scholarly journals On Disturbance Decoupled Observers for a Class of Bilinear Systems

1998 ◽  
Vol 120 (3) ◽  
pp. 371-377 ◽  
Author(s):  
M. Zasadzinski ◽  
H. Rafaralahy ◽  
C. Mechmeche ◽  
M. Darouach
Keyword(s):  
Fault Detection ◽  
Linear System ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Necessary And Sufficient Conditions ◽  
Observer Design ◽  
Unknown Inputs ◽  
Existence Conditions ◽  
Error Dynamics ◽  
Necessary And Sufficient

In this paper, the class of bilinear systems subjected to unknown inputs for which there exists a disturbance decoupled observer with linear error dynamics is characterized. It is shown that the design of this kind of observer is equivalent to the design of a disturbance decoupled observer for a linear system. This result simplifies considerably the observer design compared to those proposed in the literature, and the observer existence conditions can be easily deduced. As a corollary of this result, necessary and sufficient conditions for the existence of disturbance decoupled linear observers for bilinear systems subjected to unknown inputs are derived. This approach is extended to the fault detection of bilinear systems.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

scholarly journals Analysis of Positive Linear Continuous–Time Systems Using the Conformable Derivative

2018 ◽  
Vol 28 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Asymptotic Stability ◽  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Conformable Derivative ◽  
Continuous Time Systems ◽  
Necessary And Sufficient ◽  
Time Systems

Abstract Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.

scholarly journals Existence conditions for a class of modular subgroups of genus zero

2002 ◽  
Vol 66 (3) ◽  
pp. 517-525
Author(s):  
Joachim A. Hempel
Keyword(s):  
Rational Function ◽  
Finite Index ◽  
Modular Group ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Genus Zero ◽  
Existence Conditions ◽  
Necessary And Sufficient

Every subgroup of finite index of the modular groupPSL(2, ℤ) has asignatureconsisting of conjugacy-invariant integer parameters satisfying certain conditions. In the case of genus zero, these parameters also constitute a prescription for the degree and the orders of the poles of a rational functionFwith the property:Functions correspond to subgroups, and we use this to establish necessary and sufficient conditions for existence of subgroups with a certain subclass of allowable signatures.

scholarly journals Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear system

2014 ◽  
Vol 62 (4) ◽  
pp. 889-895 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Necessary And Sufficient Conditions ◽  
Reduced Order ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Fractional descriptor reduced-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is given and is demonstrated on two numerical examples.

scholarly journals Fractional descriptor observers for fractional descriptor continuous-time linear system

2014 ◽  
Vol 24 (1) ◽  
pp. 27-37 ◽  
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Design Procedure ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Time Linear

Abstract Fractional descriptor full-order observers for fractional descriptor continuous-time linear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the observers is demonstrated on two numerical examples.

The Stability of a Second Order Linear Periodic System

1969 ◽  
Vol 91 (2) ◽  
pp. 207-210 ◽  
Author(s):  
E. J. Davison
Keyword(s):  
Linear System ◽  
Periodic System ◽  
Sufficient Conditions ◽  
Second Order ◽  
Necessary And Sufficient Conditions ◽  
Order Linear ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Linear Periodic System

Necessary and sufficient conditions are obtained for the stability of the following second order linear system: x˙=θ(t)x,θ(t)=θt+∑i=1lTi and θ(t) =A1,0<t<T1=A2,T1<t<T1+T2⋮=Al,∑i=1l−1Ti<t<∑i=1lTi in terms of the eigenvalues and elements of the matrices Ai, i = 1, 2…l. The conditions become very simple for the case that l = 2. An example of a pendulum with a vibrating support is included.

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