Equivalence of wave linear repetitive processes and the singular 2-D Roesser state-space model

Multidimensional Systems and Signal Processing - This paper develops a direct method for transforming a polynomial system matrix describing a discrete wave linear repetitive process to a 2-D...     

On the stability and the stabilization of linear discrete repetitive processes

Multidimensional Systems and Signal Processing - This article deals with stability and stabilization issues for linear two-dimensional (2D) discrete models. More precisely, we focus on repetitive...     

Hankel-type model reduction for linear repetitive processes: differential and discrete cases

This paper investigates a Hankel-type model reduction problem for linear repetitive processes. Both differential and discrete cases are considered. For a given stable along the pass process, our attention is focused on the construction of a reduced-order stable along the pass process, which guarantees the corresponding error process to have a specified Hankel-type error performance. The Hankel-type performances are first established for differential and discrete linear repetitive processes, respectively, and the corresponding model reduction problems are solved by using the projection approach. Since these obtained conditions are not expressed in linear matrix inequality (LMI) form, the cone complementary linearization (CCL) method is exploited to cast them into sequential minimization problems subject to LMI constraints, which can be solved efficiently. Three numerical examples are provided to demonstrate the proposed theory. This work was partially supported by RGC HKU 7028/04P.     

On the reduction of 2-D polynomial systems into first order equivalent models

Multidimensional Systems and Signal Processing - In this paper we propose a novel approach for the reduction of a 2-D rectangular polynomial matrix of arbitrary degree, to first-order matrix...     

Admissibility and stabilization of singular continuous 2D systems described by Roesser model

Multidimensional Systems and Signal Processing - The paper considers first, the admissibility conditions for continuous 2D systems represented by Roesser model by dealing with non-strict LMIs....     

On the stability of linear repetitive processes described by a delay-difference equation

This paper considers linear repetitive processes which are a distinct class of two-dimensional linear systems of both physical and systems theoretic interest. Their essential unique feature is a series of sweeps, termed passes, through a set of dynamics defined over a finite and fixed duration known as the pass length. The result can be oscillations in the output sequence of pass profiles which increase in amplitude in the pass-to-pass direction. This cannot be controlled by existing techniques and instead control must be based on a suitably defined stability theory. In the literature to date, the development of such a theory has been attempted from two different starting points, and in this paper, we critically compare these for dynamics defined by a delay-difference equation.     

Numerical iterative methods and repetitive processes

Implicit schemes are a popular approach to the discretization of linear partial differential equations by finite differences. They require to solve a set of linear equations in each time step. Since finite difference discretizations lead to a local coupling, these systems of equations are sparse and can be effectively solved by iterative methods. Numerical procedures of this type are known in control theory as repetitive processes. They have mostly been used to solve problems in control like processes where passes of finite length are repeated over and over. This paper shows how the implicit discretization of partial differential equations can be cast into the framework of repetitive processes. Thus it establishes a link between yet unrelated results in numerical mathematics and control theory.     

On control laws for discrete linear repetitive processes with dynamic boundary conditions

Repetitive processes are characterized by a series of sweeps, termed passes, through a set of dynamics defined over a finite duration known as the pass length. On each pass an output, termed the pass profile, is produced which acts as a forcing function on, and hence contributes to, the dynamics of the next pass profile. This can lead to oscillations in the sequence of pass profiles produced which increase in amplitude in the pass-to-pass direction and cannot be controlled by application of standard control laws. Here we give new results on the design of physically based control laws for so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control.     

Robust stability of hybrid Roesser models against parametric uncertainty: a general approach

This paper aims at proposing a general framework for the establishement of LMI conditions to analyse the robust stability of a singular hybrid Roesser model subject to parametric uncertainties. The uncertain parameters are involved through implicit Linear Fractional Representations (LFR). Special focus is put on the influence of the number of uncertain parameters and the dimensionality of the model. More precisely it is shown that each dimension can nearly be regarded as an uncertain parameter and the other way around. Therefore, their influence on the conservatism of the obtained condition is very similar.     

