Analysis of Practical Stability for Time Delay and Distributed Parameter Systems - Dihovicni, Djordje N. (Communications - Scientific letters of the University of Zilina, 2011)
This paper points to sufficient conditions for practical stability of linear systems with time delay in state. Particularly, in control system engineering practice, despite the contribution to the contemporary control theory and system thinking, the problems of practical stability are not developed in details. Taking into account that the system can be stable in a classic way, but it can also possess inappropriate quality of dynamic behavior, and because of that, it is not applicable. For engineers it is crucial to take the system into consideration in relation to permitted states in phase space which are defined for such a problem, Dihovicni et al. (2006). Although, there are some papers covering practical stability problems, the lack of exploring it by using fundamental matrix and matrix measure was observed. Our main idea is to present definitions and conditions for practical stability, applying matrix measure approach. From a practical view point, it is crucial to find intervals on which the system is stable, and to know the function of initial state, the “prehistory” of system motion. The practical stability for a class of a distributed parameter system is also presented. The system is described in state space and a unique theory for such a problem is developed where a fundamental matrix of system and matrix measure is used. Using an efficient approach based on matrix measure and system fundamental matrix, the theorems for practical stability of distributed parameter systems are developed, and superiority of our results is illustrated with a numerical example.