State Nullification by Memoryless Output Feedback

We examine linear single-input single-output finite-dimensional systems. It is shown that a continuous time controllable and observable system can be nullified utilizing periodic sampling of the output with time-varying linear feedback. Almost any sampling rate can be used. The result relies on a characterization of linear output feedback nullification of discrete time observable and controllable systems. An algorithm for the nullification and an estimate on the time in which the algorithm is concluded are provided.Research supported by grants from the Israel Science Foundation and from the Information Society Technologies Programme of the European Commission.(Incumbent of the Hettie H. Heineman Professorial Chair in Mathematics).     

Minimal controllability for systems with delays†

In this paper we consider the problem of minimal controllability for a general class of linear spectrally controllable systems. We show that the smallest number of controls that are necessary in order that spectral controllability may hold depends only upon the matrices of the uncontrolled system and that it is equal to the smallest number of outputs necessary for the dual problem of ‘spectral observability’; moreover, any spectrally controllable system can be made minimally controllable by acting upon the control matrix only, and any spectrally observable system can be made minimally observable by acting upon the output matrix only. In the sequel this result is explained in the cases of the delayed systems and of some kind of generalized systems.     

Pole placement using dynamic compensators

The problem of designing a compensator to obtain arbitrary pole placement in the system consisting of the plant and compensator in cascade is considered. The design uses only those state variables which can be measured. It is shown that for a controllable observable plant a compensator of orderbeta = min(nu_{c} - 1, nu_{o} - 1)is sufficient to achieve this result. Herenu_{c}(nu_{o})is the controllability (observability) index of the plant. This result is obtained by first showing that any multi-input multi-output linear time-invariant system may be made controllable (observable) from a single input (output) using only output feedback. The main result is then proved in a constructive manner which explicitly relates the compensator parameters to the coefficients of the desired characteristic polynomial.     

Memoryless output feedback nullification and canonical forms,for time varying systems

We study the possibility of nullifying time-varying systems with memoryless output feedback. The systems we examine are discrete-time linear single-input single-output finite-dimensional time-varying systems. For generic completely controllable and completely observable discrete-time systems, we show that any state at any time can be steered to the origin within finite time. An algorithm for nullification and an upper bound for nullification time, depending only on the system's dimension, are provided. The algorithm is described using a representation of the system in time-varying controller canonical form. We verify that every completely controllable system has such a representation.     

Exact linearizations of input-output systems

The problem of transforming non-linear systems to linear systems is receiving much attention in the literature. In this paper, we present necessary and sufficient conditions such that a non-linear control system with output can be equivalent to a linear control system with linear output that is controllable and observable. The conditions depend on certain Lie derivatives of the output and can be verified in a finite number of steps. For simplicity, we consider only the single input/single output case.     

Nonlinear feedback control of flexible joint manipulators: a singlelink case study

A nonlinear feedback control for a flexible joint manipulator is investigated. It is shown that if the elastic (parasitic) modes are weakly observable from the output of the system, a state-space coordinate transformation and a static state feedback and control space transformation will turn the flexible system into a linear controllable and observable system. In contrast, if the parasitics are strongly observable, a dynamic state feedback is required for input-output linearization. Numerical simulations for a single link flexible joint manipulator are reported, illustrating the application of the methodology     

An improved algorithm for optimal state regulation of generalized systems

The system considered is a generalized system E = Ax + Bu, Y = Cx with matrix E singular. When the impulsive modes of the system are both controllable and observable, it is shown in this paper that these modes can be eliminated by almost any constant output feedback. For a strongly controllable and observable generalized system, after its impulsive modes are eliminated, the poles of the system can be assigned arbitrarily by state feedback. Even if the states are not available, the paper adopts an efficient method to design a compensator for the system.     

一类线性时变系统的输出反馈控制

基于线性时不变系统能控能观标准型变换及非线性系统高增益观测器方法,本文研究了一类线性时变系统 的输出反馈控制问题. 通过引入时变的状态变量坐标变换,分别设计了线性时变系统的状态反馈控制器、状态观测器以及基于 状态观测器的输出反馈控制器. 进一步地,本文分别证明了观测器动态误差是渐近收敛于零的,而状态反馈控制器以及输出反馈控制器可以 保证闭环系统的渐近稳定性.     

