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In a preceeding paper the concept of macroscopic stability was introduced, and a sufficient condition for the macroscopic asymptotic stability of a large scale interconnected system is given. The concept of macroscopic stability is introduced from the points of view that there must be certain variables representing the global characteristics of a large scale system and that in the analysis of a large scale system the behavior of these variables is important. The sufficient condition was given on the basis of the comparison function for each subsystem with regard to its input-output relation.In this paper the macroscopic stability of interconnected systems with time delay is considered. For this purpose the Matrosov's comparison theorem is generalized to the functional differential inequalities. With the aid of this theorem and comparison functions, the macroscopic asymptotic stability of interconnected systems with time delay between subsystems is studied, and it is shown that the theorem in the previous paper for a system with no time delay is also applicable to this system without any modification.Furthermore a more general comparison function is introduced for a subsystem with time delay and by means of this function and comparison theorem, conditions for the macroscopic stability of the more general interconnected systems with time delay are studied. The relation between the Lyapunov functional and the comparison function is presented for a subsystem with time delay.
- 公益社団法人 計測自動制御学会の論文
公益社団法人 計測自動制御学会 | 論文
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