Abstract
Abstract The statement of a new Lyapunov for linear systems x - . = A - x - called Integral Lyapunov function is presented and discussed. The special quality of these is that only the output variable y = c - T x - is needed for their calculation. These Lyapunov can be used to determine Lyapunov domains G in the state space which cannot be left by a trajectory. In contrast to the observer concept where the estimated state x - ^ tends to x - for t → ∞ we obtain the domain G after a finite initialization time. The Integral Lyapunov functions can be applied to indicate the proper performance of a control system. Another application, a variable structure control strategy which does not need the state vector for the feedback, is investigated. It can be shown that these controllers yield a better performance compared with a fixed P-controller
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