Successive linearizations of second order multidimensional time-invariant systems

2004 ◽  
Vol 162 (2) ◽  
pp. 79-88 ◽  
Author(s):  
Fethi Belkhouche ◽  
Boumediene Belkhouche
Keyword(s):  
Second Order ◽  
Time Invariant

scholarly journals Tuning of a time-delayed controller for a general class of second-order linear time invariant systems with dead-time

2019 ◽  
Vol 13 (3) ◽  
pp. 451-457 ◽  
Author(s):  
Raul Villafuerte-Segura ◽  
Francisco Medina-Dorantes ◽  
Leopoldo Vite-Hernández ◽  
Baltazar Aguirre-Hernández
Keyword(s):  
General Class ◽  
Dead Time ◽  
Linear Time ◽  
Second Order ◽  
Order Linear ◽  
Linear Time Invariant ◽  
Linear Time Invariant Systems ◽  
Time Invariant

An identification problem in almost and asymptotically almost periodically correlated processes

1982 ◽  
Vol 19 (2) ◽  
pp. 456-462 ◽  
Author(s):  
Y. Isokawa
Keyword(s):  
Random Process ◽  
Point Process ◽  
Identification Problem ◽  
Second Order ◽  
Linear Filter ◽  
Minimum Phase ◽  
Periodically Correlated Processes ◽  
Time Invariant

Consider a unknown realizable time-invariant linear filter driven by a point process. We are interested in the identification of this system, observing only the output random process. If the process is almost periodically correlated but not periodically correlated, we can identify the filter, using the second-order non-stationary spectrum of the process. We do not require the assumption that the filter is minimum phase.

Order Reduction of Parametrically Excited Linear and Nonlinear Structural Systems

2005 ◽  
Vol 128 (4) ◽  
pp. 458-468 ◽  
Author(s):  
Venkatesh Deshmukh ◽  
Eric A. Butcher ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Order Reduction ◽  
Second Order ◽  
Degree Of Freedom ◽  
Structural Systems ◽  
Parametrically Excited ◽  
Reduced Models ◽  
Linear And Nonlinear ◽  
Time Invariant ◽  
Time Periodic

Order reduction of parametrically excited linear and nonlinear structural systems represented by a set of second order equations is considered. First, the system is converted into a second order system with time invariant linear system matrices and (for nonlinear systems) periodically modulated nonlinearities via the Lyapunov-Floquet transformation. Then a master-slave separation of degrees of freedom is used and a relation between the slave coordinates and the master coordinates is constructed. Two possible order reduction techniques are suggested. In the first approach a constant Guyan-like linear kernel which accounts for both stiffness and inertia is employed with a possible periodically modulated nonlinear part for nonlinear systems. The second method for nonlinear systems reduces to finding a time-periodic nonlinear invariant manifold relation in the modal coordinates. In the process, closed form expressions for “true internal” and “true combination” resonances are obtained for various nonlinearities which are generalizations of those previously reported for time-invariant systems. No limits are placed on the size of the time-periodic terms thus making this method extremely general even for strongly excited systems. A four degree-of-freedom mass- spring-damper system with periodic stiffness and damping as well as two and five degree-of-freedom inverted pendula with periodic follower forces are used as illustrative examples. The nonlinear-based reduced models are compared with linear-based reduced models in the presence and absence of nonlinear resonances.

POISSON MODELS WITH DYNAMIC RANDOM EFFECTS AND NONNEGATIVE CREDIBILITIES PER PERIOD

2020 ◽  
Vol 50 (2) ◽  
pp. 585-618 ◽  
Author(s):  
Jean Pinquet
Keyword(s):  
Time Series ◽  
Random Effects ◽  
Semiparametric Models ◽  
Second Order ◽  
Risk Exposure ◽  
Autocovariance Function ◽  
Poisson Models ◽  
Poisson Distributions ◽  
Short Memory ◽  
Time Invariant

AbstractThis paper provides a toolbox for the credibility analysis of frequency risks, with allowance for the seniority of claims and of risk exposure. We use Poisson models with dynamic and second-order stationary random effects that ensure nonnegative credibilities per period. We specify classes of autocovariance functions that are compatible with positive random effects and that entail nonnegative credibilities regardless of the risk exposure. Random effects with nonnegative generalized partial autocorrelations are shown to imply nonnegative credibilities. This holds for ARFIMA(0, d, 0) models. The AR(p) time series that ensure nonnegative credibilities are specified from their precision matrices. The compatibility of these semiparametric models with log-Gaussian random effects is verified. Gaussian sequences with ARFIMA(0, d, 0) specifications, which are then exponentiated entrywise, provide positive random effects that also imply nonnegative credibilities. Dynamic random effects applied to Poisson distributions are retained as products of two uncorrelated and positive components: the first is time-invariant, whereas the autocovariance function of the second vanishes at infinity and ensures nonnegative credibilities. The limit credibility is related to the three levels for the length of the memory in the random effects. The limit credibility is less than one in the short memory case, and a formula is provided.

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