Improved condition for the stability of decentralised control of large scale systems

An improved condition for the stability of decentralised control for large scale systems is presented. An existing well-established condition for the stability of such systems gives a “global” condition in the sense that it can only be used to test the overall system stability after the design of all subsystems has been completed. The new condition is a “local” condition applied to each subsystem, which allows the subsystem controller designs to be carried out one by one and independently. With a little modification, it is also shown that an improved robust stability condition, in terms of connective stability, can also be developed. These developments are based on an algorithm for finding the smallest possible values in a matrix to satisfy the M-matrix condition