This paper deals with the problems of reconstruction and the observation method for continuous time linear dynamical systems with random parameters. The Markov model of stochastic differential equation is used to develop the physical continuous systems.
The discussion of the problem is mainly divided into three parts. Firstly, the unknown statistics of the state in random parameter systems subjected to deterministic and piecewise continuous inputs are reconstructed from the system's scalar output at
n(
n+1)/2 points in its history.
Secondly, the conditions of reconstructibility for the unknown stationary or non-stationary random inputs to the random parameter systems with known initial states are considered from the view-points of input observability.
Finally, an optimal observation matrix and optimal monitor time locations are determined from the min-max procedure on the eigen value of the symmetic matrix relative to the observability matrix, which is induced by the condition to minimize the difference between sample and population statistics in the sense of norm.
An numerical example is given to illustrate the obtained conditions and the proposed technique. The relations between the confidence intervals and the observation method are discussed in detail.
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