Abstract
The problem of determining an estimate for an upper bound on the magnitude of persistent disturbances so that the state of a dynamical system always belongs to a prescribed region of state space, has been well studied using Liapunov techniques. A major difficulty has always been to choose that Liapunov function which yields the best bound. This paper describes a systematic approach for finding a suitable Liapunov function by transforming to normal co-ordinates. The undisturbed system is assumed linear, timeinvariant and asymptotically stable. The methods applied to a scrap melting process which forms part of the model for an LD steel making plant.
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