1,403 research outputs found
Conserved- and zero-mean quadratic quantities in oscillatory systems
We study quadratic functionals of the variables of a linear oscillatory system and their derivatives. We show that such functionals are partitioned in conserved quantities and in trivially- and intrinsic zero-mean quantities. We also state an equipartition of energy principle for oscillatory systems
State maps for linear systems
Modeling of physical systems consists of writing the equations describing a phenomenon and yields as a result a set of differential-algebraic equations. As such, state-space models are not a natural starting point for modeling, while they have utmost importance in the simulation and control phase. The paper addresses the problem of computing state variables for systems of linear differential-algebraic equations of various forms. The point of view from which the problem is considered is the behavioral one, as put forward in [J. C. Willems, Automatica J. IFAC, 22 (1986), pp. 561ā580; DynamicsReported,2(1989),pp.171ā269;IEEETrans.Automat.Control,36(1991),pp. 259ā294]
Nonergodicity and Central Limit Behavior for Long-range Hamiltonians
We present a molecular dynamics test of the Central Limit Theorem (CLT) in a
paradigmatic long-range-interacting many-body classical Hamiltonian system, the
HMF model. We calculate sums of velocities at equidistant times along
deterministic trajectories for different sizes and energy densities. We show
that, when the system is in a chaotic regime (specifically, at thermal
equilibrium), ergodicity is essentially verified, and the Pdfs of the sums
appear to be Gaussians, consistently with the standard CLT. When the system is,
instead, only weakly chaotic (specifically, along longstanding metastable
Quasi-Stationary States), nonergodicity (i.e., discrepant ensemble and time
averages) is observed, and robust -Gaussian attractors emerge, consistently
with recently proved generalizations of the CLT.Comment: 6 pages 7 figures. Improved version accepted for publication on
Europhysics Letter
Stability of switched linear differential systems
We study the stability of switched systems where the dynamic modes are
described by systems of higher-order linear differential equations not
necessarily sharing the same state space. Concatenability of trajectories at
the switching instants is specified by gluing conditions, i.e. algebraic
conditions on the trajectories and their derivatives at the switching instant.
We provide sufficient conditions for stability based on LMIs for systems with
general gluing conditions. We also analyse the role of positive-realness in
providing sufficient polynomial-algebraic conditions for stability of two-modes
switched systems with special gluing conditions
Algorithms for deterministic balanced subspace identification
New algorithms for identification of a balanced state space representation are proposed. They are based on a procedure for the estimation of impulse response and sequential zero input responses directly from data. The proposed algorithms are more efficient than the existing alternatives that compute the whole Hankel matrix of Markov parameters. It is shown that the computations can be performed on Hankel matrices of the inputāoutput data of various dimensions. By choosing wider matrices, we need persistency of excitation of smaller order. Moreover, this leads to computational savings and improved statistical accuracy when the data is noisy. Using a finite amount of inputāoutput data, the existing algorithms compute finite time balanced representation and the identified models have a lower bound on the distance to an exact balanced representation. The proposed algorithm can approximate arbitrarily closely an exact balanced representation. Moreover, the finite time balancing parameter can be selected automatically by monitoring the decay of the impulse response. We show what is the optimal in terms of minimal identifiability condition partition of the data into āpastā and āfutureā
Balanced state representations with polynomial algebra
Algorithms are derived which pass directly from the differential equation describing the behavior of a finite-dimensional linear system to a balanced state representatio
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