Power system dynamics and stability: Jan Machowski, Janusz W. Bialek and James R. Bumby; Wiley, New York, 1997, ISBN 0-471-95643-0

analysis problems. When the e;ects of 0nite arithmetic and variable delays are considered, the models arising in the convergence analysis problem become nonlinear and time-varying. The chapter presents suAcient conditions for convergence of a special class of iterative algorithms referred to as synchronous block-iterative methods. It also presents convergence results for more general iterative algorithms referred to as asynchronous block iterative methods. Some results are also presented for the special case in which the equations being solved have a special structure referred to as “almost linear”. Finally, this chapter considers the convergence of iterative algorithms referred to as team algorithms which are hybrids of a number of di;erent standard algorithms for the solution of nonlinear equations. Chapter 5 applies diagonal Lyapunov methods to a number of speci0c applications. The 0rst application which is considered is Hop0eld–Tank neural networks. These are nonlinear dynamical systems with a diagonal structure. The main results given for such networks are suAcient conditions for global asymptotic stability of a unique equilibrium point. Such neural networks are considered in both continuous time and discrete time. This chapter also considers a connection between passive RLC circuits and diagonally stable matrices. Other applications considered in this chapter are digital 0lters subject to quantization errors and biological systems referred to as Trophic Chains. Chapter 6 considers various interconnected systems and large scale systems in which diagonal Lyapunov functions can be applied. The 0rst problem considered is that of diagonal stability for a large scale system which consists of the interconnection of a number of subsystems. For this class of problems, a vector Lyapunov approach is considered and a comparison principle is used to establish a suAcient condition for global asymptotic stability using a diagonal-type Lyapunov function. Another application considered in this chapter involves the