Semi-global stabilization of linear systems subject to output saturation

It is established that a SISO linear stabilizable and detectable system subject to output saturation can be semi-globally stabilized by linear output feedback if all its invariant zeros are in the closed left-half plane, no matter where the open loop poles are. This result complements a recent result that such systems can always be globally stabilized by discontinuous nonlinear feedback laws, and can be viewed as dual to a well-known result: a linear stabilizable and detectable system subject to input saturation can be semi-globally stabilized by linear output feedback if all its poles are in the open left-half plane, no matter where the invariant zeros are.     

Non-fragile positive real control for uncertain linear neutral delay systems

This paper is concerned with the problem of non-fragile positive real control for uncertain neutral delay systems with time-invariant norm-bounded parameter uncertainty. Time delays are assumed to appear in both the state and the controlled output equations. The state feedback gains are with norm-bounded controller uncertainties. For both the cases with additive and multiplicative controller uncertainties, we address the problem of designing memoryless state feedback controllers such that, for all admissible uncertainties, the resulting closed-loop system is stable and the closed-loop transfer function is extended strictly positive real. Sufficient conditions for the existence of desired controllers are given in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, the expected memoryless state feedback controller can be easily constructed via convex optimization. An illustrative example is given to demonstrate the validity and applicability of the proposed approach.     

Output feedback pole-assignment procedure

A new algorithm based on pole-assignment considerations for linear time-invariant m-input p-output systems by means of static output feedback is presented for the case in which the number of inputs m and the number of outputs p are less than the order of the system n. This algorithm determines the output-feedback matrix required to assign max (p, m) - 1 poles, and simultaneously calculates the coefficients of the residual polynomial, the roots of which are the remaining unassigned poles. The root-locus method is used to find an appropriate feedback gain to provide acceptable locations for the unassigned poles. Some numerical examples are provided to illustrate this method.     

Determining dynamic output feedback of the least order for SIMO systems to locate poles in a specified region†

This paper presents a new theory for determining dynamic output feedback of the least order for a linear, time-invariant, controllable and observable SIMO system, such that poles of the closed-loop system lie in a given region Γ in the complex plane. When some poles have prespecified stationary locations in the complex plane, dynamic output feedback is obtained in the sense that the remaining poles lie in Γ This theory applies to continuous-time as well as discrete-time systems. Here a design algorithm for complete system realization and an illustrative example are given.     

Robust H∞ control for uncertain discrete singular systems with pole placement in a disk

This paper addresses the design of robust H_∞ controllers for uncertain discrete singular systems with time-invariant uncertainty in both the state and measurement matrices. The singular system to be controlled is not assumed to be regular. A regular dynamic output feedback controller is designed such that a prescribed H_∞ performance condition is satisfied and the closed-loop poles are placed in a specified disk while the regularity, causality and stability of the closed-loop system can be guaranteed for all admissible uncertainties. The desired controller can be obtained by solving a set of matrix inequalities. A numerical example is given to demonstrate the application of the proposed method.     

用输出反馈配置鲁棒极点*

本文讨论了线性定常多变量系统在时域上用输出反馈配置鲁棒极点的问题。用输出反馈配置极点时,有一些自由度,可以利用这些自由度指定特征向量。本文给出一种数值方法,它用于选择一组尽可能正交的特征向量,使闭环系统矩阵A+BKC尽可能接近正规,从而使闭环极点对于矩阵的系数变化是鲁棒的。     

Pole assignment for linear periodic systems by memoryless outputfeedback

We consider linear periodic discrete-time systems. We are interested in the problem of placing the poles of the monodromy map by means of periodic output feedback of the same or multiple period. It is well known that, in general, the poles of time-invariant systems cannot be assigned by constant output feedback. This is in contrast with what can be obtained in the context of time-variant systems. The main contribution of this paper is that periodic output feedback suffices for pole placement of periodic systems     

A new approach for the design of multivariable feedback systems

A new design technique for multivariable feedback systems is presented. In this approach, n —1 open-loop transfer functions at different inputs of the plant, with all other feedback paths closed, are specified in advance, and are achieved exactly. The nth open-loop transfer function is a by-product of the design process, such that the overall feedback system is stabilized. The design approach is fitted to solve problems in which the plant elements can have non-stable poles and non-minimum phase zeros. The design process is straightforward, no iterations are necessary, and the achieved design copes exactly with the design specifications. The gainbandwidths of the different lis and the overall loop gain l* might be constrained due to non-stable poles and zeros of the plant elements. Based on the obtained different loop gains, any input output matrix T can bo achieved with the aid of an appropriate prefilter matrix F.     