Parallel concatenated convolutional codes from linear systems theory viewpoint

The aim of this work is to characterize two models of concatenated convolutional codes based on the theory of linear systems. The problem we consider can be viewed as the study of composite linear system from the classical control theory or as the interconnection from the behavioral system viewpoint. In this paper we provide an input–state–output representation of both models and introduce some conditions for such representations to be both controllable and observable. We also introduce a lower bound on their free distances and the column distances.     

Stabilization of linear systems in the presence of output measurement saturation

This note considers siso nonlinear systems, which have a linear controllable and observable part followed by a measurement saturation nonlinearity. A controller is presented, which feeds back only the saturating output measurements and nevertheless globally asymptotically stabilizes the system. The equilibrium is actually reached in finite time, i.e. the controller is dead beat.     

Fractional representations of linear systems

A fractional representation of an arbitrary linear system is obtained that can be viewed as a generalization of a classical fractional representation of a transfer function. Conversely, a state-space model, not necessarily observable or controllable, can be assigned to any such fractional model. It is then shown that the categories of state-space and fractional representations of a linear system are equivalent.     

Control and state observation of periodic linear multimodal systems

This paper investigates the control and state observation problem for periodic linear controllable and observable multimodal systems. For a controllable periodic linear multimodal system, this paper proposes an alternative minimum-norm dynamic state feedback control scheme for state transition matrix assignment. Also presented is a new design of state observers for an observable periodic linear multimodal system. Finally, an analysis of closed-loop behaviour of controlled periodic linear multimodal systems using a state-estimate is given     

Exact pole assignment by output feedback Part 1

We shall prove that exact assignment of distinct poles using output feedback is possible in any controllable and observable linear time-invariant multivariable system in which the number of inputs plus the number of outputs exceeds the number of states, except in clearly identified circumstances. Furthermore we give a construction for the entire class of pathological cases. The main part of our argument is concerned with the assigning of complex conjugate eigenvalues by means of a real feedback matrix; indeed we begin by giving a simple algorithm which is effective over any field. Although this problem has been discussed by numerous authors in the past, they have usually presented only generic results. We examine the complete class of systems satisfying the hypotheses mentioned.     

面向控制的压电主动结构建模方法

以压电悬臂板为分析对象,通过对系统输入一输出数据作变换处理,隐式地设计最小拍状态观测器,基于状态观测器的Markov参数计算系统Markov参数,亦即系统脉冲响应采样值,然后采用特征系统实现算法辨识得到系统最小实现,所建立的智能结构的状态空间模型能控、能观,为控制器设计提供了一个较为精确的数学模型．     

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.     

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.     

On sampling without loss of observability/controllability

This paper presents a (nonequidistant, periodic) sampling pattern, which has the property that the sample and zero-order hold operations, applied to any observable and controllable continuous-time system of order not exceeding N, results in a discrete-time system which is also observable and controllable     

Algebraic properties of singular systems subject to decentralized output feedback

This paper investigates algebraic properties of decentralized singular systems (DSSs) under local static output feedback. New concepts of the geometric multiplicity (GM) of the finite decentralized fixed mode (DFM), the decentralized output feedback variable polynomial (DVP), and the finite decentralized output feedback cycle index (DCI) of the DSS are defined. The formulas for determining the GM and the DCI are given in terms of the DFM and the system matrices. It is shown that almost any decentralized output feedback can make the zeros of the DVP (i.e., the closed-loop poles that are variable) distinct and away from any given finite set in the complex plane. It is also shown that the finite DFM of the DSS are those uncontrollable and/or observable finite modes of the closed-loop DSS through any single channel. Finally, the minimal number of the inputs and outputs that guarantee the finite modes of the closed-loop DSS controllable and observable is shown to be the finite DCI of the DSS. An illustrative example is provided.     

Synthesis of a suboptimal controller by output for dampening limited disturbances

In the framework of the method of invariant ellipsoids, for a linear dynamic object a suboptimal linear dynamic controller by output is synthesized, at which the upper estimate of a maximum value of the norm of the controllable output reaches a minimum at all initial states of a system from a certain domain and at any disturbances bounded by the norm.     

Observers for linear multivariable systems with applications

This paper presents an algorithm for the design of asymptotic state estimators (observers) for index-invariant uniformly observable time-varying linear finite-dimensional multivariable systems. The results obtained indicate that asymptotic estimators can be employed in optimally designed regulators provided an increase from the optimal cost is tolerable. It is also shown that any uniformly observable and uniformly controllable plant with index-invariant observability and controllability matrices can be stabilized with an observer.