The canonical form of the equations of state of linear time-varying dynamic systems

10.12737/5201 ◽  
2014 ◽  
Vol 2 (4) ◽  
pp. 422-425
Author(s):  
N. Mihaylov
Keyword(s):  
Canonical Form ◽  
Dynamic Systems ◽  
Equations Of State ◽  
Linear Time ◽  
Time Varying

Diagonalization algorithms for linear time-varying dynamic systems

2000 ◽  
Vol 31 (8) ◽  
pp. 1053-1057 ◽  
Author(s):  
P. Van Der Kloet ◽  
F. L. Neerhoff
Keyword(s):  
Dynamic Systems ◽  
Linear Time ◽  
Time Varying

Further Remarks on the Existence of Periodic Solutions of Linear Time Varying Periodic Fractional Order Systems

2017 ◽  
Author(s):  
XueFeng Zhang ◽  
YangQuan Chen
Keyword(s):  
Laplace Transform ◽  
Periodic Solutions ◽  
Fractional Order ◽  
Dynamic Systems ◽  
Linear Time ◽  
Periodic Systems ◽  
Time Varying ◽  
Fractional Order Systems ◽  
Order Linear ◽  
Existence Of Periodic Solutions

Existence of periodic solutions of fractional order dynamic systems is an important and difficult issue in fractional order systems field. In this paper, the non existence of completely periodic solutions and existence of partly periodic solutions of fractional order linear time varying periodic systems and fractional order nonlinear time varying periodic systems are discussed. A new property of Laplace transform of periodic function is derived. The non existences of completely periodic solutions of fractional order linear time varying periodic systems and fractional order nonlinear time varying periodic fractional order systems are presented by Laplace transform method and contradiction approach. The existence of partly periodic solutions of fractional order dynamic systems are proved by constructing numerical examples and considering Laplace transform property approaches. The examples and state figures are given to illustrate the effectiveness of conclusion presented.

Control of Dynamic Systems With Nonlinearities and Time Varying Parameters

1993 ◽  
Author(s):  
Dirk Söffker ◽  
Peter C. Müller
Keyword(s):  
Dynamic Systems ◽  
Disturbance Rejection ◽  
Linear Time ◽  
Time Varying ◽  
Varying Parameters ◽  
Linear Time Invariant ◽  
Time Variance ◽  
Disturbance Rejection Control ◽  
Time Varying Parameters ◽  
Time Invariant

Abstract The well-known theory of disturbance rejection control and the experience of using a generalized technique with universal fault model for building observers and regulators for the estimation and compensation of disturbances and unmodeled or uncertain effects as well, could be used for controlling dynamic systems with time varying parameters and nonlinearities. Based on a linear time-invariant model the effects of non-linearities and unmodeled dynamics are estimated by an extended observer scheme. Using this information these dynamic effects will be compensated by the developed compensation scheme. Here also different compensation techniques of disturbance rejection control are discussed, compared, and modified. The simulation example of an inverted flexible pendulum shows the efficiency of the method controlling an unstable mechanical system without exact knowledge of structure and parameters of nonlinearity and time-variance.

SOME ANALYTIC CALCULATIONS OF THE CHARACTERISTIC EXPONENTS

2007 ◽  
Vol 17 (10) ◽  
pp. 3675-3678 ◽  
Author(s):  
P. VAN DER KLOET ◽  
F. L. NEERHOFF ◽  
N. H. WANING
Keyword(s):  
Dynamic Systems ◽  
Linear Time ◽  
Equilibrium Points ◽  
Analytic Solutions ◽  
Nonlinear Dynamic Systems ◽  
Time Varying ◽  
Variational Equations ◽  
Linear Time Invariant ◽  
Characteristic Exponents ◽  
Time Invariant

As is well known, the variational equations of nonlinear dynamic systems are linear time-varying (LTV) by nature. In the modal solutions for these LTV equations, the earlier introduced dynamic eigenvalues play a key role. They are closely related to the Lyapunov- and Floquet-exponents of the corresponding nonlinear systems. In this contribution, we present some simple examples for which analytic solutions exist. It is also demonstrated by example how the classical linear time-invariant (LTI) solutions are related to the equilibrium points of the general LTV solutions.

scholarly journals On Nonnegative Solutions of Fractionalq-Linear Time-Varying Dynamic Systems with Delayed Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Dynamic Systems ◽  
Fractional Derivatives ◽  
Linear Time ◽  
Asymptotic Properties ◽  
Time Varying ◽  
Caputo Fractional Derivatives ◽  
Nonnegative Solutions ◽  
Time Varying Systems ◽  
Fractional Differential ◽  
The Stability

This paper is devoted to the investigation of nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic linear time-varying systems involving delayed dynamics with delays. The dynamic systems are described based onq-calculus and Caputo fractional derivatives on any order.

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