Connective Stability of Discontinuous Large Scale Systems

In practice we frequently encounter systems which are most appropriately represented by discontinuous ordinary differential equations. Such equations are investigated qualitatively by Filippov [Z], He [3], Michel and Porter [S, 61, and others. Many such systems often are complex and of a very large scale. It is possible to view such systems as consisting of several simpler subsystems which when interconnected in an appropriate fashion yield the original large scale systems. The behavior of such systems are studied by He [4], Michel and Porter [5, 61, etc. In this paper, we develop the connective stability which was established for the continuous large scale systems by Siljak [ 10, 111 to the discontinuous large scale systems. Following He [4], the decomposition-aggregation method and comparison principle are used to derive sufficient conditions such that the trivial solution of the discontinuous large scale systems is connectively stable, uniformly, and connectively stable, respectively.