Observer-based output feedback control of discrete-time linear systems with input and output delays

In this paper, we study observer-based output feedback control of discrete-time linear systems with both multiple input and output delays. By generalising our recently developed truncated predictor feedback approach for state feedback stabilisation of discrete-time time-delay systems to the design of observer-based output feedback, two types of observer-based output feedback controllers, one being memory and the other memoryless, are constructed. Both full-order and reduced-order observer-based controllers are established in both the memory and memoryless schemes. It is shown that the separation principle holds for the memory observer-based output feedback controllers, but does not hold for the memoryless ones. We further show that the proposed observer-based output feedback controllers solve both the l₂ and l_∞ semi-global stabilisation problems. A numerical example is given to illustrate the effectiveness of the proposed approaches.     

On impulsive algebraic multiplicities of linear time-invariant singular systems under feedback

Impulsive algebraic multiplicities of linear time-invariant singular systems under output feedback or decentralized output feedback are characterized in terms of system matrices directly. The multiplicities describe the number of impulsive modes that can be eliminated and indicate the number of finite poles that can be assigned by the respective feedback. These characterizations also lead to new regularizability conditions for singular systems.     

Structural properties and poles assignability of LTI singular systems under output feedback

This paper studies the structural properties of both finite poles and the infinite pole of linear time-invariant singular systems under output feedback. Three main problems are studied, namely, (1) the algebraic structures of both finite poles and the infinite pole; (2) the assignability of finite poles and the elimination of the infinite pole by output feedback; and (3) the controllability and observability of the system with minimal number of inputs and outputs. New generic solutions to these problems are presented in terms of some new concepts defined in this paper including the geometric multiplicity of the infinite pole, the finite and impulsive output feedback cycle indices of the system. Determination of these multiplicities and indices are discussed. An assignability equivalence is established between the variable finite poles and the poles of a controllable and observable non-singular system. The number of the independent infinite poles that can be reduced is given in terms of the system matrices. The minimal number of inputs and outputs that guarantee controllability and observability are shown to be the output feedback cycle indices.     

Disturbance attenuation over a first-order moving average Gaussian noise channel

In this paper, the problem of disturbance attenuation has been studied for a linear time-invariant feedback control system with a first-order moving average Gaussian noise channel. By applying the concept of entropy power, a lower bound of signal-to-noise ratio has been achieved which is necessary for stabilisation of a system with the limited channel input power constraint. Moreover, the problem of minimising the influence of a stochastic disturbance on the output has also been investigated, and the controller design method has been obtained by using Youla parameterisation and H₂ theory. It is shown that the minimum variance of the system output depends not only on the disturbance variance, noise variance and unstable poles, but also on the non-minimum phase zeros and channel parameter. Finally, the effectiveness of the proposed results is illustrated by a numerical example.     

Robust state feedback control of LTV systems: nonlinear is betterthan linear

Examples of linear control systems with fast time-varying uncertain coefficients are given, which can be stabilized by a nonlinear memoryless state feedback, but cannot be stabilized by a linear time-invariant dynamic state feedback. By means of one of these examples the authors show that the closed loop quadratic stability margin may be infinitely smaller than the actual stability margin     

