This paper surveys the control theoretic literature on decentralized and hierarchical control, and methods of analysis of large scale systems.

Survey of decentralized control methods for large scale systems

This brief solves some synthesis problems for a class of linear systems for which the state takes nonnegative values whenever the initial conditions are nonnegative. In particular, the synthesis of state-feedback controllers is solved in terms of linear programming problem, including the requirement of positiveness of the controller and its extension to uncertain plants. In addition, the synthesis problem with nonsymmetrical bounds on the stabilizing control is treated

Controller Synthesis for Positive Linear Systems With Bounded Controls

Recent research into large-scale system stability has proceeded via two apparently unrelated approaches. For Lyapunov stability, it is assumed that the system can be broken down into a number of subsystems, and that for each subsystem one can find a Lyapunov function (or something akin to a Lyapunov function). The alternative approach is an input-output approach; stability criteria are derived by assuming that each subsystem has finite gain. The input-output method has also been applied to interconnections of passive and of conic subsystems. This paper attempts to unify many of the previous results, by studying linear interconnections of so-called "dissipative" subsystems. A single matrix condition is given which ensures both input-output stability and Lyapunov stability. The result is then specialized to cover interconnections of some special types of dissipative systems, namely finite gain systems, passive systems, and conic systems.

Stability criteria for large-scale systems

Application of M-matrices to the stability problems of composite dynamical systems

The composite-system method for analyzing stability of large-scale system is studied focusing on the quadratic-order theorems using M -matrices. Here, by the term "composite-system method", we refer to the method to decompose a large-scale system into smaller subsystems and to make two-step analysis (i.e., first to analyze subsystems and second to combine the results to reduce the property of the whole). Theories about Lyapunov stability and about input-output stability are described from a unified standpoint and their mutual relation is clarified. As an application, multi-input multi-output systems. The contents are generally useful for stability analysis of large-scale nonlinear systems.

Stability of large-scale nonlinear systems--Quadratic-order theory of composite-system method using M-matrices

A sufficient condition for asymptotic stability in the large is proposed for nonlinear systems. It is applicable if the system in question can be decomposed into subsystems, if appropriate Lyapunov functions are obtained for the subsystems, and if the connections between subsystems have bounded dc gains. It is generally less restrictive than the condition previously presented by Bailey for similar systems. An estimate of transient behavior, together with the stability condition, is also given.

B. Kondo

Papers

Stability and transient behavior of composite nonlinear systems