A new formulation of Q-Markov covariance equivalent realization

Abstract

The Q-Markov Covariance Equivalent Realization ( Q-Markov Cover) is a state space realization which matches the first Q Markov parameters and covariance parameters of a system. King, Desai, and Skelton [5] developed a generalized approach to generate Q-Markov Covers. Desai and Skelton [3] presented a recursive computational algorithm for generating Q-Markov Covers when Q is very large. Based on the works of the above two papers, we developed a new formula for generating Q-Markov Covers, and also an algorithm to compute them when Q is very large. The new formula has been applied for model identification of large flexible structures by Liu and Skelton [6–8]. Compared with previously developed formulas and algorithms, the new formula and algorithm are relatively straightforward and easy to program. This formula may simplify the further analytical study of Q-Markov Covers and its application to system identification.