Finite-region boundedness and stabilization for 2D continuous-discrete systems in Roesser model

This paper investigates the finite-region boundedness (FRB) and stabilization problems for two-dimensional continuous-discrete linear Roesser models subject to two kinds of disturbances. For two-dimensional continuous-discrete system, we first put forward the concepts of finite-region stability and FRB. Then, by establishing special recursive formulas, sufficient conditions of FRB for two-dimensional continuous-discrete systems with two kinds of disturbances are formulated. Furthermore, we analyze the finite-region stabilization issues for the corresponding two-dimensional continuous-discrete systems and give generic sufficient conditions and sufficient conditions that can be verified by linear matrix inequalities for designing the state feedback controllers which ensure the closed-loop systems FRB. Finally, viable experimental results are demonstrated by illustrative examples

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

Finite-region stability of 2-D singular Roesser systems with directional delays

In this paper, the problem of finite-region stability is studied for a class of two-dimensional (2-D) singular systems described by using the Roesser model with directional delays. Based on the regularity, we first decompose the underlying singular 2-D systems into fast and slow subsystems corresponding to dynamic and algebraic parts. Then, with the Lyapunov-like 2-D functional method, we construct a weighted 2-D functional candidate and utilize zero-type free matrix equations to derive delay-dependent stability conditions in terms of linear matrix inequalities (LMIs). More specifically, the derived conditions ensure that all state trajectories of the system do not exceed a prescribed threshold over a pre-specified finite region of time for any initial state sequences when energy-norms of dynamic parts do not exceed given bounds

A necessary and sufficient LMI condition for stability of 2D mixed continuous-discrete-time systems

WeA10 Regular Session: Linear Systems I, Paper WeA10.6This paper addresses the problem of establishing stability of 2D mixed continuous-discrete-time systems. Traditional stability analysis for 2D systems gives a sufficient condition based on 2D version of a Lyapunov equation. Here, a linear matrix inequality (LMI) condition is proposed that extends these results by introducing complex Lyapunov functions depending polynomially on a parameter and by exploiting the Gram matrix method. It is shown that this condition is sufficient for 2D exponential stability for any chosen degree of the Lyapunov function candidate, and it is also shown that this condition is also necessary for a sufficiently large degree. Moreover, an a priori bound on the degree required for achieving necessity is given. Some numerical examples illustrate the proposed methodology.published_or_final_versio

On the Control of Distributed Parameter Systems using a Multidimensional Systems Setting

The unique characteristic of a repetitive process is a series of sweeps, termed passes, through a set of dynamics defined over a finite duration with resetting before the start of the each new one. 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 leads to the possibility that the output, i.e. the sequence of pass profiles, will contain oscillations which increase in amplitude in the pass-to-pass direction. Such behavior cannot be controlled by standard linear systems approach and instead they must be treated as a multidimensional system, i.e. information propagation in more than one independent direction. Physical examples of such processes include long-wall coal cutting and metal rolling. In this paper, stability analysis and control systems design algorithms are developed for a model where a plane, or rectangle, of information is propagated in the passto- pass direction. The possible use of these in the control of distributed parameter systems is then described using a fourthorder wavefront equation

H∞ and guaranteed cost control of discrete linear repetitive processes

AbstractRepetitive processes are a distinct class of 2D systems (i.e. information propagation in two independent directions) of both systems theoretic and applications interest. In general, they cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or 2D systems theory. Here first we give major new results on the design of control laws using an H∞ setting and including the possibility of uncertainty in the process model. Then we give the first ever results on guaranteed cost control, i.e. including a performance criterion in the design. The designs in both cases can be computed using linear matrix inequalities. These results are for so-called discrete linear repetitive processes which arise in applications areas such as iterative learning control

Robust synchronization for 2-D discrete-time coupled dynamical networks

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Finite-region stabilization via dynamic output feedback for 2-D Roesser models

Finite-region stability (FRS), a generalization of finite-time stability, has been used to analyze the transient behavior of discrete two-dimensional (2-D) systems. In this paper, we consider the problem of FRS for discrete 2-D Roesser models via dynamic output feedback. First, a sufficient condition is given to design the dynamic output feedback controller with a state feedback-observer structure, which ensures the closed-loop system FRS. Then, this condition is reducible to a condition that is solvable by linear matrix inequalities. Finally, viable experimental results are demonstrated by an illustrative example