STRING STABILITY OF INTERCONNECTED SYSTEMS

In this paper we introduce the notion of string stability of a countab ly infinite interconnection of a class of nonlinear systems. Intuitive ly, string stability implies uniform boundedness of all the states of the interconnected system for all time if the initial states of the in terconnected system are uniformly bounded, It is well known that the i nput-output gain of all the subsystems less than unity guarantees that the interconnected system is input-output stable. We derive sufficien t (''weak coupling'') conditions which guarantee the asymptotic string stability of a class of interconnected systems, Under the same ''weak coupling'' conditions, string-stable interconnected systems remain st ring stable in the presence of small structural/singular perturbations . In the presence of parameter mismatch, these ''weak coupling'' condi tions ensure that the states of all the subsystems are all uniformly b ounded when a gradient-based parameter adaptation law is used and that the states of all the systems go to zero asymptotically.