Linear systems with non-stationary random inputs†

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Abstract
This paper concerns the response correlation matrix of a linear time variable system with stationary or non-stationary stochastic inputs modulated by linear homogeneous operators. By adapting Lanczos' ‘selected points’ method an algorithm is introduced to compute the state covariance matrix of systems with deterministic initial state. Certain computational features of response correlation matrices of systems with random initial state and random inputs are also outlined. Limited numerical studies indicate that the proposed method is efficient to treat uni-dimensional and small-order multi-dimensional systems. Mean square response comparisons with some of the previously studied systems indicate good agreement and the saving in machine time appears to be substantial.