TAILIEUCHUNG - VECTOR DISSIPATIVITY THEORY FOR DISCRETE-TIME LARGE-SCALE NONLINEAR DYNAMICAL SYSTEMS WASSIM M.

VECTOR DISSIPATIVITY THEORY FOR DISCRETE-TIME LARGE-SCALE NONLINEAR DYNAMICAL SYSTEMS WASSIM M. HADDAD, QING HUI, VIJAYSEKHAR CHELLABOINA, AND SERGEY NERSESOV Received 15 October 2003 In analyzing large-scale systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems and the nature of the system interconnections. In this paper, we develop an analysis framework for discrete-time large-scale dynamical systems based on vector dissipativity notions. Specifically, using vector storage functions and vector supply rates, dissipativity properties of the discrete-time composite large-scale system are. | VECTOR DISSIPATIVITY THEORY FOR DISCRETE-TIME LARGE-SCALE NONLINEAR DYNAMICAL SYSTEMS WASSIM M. HADDAD QING HUI VIJAYSEKHAR CHELLABOINA AND SERGEY NERSESOV Received 15 October 2003 In analyzing large-scale systems it is often desirable to treat the overall system as a collection of interconnected subsystems. Solution properties of the large-scale system are then deduced from the solution properties of the individual subsystems and the nature of the system interconnections. In this paper we develop an analysis framework for discrete-time large-scale dynamical systems based on vector dissipativity notions. Specifically 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 interconnection 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. Introduction Modern complex dynamical systems are highly interconnected and mutually interdependent both physically and through a multitude of information and communication network constraints. The sheer size . dimensionality and complexity of these large-scale dynamical systems often necessitate a hierarchical decentralized architecture for analyzing and controlling these systems. Specifically in the analysis and control-system design of complex large-scale dynamical systems it is often desirable to treat the overall system as a collection of interconnected subsystems. The behavior of the aggregate or composite . large-scale system can then be predicted from the behaviors of the individual subsystems and their interconnections.

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