Vector dissipativity theory for discrete-time large-scale nonlinear dynamical systems
- PDF / 866,868 Bytes
- 30 Pages / 468 x 680 pts Page_size
- 41 Downloads / 140 Views
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 dissipativity 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 (i.e., 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 (i.e., large-scale) system can then be predicted from the behaviors of the individual subsystems and their interconnections. The need for decentralized analysis and control design of large-scale systems is a direct consequence of the physical size and complexity of the dynamical model. In particular, computational complexity may be too large for model analysis while severe constraints on communication links between system sensors, actuators, and processors may render centralized control architectures impractical. Copyright © 2004 Hindawi Publishing Corporation Advances in Difference Equations 2004:1 (2004) 37–66 2000 Mathematics Subject Classification: 93A15, 93D30, 93C10, 70K20, 93C55 URL: http://dx.doi.org/10.1155/S1687183904310071
38
Vector dissipativity and discrete-time large-scale systems
An approach to analyzing large-scale dynamical systems was introduced by the pioˇ neering work of Siljak [19] and involves the notion of connective stability. In particular, the large-scale dynamical system is decomposed into a collection of subsystems with local dynamics and uncertain interactions. Then, each subsystem is considered independently so that the stability of each subsystem is combined with the interconnection constraints to obtain a vector Lyapunov function for the composite large-scale dynamical system guaranteeing connective stabi
Data Loading...
