A new approach to the parameter estimation of linear time-invariant delayed systems via modified Laguerre polynomials

1985 ◽  
Vol 16 (12) ◽  
pp. 1505-1515 ◽  
Author(s):  
RONG-YEU CHANG ◽  
KUN-CHOU CHEN ◽  
MAW-LING WANG
Keyword(s):  
Parameter Estimation ◽  
Linear Time ◽  
Laguerre Polynomials ◽  
Delayed Systems ◽  
New Approach ◽  
Linear Time Invariant ◽  
Time Invariant ◽  
Modified Laguerre Polynomials

Equivalency of Stability Transitions Between the SDS (Spectral Delay Space) and DS (Delay Space)

2013 ◽  
Author(s):  
Qingbin Gao ◽  
Umut Zalluhoglu ◽  
Nejat Olgac
Keyword(s):  
Linear Time ◽  
Broad Class ◽  
Delay Systems ◽  
Multiple Delays ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Time In Literature ◽  
The Stability ◽  
Time Invariant ◽  
Delay Space

It has been shown that the stability of LTI time-delayed systems with respect to the delays can be analyzed in two equivalent domains: (i) delay space (DS) and (ii) spectral delay space (SDS). Considering a broad class of linear time-invariant time delay systems with multiple delays, the equivalency of the stability transitions along the transition boundaries is studied in both spaces. For this we follow two corresponding radial lines in DS and SDS, and prove for the first time in literature that they are equivalent. This property enables us to extract local stability transition features within the SDS without going back to the DS. The main advantage of remaining in SDS is that, one can avoid a non-linear transition from kernel hypercurves to offspring hypercurves in DS. Instead the potential stability switching curves in SDS are generated simply by stacking a finite dimensional cube called the building block (BB) along the axes. A case study is presented within the report to visualize this property.

Computing Impulse Response of Room Acoustics Using the Ray-Tracing Method in Time Domain

2010 ◽  
Vol 35 (4) ◽  
pp. 505-519 ◽  
Author(s):  
Adil Alpkocak ◽  
Malik Sis
Keyword(s):  
Impulse Response ◽  
Linear Time ◽  
Simulation Software ◽  
Room Acoustics ◽  
New Approach ◽  
Linear Time Invariant ◽  
Linear Time Invariant System ◽  
Time Invariant ◽  
Time Invariant System

AbstractThis paper proposes a new approach for calculating the impulse response of room acoustics. Impulse response provides unique characterization of any discrete lineartime invariant (LTI) systems. We assume that the room is a linear time-invariant system and the impulse response is calculated simply by sending a Dirac Impulse into the system as input and getting the response from the output. Then, the output of the system is represented as a sum of time-shifted weighted impulse responses. Both mathematical justifications for the proposed method and results from simulation software developed to evaluate the proposed approach are presented in detail.

scholarly journals Modified Schur-Cohn Criterion for Stability of Delayed Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Juan Ignacio Mulero-Martínez
Keyword(s):  
Linear Time ◽  
Discrete Systems ◽  
Delayed Systems ◽  
Triangular Matrices ◽  
Numerical Errors ◽  
Real Roots ◽  
Linear Time Invariant ◽  
Alternative Approach ◽  
Linear Time Invariant Systems ◽  
Time Invariant

A modified Schur-Cohn criterion for time-delay linear time-invariant systems is derived. The classical Schur-Cohn criterion has two main drawbacks; namely, (i) the dimension of the Schur-Cohn matrix generates some round-off errors eventually resulting in a polynomial ofswith erroneous coefficients and (ii) imaginary roots are very hard to detect when numerical errors creep in. In contrast to the classical Schur-Cohn criterion an alternative approach is proposed in this paper which is based on the application of triangular matrices over a polynomial ring in a similar way as in the Jury test of stability for discrete systems. The advantages of the proposed approach are that it halves the dimension of the polynomial and it only requires seeking real roots, making this modified criterion comparable to the Rekasius substitution criterion.

FUZZY CENTRE BASED SOLUTION OF FUZZY COMPLEX LINEAR SYSTEM OF EQUATIONS

2013 ◽  
Vol 21 (04) ◽  
pp. 629-642 ◽  
Author(s):  
DIPTIRANJAN BEHERA ◽  
S. CHAKRAVERTY
Keyword(s):  
Linear Time ◽  
Linear Equations ◽  
Electric Circuit ◽  
System Of Linear Equations ◽  
New Approach ◽  
Linear System Of Equations ◽  
Linear Time Invariant ◽  
Complex Linear ◽  
Time Invariant ◽  
Good Agreement

A new approach to solve Fuzzy Complex System of Linear Equations (FCSLE) based on fuzzy complex centre procedure is presented here. Few theorems related to the investigation are stated and proved. Finally the presented procedure is used to analyze an example problem of linear time invariant electric circuit with complex crisp coefficient and fuzzy complex sources. The results obtained are also compared with the known solutions and are found to be in good agreement.

ON EFFICIENCY OF EKF FOR PARAMETER ESTIMATION OF LTI SYSTEM FROM NON-STATIONARY ACCELERATION RESPONSES

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Swarup Mahato ◽  
Arunasis Chakraborty
Keyword(s):  
Parameter Estimation ◽  
Linear Time ◽  
Modal Parameters ◽  
Acceleration Response ◽  
Identification Scheme ◽  
Linear Time Invariant ◽  
Lti System ◽  
Eigen Values ◽  
Predictor Corrector ◽  
Time Invariant

Parameters of the linear time invariant (LTI) dynamic system using extended Kalman filter (EKF) are identified in this work. The efficiency of EKF for parameter estimation of LTI system is studied. For this purpose, a three-story steel frame is used in the laboratory, and the recorded ground motion is applied to measure the acceleration response at different floor levels. Using these responses, the EKF-based predictor-corrector algorithm is used to identify the modal parameters. It has been observed that the EKF-based identification scheme can converge to different system matrices (i.e., mass and stiffness) in different experiments for the same structure. However, their eigen values (i.e., natural frequency and mode) remain the same.

Model parameter estimation of linear time-invariant systems from combined data of forced and initial condition responses

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Ya Guo ◽  
Jinglu Tan
Keyword(s):  
Parameter Estimation ◽  
State Space ◽  
Linear Time ◽  
Initial Condition ◽  
Model Parameter ◽  
Model Parameter Estimation ◽  
Linear Time Invariant ◽  
Forced Responses ◽  
Time Invariant ◽  
Combined Data

AbstractMany systems can be represented as linear time-invariant (LTI) systems in state space with ordinary differential equations (ODE). Forced responses are often used for model parameter estimation; however, some models are not uniquely identifiable from the data of forced responses, or experiments with pure forced response may not be the optimal design. It is thus meaningful to look for other types of data for model parameter estimation through redesigning experiments. In this work, we compare the influence of forced and initial condition responses on the deterministic identifiability of LTI systems in state space with ODEs as model structure. It is clearly demonstrated that one initial condition vector is equivalent to one column vector of the control matrix for constraining system eigenvectors. The combination of forced and initial condition responses can improve the identifiability of models that are not identifiable only from forced responses. Explicit formulations and an algorithm are derived to identify model parameters from the combined data of forced and initial condition responses.

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