designed. One is a discrete-time semiglobal and practical reduced-order observer for the exact model and the other is a continuous-time semiglobal and practical full-order observer for continuous-time strict feedback systems with sampled observation. Then by combining the designed continuous-time observers and continuous-time state feedback laws that are continuous, zero at the origin, and uniformly globally asymptotically stabilise continuous-time systems, output feedback semiglobally practically uniformly asymptotically stabilising controllers are constructed. Numerical examples are given to illustrate the proposed design of observers and output feedback controllers.     

A result on output feedback linear quadratic control

In this note we consider the static output feedback linear quadratic control problem. We present both necessary and sufficient conditions under which this problem has a solution in case the involved cost depends only on the output and control variables.This result is used to present both necessary and sufficient conditions under which the corresponding linear quadratic differential game has a Nash equilibrium in case the players use static output feedback control.Another consequence of this result is that the conditions also provide sufficient conditions for the static output stabilizability problem. Of course, in case these conditions are not met this does not mean that the system is not stabilizable via static output feedback.     

Generalized pole placement via static output feedback: A methodology based on projections

This paper presents an algorithm for solving static output feedback pole placement problems of the following rather general form: given n subsets of the complex plane, find a static output feedback that places in each of these subsets a pole of the closed-loop system. The algorithm presented is iterative in nature and is based on alternating projection ideas. Each iteration of the algorithm involves a Schur matrix decomposition, a standard least-squares problem and a combinatorial least-squares problem. While the algorithm is not guaranteed to always find a solution, computational results are presented demonstrating the effectiveness of the algorithm.     

结构振动的时滞输出反馈控制器设计

研究结构振动的时滞输出反馈控制,通过部分可测输出量实现整个系统的主动振动控制．首先将系统的运动微分方程改写成状态空间模型,其控制输入中存在时滞．再利用一个线性项加积分项的变换将原时滞输入系统转化成无时滞的形式．在此基础上,应用输出反馈原理和合理的性能指标设计出系统的控制律．最后以一个三层建筑结构为例,研究系统在地震载荷下的动态响应．在数值计算中,时滞量取为采样周期的整数倍,积分步长取为采样周期．仿真结果表明,本文提出的时滞输出反馈控制律是有效且实用的．     

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.     

Design of periodic output feedback and fast output sampling based controllers for systems with slow and fast modes

It is well known that the straight forward application of controller design methods to two‐time‐scale systems is susceptible to numerical ill‐conditioning and stiffness problems. However, it has been demonstrated in this paper that the presence of time‐scales can be exploited for achieving better computational efficiency in case of the design of controllers based on periodic output feedback and fast output sampling principles. In particular, an approach for design of periodic output feedback and fast output sampling controllers for a two‐time‐scale system by decomposition into a slow and a fast subsystem problems, has been presented. These smaller order problems are then separately solved and the results thus obtained for the slow and fast subsystems are combined to obtain the solution of the original design problems. The procedure has been illustrated with the help of a very simplified nuclear reactor model. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

A note on asymptotic stabilization of linear systems by periodic, piecewise constant, output feedback

This note studies the asymptotic stabilization problem for controllable and observable, single-input single-output, linear, time-invariant, continuous-time systems by means of memoryless output feedback of the form u(t)=k(t)y(t), with k(t) periodic and piecewise constant. A necessary and sufficient condition, together with a simpler to test sufficient condition, given in terms of a bilinear matrix inequality, is presented. A few illustrative examples complete the paper.     

On the order of nonlinear time-invariant stabilizing controllers

Here we consider the problem of stabilizing a finite-dimensional, stabilizable and detectable, linear time-invariant (LTI) plant in the sense that the plant state goes to zero while the controller state converges. With r the dimension of the plant output, we show that there exists a nonlinear time-invariant controller of order r+3 which stabilizes all such systems.     

