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

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.

Krein Space-based Hθ Fault Estimation for Linear Discrete Time-varying Systems

2009 ◽  
Vol 34 (12) ◽  
pp. 1529-1533 ◽  
Author(s):  
Mai-Ying ZHONG ◽  
Shuai LIU ◽  
Hui-Hong ZHAO
Keyword(s):  
Discrete Time ◽  
Krein Space ◽  
Fault Estimation ◽  
Time Varying ◽  
Time Varying Systems ◽  
Kreĭn Space

scholarly journals The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems

Eng ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 99-125
Author(s):  
Edward W. Kamen
Keyword(s):  
Discrete Time ◽  
Initial Conditions ◽  
Linear Time ◽  
Order Term ◽  
Initial Time ◽  
Time Varying ◽  
Varying Coefficients ◽  
Time Signals ◽  
Time Varying Systems ◽  
Time Varying Coefficients

A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in z−1, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary z-transform, and that it is possible to do scaling of z−i by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of zi at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

Sign in / Sign up

Export Citation Format

Share Document