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CONTROLLABILITY AND OBSERVABILITY OF DISTRIBUTED PARAMETER SYSTEMS

In this paper, the main purpose is to obtain explicit conditions of controllability and observability for distributed parameter systems. At first a distributed parameter system, governed by a simultaneous linear partial differential equation, is transformed into an infinite set of lumped parameter systems using a countable basis in an element space of the state product space. Thereafter, it is shown that the conditions for the distributed parameter system are given by those for each lumped parameter system in each case of controllability and observability. The explicit conditions of controllability and observability for distributed parameter systems are obtained. This theory is illustrated by its application to various types of systems with distributed, pointwise, scanning and boundary controls or outputs. Finally, the concepts of N-step controllability and N-step observability are introduced and the conditions are also presented for discrete-time distributed parameter systems.