Pole assignment for linear time-invariant systems by periodic memoryless output feedback

It is well known that the poles of a linear time-invariant controllable and observable system can be assigned arbitrarily by state feedback. When only the output is available, pole assignment is still possible by means of dynamic output feedback. In this paper the potential of time-varying memoryless output feedback is considered. It is shown that, up to some technical conditions, it is indeed possible to allocate the poles of a linear time-invariant discrete-time system by memoryless output feedback with periodic gains. The period of the gains is (n + 1) with n the order of the system. The power of the design technique is proved to be comparable to what can be achieved by the classical dynamic feedback approach.     

ESA in high‐order linear systems via output feedback

This paper considers eigenstructure assignment in high‐order linear systems via output feedback. Parametric expressions for the left and right closed‐loop eigenvectors associated with the finite closed‐loop eigenvalues and two simple and complete parametric solutions for the feedback gain matrices are obtained on the basis of the parametric solutions of the generalized high‐order Sylvester matrix equations. This approach does not impose any restrictions on the closed‐loop eigenvalues. An illustrative example shows the effect of the proposed approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Static output feedback control for stochastic hybrid systems: LMI approach

This paper deals with the stabilization problem of the class of uncertain stochastic hybrid systems. The uncertainties are norm bounded type. Under the complete access to the system mode a static output feedback controller that makes the closed-loop dynamics of this class of systems regular, impulse-free and stochastically stable is designed. The gains of this controller are the solution of some linear matrix inequalities (LMIs).     

Finite‐time output feedback stabilization of nonlinear high‐order feedforward systems

This paper considers the global finite‐time output feedback stabilization of a class of nonlinear high‐order feedforward systems. By using the homogeneous domination method together with adding a power integrator method and overcoming several troublesome obstacles in the design and analysis, a global finite‐time output feedback controller with reduced‐order observer is recursively designed to globally finite‐time stabilize nonlinear high‐order feedforward systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Periodic output feedback stabilization of single-input single-output continuous-time systems with odd relative degree

The paper considers the long-standing open problem of static output feedback stabilization with periodic output feedback. Extending the tools from vibrational control theory, we are able to derive some original results for this problem. We provide some sufficient conditions for stabilization with periodic output feedback. The proposed approach is constructive, and for some low dimensional cases, the sufficient conditions that we present are also necessary.     

Design of output feedback consensus controllers for nonlinear sampled-data multi-agent systems of strict-feedback form

Design of reduced-order observer-based output feedback consensus controllers for nonlinear sampled-data multi-agent systems of strict-feedback form is considered based on nonlinear sampled-data control and consensus control theories. As a practical application of the proposed design method, output feedback consensus control for sampled-data fully actuated ships is also discussed.     

On discrete dynamic output feedback min-max controllers

The paper considers output feedback min-max controllers for non-square discrete time uncertain linear systems. Based on previous work, it is demonstrated that static output feedback min-max controllers are only realizable for a specific class of systems. To broaden this class, a compensator based framework is proposed to introduce additional degrees of freedom. The conditions for the existence of such dynamic output feedback min-max controllers are given and are shown to be relatively mild. Furthermore, a simple parameterization of the available design freedom is proposed. An explicit procedure is described which shows how a Lyapunov matrix, which satisfies both a discrete Riccati inequality and a structural constraint, can be obtained using Linear matrix inequality optimization. This Lyapunov matrix is used to calculate the robustness bounds associated with the closed-loop system. A simple aircraft example is provided to demonstrate the efficacy of the design approach.     

Robust output feedback stabilization of nonlinear systems with low‐order and high‐order nonlinearities

In this paper, we consider the problem of global output feedback stabilization for a class of nonlinear systems whose nonlinearities are assumed to be bounded by both low‐order and high‐order nonlinearities multiplied by a polynomial‐type output‐dependent growth rate. Instead of the previously proposed dual observer, based on the homogeneous domination approach, a new reduced‐order observer is constructed, which greatly simplifies the closed‐loop controller and is able to cover a more general class of nonlinear systems. Copyright © 2015 John Wiley & Sons, Ltd.