Continuous feedback guaranteeing uniform ultimate boundedness for uncertain linear delay systems: An application to river pollution control

Abstract

We employ the stability result of Thowsen on a class of linear delay systems containing uncertain elements and subject to uncertain inputs to manage a simple one-reach model of a river system with time delay and subject to uncertain but bounded input as well as parameter disturbances. Two important indices of water quality, namely, biochemical oxygen demand (BOD) and dissolved oxygen (DO) are used as state variables, while controls in the form of effluent discharge rate of BOD and in-stream aeration rate of DO are employed to steer the system to a calculable neighborhood of a desired steady state and then maintain it there.