Identification of time-varying systems using a two-dimensional B-spline algorithm

2012 ◽  
Author(s):  
Peter Zoltan Csurcsia ◽  
Johan Schoukens ◽  
Istvan Kollar
Keyword(s):  
Time Varying ◽  
Two Dimensional ◽  
B Spline ◽  
Time Varying Systems

Properties of the Lower Bohl Exponents of Diagonal Discrete Linear Time-Varying Systems

2015 ◽  
Vol 789-790 ◽  
pp. 1052-1058
Author(s):  
Michał Niezabitowski
Keyword(s):  
Dynamical Systems ◽  
Linear System ◽  
Control Theory ◽  
Lyapunov Exponents ◽  
Discrete Time ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
Time Varying Systems

The Bohl exponents, similarly as Lyapunov exponents, are one of the most important numerical characteristics of dynamical systems used in control theory. Properties of the Lyapunov characteristics are well described in the literature. Properties of the second above-mentioned exponents are much less investigated in the literature. In this paper we show an example of two-dimensional discrete time-varying linear system with bounded coefficients for which the number of lower Bohl exponents of solutions may be greater than dimension of the system.

scholarly journals Observability conditions of linear time-varying systems and its computational complexity aspects

2002 ◽  
Vol 8 (4-5) ◽  
pp. 439-449 ◽  
Author(s):  
Konstantin E. Starkov
Keyword(s):  
Computational Complexity ◽  
Analytic Function ◽  
Finite Number ◽  
Linear Time ◽  
Time Varying ◽  
Two Dimensional ◽  
Exponential Functions ◽  
Time Varying Systems ◽  
Necessary And Sufficient ◽  
Matrix Exponentials

We propose necessary and sufficient Observability conditions for linear time-varying systems with coefficients being time polynomials. These conditions are deduced from the Gabrielov–Khovansky theorem on multiplicity of a zero of a Noetherian function and the Wei–Norman formula for the representation of a solution of a linear time-varying system as a product of matrix exponentials. We define a Noetherian chain consisted of some finite number of usual exponentials corresponding to this system. Our results are formulated in terms of a Noetherian chain generated by these exponential functions and an upper bound of multiplicity of zero of one locally analytic function which is defined with help of the Wei–Norman formula. Relations with Observability conditions of bilinear systems are discussed. The case of two-dimensional systems is examined.

On robust Kalman filter for two-dimensional uncertain linear discrete time-varying systems: A least squares method

Automatica ◽  
2019 ◽  
Vol 99 ◽  
pp. 203-212 ◽  
Author(s):  
Dong Zhao ◽  
Steven X. Ding ◽  
Hamid Reza Karimi ◽  
Yueyang Li ◽  
Youqing Wang
Keyword(s):  
Kalman Filter ◽  
Least Squares ◽  
Discrete Time ◽  
Least Squares Method ◽  
Time Varying ◽  
Two Dimensional ◽  
Robust Kalman Filter ◽  
Time Varying Systems
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