%0 Journal Article
%T Stability Analysis of 2D Discrete Linear System Described by the Fornasini-Marchesini Second Model with Actuator Saturation
%A Richa Negi
%A Haranath Kar
%A Shubhi Purwar
%J ISRN Computational Mathematics
%D 2012
%R 10.5402/2012/847178
%X This paper proposes a novel antiwindup controller for 2D discrete linear systems with saturating controls in Fornasini-Marchesini second local state space (FMSLSS) setting. A Lyapunov-based method to design an antiwindup gain of 2D discrete systems with saturating controls is established. Stability conditions allowing the design of antiwindup loops, in both local and global contexts have been derived. Numerical examples are provided to illustrate the applicability of the proposed method. 1. Introduction An important problem which is always inherent to all dynamical systems is the presence of actuator saturation nonlinearities. Such nonlinearities may lead to performance degradation and even instability for feedback control systems. The stability analysis of the continuous as well as discrete time linear systems with saturating controls has been widely considered for one-dimensional (1D) systems [1每10]. The commonly used techniques to design controllers taking into account actuator saturation are (i) constrained model predictive control [4, 11], (ii) scheduled controllers [12], and (iii) antiwindup compensators [13每18]. Model predictive controllers find applications in chemical industries for the control of systems with saturations. Scheduled controllers also called piecewise linear controller or gain scheduling schemes are often used in aerospace industry. Antiwindup compensators are widely used in practice for the control systems with saturating actuators [14, 15]. Design of antiwindup controllers can be carried out using linear design methods which explain its usefulness and popularity among control engineers. The actuator saturation problem is tackled following the ※antiwindup paradigm§ which employs a two-step design procedure. The main idea here is to design a linear controller ignoring the saturation nonlinearities and then augment this controller with extra dynamics to minimize the adverse effects of saturation on the closed loop performance. Several results as well as design schemes on the antiwindup problem and compensation gain are formulated and the stability conditions have been mentioned for 1D systems [7每10, 14每18]. In the recent years, two-dimensional (2D) discrete systems have found various applications in many areas such as filtering, image processing, seismographic data processing, thermal processes, gas absorption, and water stream heating [19每22]. Mathematically, a 2D discrete system is represented by a set of difference equations with two space coordinates. The stability properties of 2D discrete systems described by
%U http://www.hindawi.com/journals/isrn.computational.mathematics/2012/847178/