Decoupling and iterative approaches to the control of discrete linear repetitive processes

This paper reports new results on the analysis and control of discrete linear repetitive processes which are a distinct class of 2D discrete linear systems of both systems theoretic and applications interest. In particular, we first propose an extension to the basic state-space model to include a coupling term previously neglected but which arises in some applications and then proceed to show how computationally efficient control laws can be designed for this new model.     

On the Asymptotic Stability of Positive 2-D Systems Described by the Roesser Model

This brief investigates the asymptotic stability of positive 2D systems described by the Roesser model. A necessary and sufficient condition is derived for the asymptotic stability, which amounts to checking the spectrum radius of the system matrix. Furthermore, it can be shown that the asymptotic stability of positive 2D systems is equivalent to that of the traditional 1D systems. This observation would greatly facilitate the analysis and synthesis of positive 2D systems.     

Strong practical stability and stabilization of discrete linear repetitive processes

This paper considers two-dimensional (2D) discrete linear systems recursive over the upper right quadrant described by well known state-space models. Included are discrete linear repetitive processes that evolve over subset of this quadrant. A stability theory exists for these processes based on a bounded-input bounded-output approach and there has also been work on the design of stabilizing control laws, elements of which have led to the assertion that this stability theory is too strong in many cases of applications interest. This paper develops so-called strong practical stability as an alternative in such cases. The analysis includes computationally efficient tests that lead directly to the design of stabilizing control laws, including the case when there is uncertainty associated with the process model. The results are illustrated by application to a linear model approximation of the dynamics of a metal rolling process.

金属锻造重复过程的输出反馈控制

研究了金属锻造重复过程的输出反馈控制问题.通过设计一个输出反馈控制器使金属锻造重复过程稳定,给出控制器存在的充分条件,并将控制器的设计转化为一个凸优化的求解问题.仿真实例证实了该设计方法的有效性.     

Guaranteed cost control of uncertain differential linear repetitive processes

This paper deals with the problem of designing a control law for differential linear repetitive processes based on minimizing a cost function in the presence of uncertainties in the process model. This control law results in a closed-loop stable process with an associated cost function which is bounded for all admissible uncertainties. Moreover, an optimization algorithm is developed to design this law such that it minimizes the upperbound of the closed-loop cost function.     

Existence of optimal solutions of two-directionally continuous linear repetitive processes

In the paper, an existence theorem for a Lagrange optimal control problem connected with a two-directionally continuous variant of a linear autonomous repetitive process is derived. As a corollary, existence of an optimal solution in the case of cost functional depending on a fixed ??end-function?? is obtained.     

On observability of singular systems

Concepts of observability and strong observability for singular systems are introduced and characterized geometrically in terms of the system matrices without using the Weierstrass decomposition. Duality relations between observability and controllability and that between reachability and strong observability are established. A canonical form for the action of the output injection group on the set of observable systems is presented.     

自相似过程的几种模型

本文综述了目前在自相似过程建模研究方面所获得的主要成果，分析了各自的优缺点，这对于自相似信号的处理具有一定的指导意义。     

On the analysis of two-dimensional discrete singular systems

In contrast to 1-D systems, the 2-D systems have no natural notion of causality. An artificial restriction traditionally imposed to allow recursive solution of these systems is that of recursibility. In this paper we study 2-Dsingular systems, taking advantage of the nonoriented or noncausal nature of these systems to provide a solution even if the requirement of recursibility does not hold. It is shown thatnonrecursible masks may be described using singular 2-D systems. The analysis approach relies on thefundamental matrix.Research supported by the US Fulbright Foundation in Greece and NSF Grant ECS-8805932.     

Maximum principle for optimal control of two-directionally continuous linear repetitive processes

In the paper, maximum principle for a two-directionally continuous variant of a linear autonomous repetitive process with cost functional depending on a fixed “end-function” is obtained. Maximum condition has a pointwise form, a conjugate system has a Fornasini-Marchesini form. The result is derived from the extremum principle for smooth-convex problems, due to Ioffe and Tikhomirov.