容错控制系统鲁棒H∞和自适应补偿设计

通过设计动态输出反馈控制策略研究线性时不变系统执行器故障下的鲁棒自适应容错H∞控制问题. 结合自适应技术和线性矩阵不等式(Linear matrix inequalities, LMI)技术, 设计一个控制策略同时实现系统的故障补偿控制和性能优化控制. 在设计中, 提出由自适应律在线调节控制增益方程补偿未知执行器故障和摄动; 并设计一个基于模式依赖李亚普诺夫方程的LMI条件解出控制参数及次优H∞性能. 所设计的动态输出反馈控制器可以处理一般执行器卡死故障, 并得到更少保守性的H∞性能指标. 此外, 一个更具挑战性的问题, 即通过自适应机构补偿故障致使系统多少性能退化得到论证. 所提方法的有效性由一个解耦线性化动态飞行器系统仿真验证.     

On the decoupling of multivariable control systems with time delays†

The decoupling problem is solved for an m-input m-output linear time-invariant system with multiple delays in the state and/or the control. The conditions under which such a system can be decoupled are found and the class of the feedback decoupling operators is given. These operators are realized by means of digital filters. Then, the more general linear model in which the input effects directly the output is considered which, upon the introduction of both feedback and feedforward, is shown to be decoupled, Two illustrative examples are included to support the theoretical results.     

A design procedure for pole assignment using output feedback

A new design procedure is presented for assigning closed-loop eigenvalues of multi-variable, linear systems using output feedback control. Subject to certain mild restrictions, the number of poles which can be assigned to arbitrary, distinct locations is mill [m + r ? 1, n], where m, r and n are the dimensions of the output, control and state vectors, respectively. The design procedure provides an extension of the results of Davison and Chatterjee (1971) and Jameson (1970) but allows a significantly larger number of eigenvalues to be assigned. The simplicity of the design procedure is demonstrated by a numerical example.     

Persistent disturbance rejection via static-state feedback

In contrast with ℋ_∞ and ℋ₂ control theories, the problem of persistent disturbance rejection (l¹ optimal control) leads to dynamic controllers, even when the states of the plant are available for feedback. Using viability theory, Shamma showed (1993), in a nonconstructive way, that in the state-feedback case the same performance achieved by any dynamic linear time-invariant controller can be achieved using memoryless nonlinear state feedback. In this paper we give an alternative, constructive proof of these results for discrete- and continuous-time systems. The main result of the paper shows that in both cases, the l¹ norm achieved by any stabilizing state-feedback linear dynamic controller can be also achieved using a memoryless variable structure controller     

Pole-assignment with periodic output feedback: computer assisted study on a 2-dimensional linear system

In this paper we study the single-input single-output discrete time linear system where X_k ∈ R², and where the input u_k is defined by the time-varying output feedback We examine conditions under which the system using periodic output feedback can have its closed-loop poles arbitrarily assigned.     

Pole assignment using dynamic output feedback compensators

The design of dynamic output feedback compensators for the pole assignment of linear time-invariant multivariable systems is considered. A systematic procedure is developed for the synthesis of the transfer function matrix of the compensator. A certain number of poles can be arbitrarily assigned by the proposed compensator. Moreover, in order to assign more poles using a compensator of the same order as before, a new approximate assignment approach based on the least-square-error algorithm is proposed. A numerical example is given to demonstrate the effectiveness of the proposed approaches.     

The singular-G method for unstable non-minimum-phase plants†

In linear time-invariant feedback systems with plants which have both poles and zeros in the right half-plane, it is always possible to stabilize the system for a fixed plant. But in the previous optimum techniques, the stability margins might be so small as to render the design wholly impractical. This problem was overcome in the X-29 aircraft in a multiple-input-multiple-output (MIMO) setting, by use of a singular-G (compensation) matrix inside the loop. Excellent stability margins were then achievable over a wide plant parameter range, by means of a fixed-G compensation matrix.

This paper extends the singular-G technique to the single-input-single-output (SISO) plant. The latter is converted into an equivalent N × N MIMO plant by means of N parallel independent time-varying modulators acting on the plant output, a technique previously used for non-linear network synthesis. The singular-G method is then applicable to the equivalent N × N MIMO plant. The detailed design procedure is presented by means of an example with N = 2.