KYBERNETIKA — VOLUME 32 (1996), NUMBER 6, PAGES 575-590 BALANCING OF SYSTEMS WITH PERIODIC J UMPS 1 RAVI ARIPIRALA AND VASSILIS L. SYRMOS In this paper we study the balancing and model-reduction of linear systems with discrete jumps at periodic time instants. These systems arise in the study of linear systems with sampled data control and filtering problems. We study the balancing for the case of fixed and infinite intervals. We show that the system balancing can be used to obtain a reduced order-model of the system with the properties of the original system. An example is provided to illustrate the procedure. 1. INTRODUCTION In the recent past considerable interest has been shown in the design of controllers for continuous systems with sampled data measurements. This is largely due to the ease of implementation of the controller with the use of a digital computer. The emphasis has been on direct design of the digital controllers without resorting to discretization of the plant or the controller to take into consideration the intersample behavior of the system [1, 2, 14]. The study of these problems has given rise to linear systems with finite discrete jumps at periodic instants [14]. The systems with jumps arise naturally in H2 and Hoo optimization problems. These systems have the properties of both continuous and discrete systems and in fact both the continuous time and discrete time systems can be derived as special cases [14]. On the other hand the notion of balanced realizations of systems was introduced by Moore in [6] and studied extensively in [6, 15]. The balanced systems were used to study the concept of model reduction by [6] and connections to the Hankel-norm approximations were drawn in [3]. It was shown that the internal realization of the system in certain co-ordinates has minimum sensitivity with regard to parameter variations in [7, 16]. Applications to filter design with minimum sensitivity were also explored. The concept was extended to time varying systems in [9] and [17]. In fact [17] explores the possibility of input-output balancing for various gramians and gives necessary and sufficient conditions for the balancing transformations to exist in terms of the parameters of the system. While [9] explored the balanced realizations for uniform realizations, [17] considered balancing over a general class of intervals. a This research was supported by the National Science Foundation under grant NCR-9210408 and by the Advanced Research Projects Agency under contract MDA-972-93-1-0032 and MDA- 972-95-3-0016.