VECTOR DISSIPATIVITY THEORY FOR DISCRETE-TIME LARGE-SCALE NONLINEAR DYNAMICAL SYSTEMS

In analyzing large-scale systems, it is often desirable to treat the overall system as a col-lection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems and the na-ture of the system interconnections. In this paper, we develop an analysis framework for discrete-time large-scale dynamical systems based on vector dissipativity notions. Specif-ically, using vector storage functions and vector supply rates, dissipativity properties of the discrete-time composite large-scale system are shown to be determined from the dissi-pativity properties of the subsystems and their interconnections. In particular, extended Kalman-Yakubovich-Popov conditions, in terms of the subsystem dynamics and inter-connection constraints, characterizing vector dissipativeness via vector system storage functions are derived. Finally, these results are used to develop feedback interconnection stability results for discrete-time large-scale nonlinear dynamical systems using vector Lyapunov functions. 1