The theory of state observers for linear deterministic systems with lumped parameters founded by Lueneberger is extended for distributed parameter systems with several state variables.A definition of the asymptotic state observer with distributed parameters is given, from which conditions for the sysnthesis of observers are deduced. Two special cases, the observers of full and reduced order, are discussed and illustrated with two examples. The utilization of an observer in the feedback control loop is also investigated. The theoretical results of this paper form a basis for future applications.
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