Positive real control of two-dimensional systems: Roesser models and linear repetitive processes

This paper considers the problem of positive real control for two-dimensional (2-D) discrete systems described by the Roesser model and also discrete linear repetitive processes, which are another distinct sub-class of 2-D linear systems of both systems theoretic and applications interest. The purpose of this paper is to design a dynamic output feedback controller such that the resulting closed-loop system is asymptotically stable and the closed-loop system transfer function from the disturbance to the controlled output is extended strictly positive real. We first establish a version of positive realness for 2-D discrete systems described by the Roesser state space model, then a sufficient condition for the existence of the desired output feedback controllers is obtained in terms of four LMIs. When these LMIs are feasible, an explicit parameterization of the desired output feedback controllers is given. We then apply a similar approach to discrete linear repetitive processes represented in their equivalent 1-D state-space form. Finally, we provide numerical examples to demonstrate the applicability of the approach.     

H/sub /spl infin// control of differential linear repetitive processes

Repetitive processes are a distinct class of two-dimensional (2-D) systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard [termed one-dimensional (1-D) here] or 2-D systems theory. Here, we give new results on the relatively open problem of the design of control laws using an H/sub /spl infin// setting. These results are for the sub-class of so-called differential linear repetitive processes which arise in applications.     

The Fornasini-Marchesini and the Roesser models: algebraic methodsfor recasting

This paper is devoted to giving a new method for recasting the Fornasini-Marchesini model of the two-dimensional system to the Roesser form, endowed with an important feature, that the dimensions of both models are the same. The two-dimensional similarity transformation and spectral transformations of the transfer function variables are used for this purpose. Both the standard and singular cases are considered     

Characterization of a class of spatially interconnected systems (ladder circuits) using two-dimensional systems theory

Multidimensional Systems and Signal Processing - This paper considers a class of spatially interconnected systems formed by ladder circuits using two-dimensional systems theory. The individual...