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This paper has solved the inverse eigenvalue problem for "fixed-free" mass-chain systems with inerters. It is well known that for a spring-mass system wherein the adjacent masses are linked through a spring, the natural frequency assignment can be achieved by choosing appropriate masses and spring stiffnesses if and only if the given positive eigenvalues are distinct. However, when we involve inerters, multiple eigenvalues in the assignment are allowed. In fact, arbitrarily given a set of positive real numbers, we derive a necessary and sufficient condition on the multiplicities of these numbers, which are assigned as the natural frequencies of the concerned mass-spring-inerter system.

This paper is concerned with the least squares estimator for a basic class of nonlinear autoregressive models, whose outputs are not necessarily to be ergodic. Several asymptotic properties of the least squares estimator have been established under mild conditions. These properties suggest the strong consistency of the least squares estimates in nonlinear autoregressive models which are not divergent.

This paper studies the identification of nonlinearly parameterized control systems in given experiments. Several identifiability criteria are established and an implementable algorithm is proposed for practicality with the convergence rate explicitly computed.

This report presents some supplementary material to the paper entitled "Passive controller realization of a biquadratic impedance with double poles and zeros as a seven-element Series-parallel network for effective mechanical control" [1].

We attempt to answer the question what data brings adaptive diffusion algorithms converging to true parameters. The discussion begins with the diffusion recursive least squares (RLS). When unknown parameters are scalar, the necessary and sufficient condition of the convergence for the diffusion RLS is established, in terms of the strong consistency and mean-square convergence both. However, for the general high dimensional parameter case, our results suggest that the diffusion RLS in a connected network might cause a diverging error, even if local data at every node could guarantee the individual RLS tending to true parameters. Due to the possible failure of the diffusion RLS, we prove that the diffusion Robbins-Monro (RM) algorithm could achieve the strong consistency and mean-square convergence simultaneously, under some cooperative information conditions. The convergence rates of the diffusion RM are derived explicitly.

This report includes the original manuscript and the supplementary material of "Realization of Biquadratic Impedance as Five-Element Bridge Networks".

This is supplementary material to "Realizations of a special class of admittances with strictly lower complexity than canonical forms" [1], which presents the detailed proofs of some results. For more background information, refer to [2]-[22] and references therein., Comment: 6 pages, 2 figures, supplementary report to a journal paper