Exponential stability of nondissipative linear system in Banach space and application to unbounded bilinear systems

2017 ◽  
Vol 109 ◽  
pp. 53-62 ◽  
Author(s):  
M. Ouzahra
Keyword(s):  
Banach Space ◽  
Linear System ◽  
Exponential Stability ◽  
Bilinear Systems

On the modeling of linear system input stochastic processes with given accuracy and reliability

2018 ◽  
Vol 24 (2) ◽  
pp. 129-137
Author(s):  
Iryna Rozora ◽  
Mariia Lyzhechko
Keyword(s):  
Banach Space ◽  
Stochastic Process ◽  
Linear System ◽  
Stochastic Processes ◽  
Impulse Response Function ◽  
Output Process ◽  
Gaussian Stochastic Process ◽  
System Input ◽  
Time Invariant ◽  
Gaussian Stochastic Processes

AbstractThe paper is devoted to the model construction for input stochastic processes of a time-invariant linear system with a real-valued square-integrable impulse response function. The processes are considered as Gaussian stochastic processes with discrete spectrum. The response on the system is supposed to be an output process. We obtain the conditions under which the constructed model approximates a Gaussian stochastic process with given accuracy and reliability in the Banach space{C([0,1])}, taking into account the response of the system. For this purpose, the methods and properties of square-Gaussian processes are used.

scholarly journals On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Aftab Khan ◽  
Gul Rahmat ◽  
Akbar Zada
Keyword(s):  
Banach Space ◽  
Exponential Stability ◽  
Complex Banach Space ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Uniform Exponential Stability ◽  
Discrete Semigroup ◽  
Exponentially Stable ◽  
Discrete Semigroups

We prove that a discrete semigroup𝕋={T(n):n∈ℤ+}of bounded linear operators acting on a complex Banach spaceXis uniformly exponentially stable if and only if, for eachx∈AP0(ℤ+,X), the sequencen↦∑k=0n‍T(n-k)x(k):ℤ+→Xbelongs toAP0(ℤ+,X). Similar results for periodic discrete evolution families are also stated.

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.

Uniform exponential stability of periodic discrete switched linear system

2017 ◽  
Vol 354 (14) ◽  
pp. 6247-6257 ◽  
Author(s):  
Akbar Zada ◽  
Bakht Zada ◽  
Jinde Cao ◽  
Tongxing Li
Keyword(s):  
Linear System ◽  
Exponential Stability ◽  
Switched Linear System ◽  
Uniform Exponential Stability

scholarly journals Exponential dichotomy of strongly discontinuous semigroups

1984 ◽  
Vol 30 (3) ◽  
pp. 435-448 ◽  
Author(s):  
P. Preda ◽  
M. Megan
Keyword(s):  
Banach Space ◽  
Exponential Stability ◽  
General Class ◽  
Exponential Dichotomy ◽  
Continuous Semigroup ◽  
Sufficient Conditions ◽  
Semigroups Of Operators ◽  
Strongly Continuous Semigroup ◽  
Strongly Continuous Semigroups ◽  
Necessary And Sufficient

In this paper we give necessary and sufficient conditions for exponential dichotomy of a general class of strongly continuous semigroups of operators defined on a Banach space. As a particular case we obtain a Datko theorem for exponential stability of a strongly continuous semigroup of class C0 defined on a Banach space.

scholarly journals Exponential Stability of an Abstract Nondissipative Linear System

2001 ◽  
Vol 40 (1) ◽  
pp. 149-165 ◽  
Author(s):  
Kangsheng Liu ◽  
Zhuangyi Liu ◽  
Bopeng Rao
Keyword(s):  
Linear System ◽  
Exponential Stability
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