抄録
In this paper, we propose a new algorithmic method to determine the maximal parts of the input and the state at each time instant which are reconstructable exactly from the output alone for both continuous and discrete linear time-invariant systems with unknown initial states. Simultaneously this method contains the practical computational method of reconstructing the parts of the input and the state from the outputs.
For these purposes, we provide two new computationally efficient algorithms. The first algorithm is the extension result of one developed by Moylan (1977) which constructs the stable inverse system. This algorithm partitions the parts of inputs and states which become to be known at each iteration step, and at the same time subtracts these parts from the original system so that the original system may be reduced to the so-called “contracted system” of it.
In continuous systems it is shown that no part of the inputs or the states in the contracted system can be determined by the knowledge of the outputs and that the reconstructable parts of the input and the state at each time instant are constant.
On the contrary it is shown in discrete systems that the reconstructable parts of the input and the state vary and monotonously increase as time increases. Then the second algorithm is developed for the purpose of reconstructing these parts, and it is applied to the contracted system.
