Q-Markov Covariance equivalent realizations for unstable and marginally stable systems. (1st August 2023)

• Record Type: Journal Article
• Authors: Shen, Yuling; Chen, Muhao; Majji, Manoranjan; Skelton, Robert E.
• Is Part Of: Mechanical systems and signal processing. Volume 196(2023)
• Publication Date: 2023-08-01
• Subjects: QMC -- System identification -- Markov parameter -- Covariance parameter -- Unstable systems; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2023.110343
• Languages: English
• ISSNs: 0888-3270

Abstract

Abstract: An observer-based q-Markov Covariance equivalent realization (QMC) formulation is presented in the paper. It is shown that by inserting an observer in the input–output relationship associated with the dynamical system, a QMC approach can be developed that is applicable to systems with marginally stable or unstable equilibrium points. A system of equations governing all linear state-space realizations, along with the corresponding observers, is derived from matching a set of Markov and Covariance parameters. The solution to this equation system is shown to parameterize all state-space realizations that match the pre-specified correlation functions. Four numerical examples are used to show the utility of the proposed approach. The numerical results show that the observer-based QMC presented in the paper can identify linear SISO and MIMO systems with stable, marginally stable, and unstable characteristics.