scholarly journals Linear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

2007 ◽  
Vol 2007 (1) ◽  
pp. 026196 ◽  
Author(s):  
JinRong Wang ◽  
X Xiang ◽  
W Wei
Keyword(s):  
Banach Space ◽  
Periodic System ◽  
Time Varying ◽  
Generating Operators

scholarly journals Periodic Solutions of Semilinear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Mixed Type ◽  
Evolution Operator ◽  
Mild Solutions ◽  
Integral Operators ◽  
Periodic Systems ◽  
Time Varying ◽  
Type Integral ◽  
Generating Operators

A class of semilinear impulsive periodic systems with time-varying generating operators on Banach space is considered. Using impulsive periodic evolution operator given by us, theT0-periodicPC-mild solution is introduced and suitablePoincaréoperator is constructed. Showing the compactness ofPoincaréoperator and using a new generalized Gronwall inequality with mixed type integral operators given by us, we utilize Leray-Schauder fixed point theorem to prove the existence ofT0-periodicPC-mild solutions. Our method is an innovation and it is much different from methods of other papers. At last, an example is given for demonstration.

scholarly journals Existence and Global Asymptotical Stability of Periodic Solution for theT-Periodic Logistic System with Time-Varying Generating Operators andT0-Periodic Impulsive Perturbations on Banach Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei ◽  
Qian Chen
Keyword(s):  
Banach Spaces ◽  
Mild Solution ◽  
Sufficient Conditions ◽  
Asymptotical Stability ◽  
Time Varying ◽  
Global Asymptotical Stability ◽  
Globally Asymptotically Stable ◽  
Impulsive Perturbations ◽  
Generating Operators ◽  
Well Posed

This paper studies the existence and global asymptotical stability of periodic PC-mild solution for theT-periodic Logistic system with time-varying generating operators andT0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posedT-periodic system with time-varying generating operators andT0-periodic impulsive perturbations are given. It is shown that the system have a unique periodic PC-mild solution which is globally asymptotically stable whenTandT0are rational dependent and its period must benT0for somen∈N. At last, an example is given for demonstration.

scholarly journals Adiabatic theorems for general linear operators with time-independent domains

2019 ◽  
Vol 31 (05) ◽  
pp. 1950014 ◽  
Author(s):  
Jochen Schmid
Keyword(s):  
Banach Space ◽  
Spectral Gap ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Linear Operators ◽  
General Linear ◽  
Regularity Conditions ◽  
Time Varying ◽  
Open Quantum ◽  
Adiabatic Switching

We establish adiabatic theorems with and without spectral gap conditions for general — typically dissipative — linear operators [Formula: see text] with time-independent domains [Formula: see text] in some Banach space [Formula: see text]. Compared to the previously known adiabatic theorems — especially those without a spectral gap condition — we do not require the considered spectral values [Formula: see text] of [Formula: see text] to be (weakly) semisimple. We also impose only fairly weak regularity conditions. Applications are given to slowly time-varying open quantum systems and to adiabatic switching processes.

Biorthogonal Wavelet Based Identification of Fast Linear Time-Varying Systems—Part I: System Representations12

2000 ◽  
Vol 123 (4) ◽  
pp. 585-592 ◽  
Author(s):  
Haipeng Zhao ◽  
Joseph Bentsman
Keyword(s):  
Banach Space ◽  
Discrete Time ◽  
Linear Time ◽  
Block Diagram ◽  
Approximation Problem ◽  
Time Varying ◽  
Input Output ◽  
Time Frequency ◽  
Time Varying Systems ◽  
System Representation

An analytical framework is developed that permits the input-output representations of discrete-time linear time-varying (LTV) systems in terms of biorthogonal bases on compact time intervals. Using these representations, the companion paper, Part II develops computational procedures for rapid identification of fast nonsmooth LTV systems based on short data records. One of the representations proposed is also used in H. Zhao and J. Bentsman, “Block Diagram Reduction of the Interconnected Linear Time-Varying Systems in the Time Frequency Domain,” accepted for publication by Multidimensional Systems and Signal Processing to form system interconnections, or wavelet networks, and develop subsystem connectibility conditions and reduction rules. Under the assumption that the inputs and the outputs of the plants considered in the present work belong to lp spaces, where p=2 or p=∞, their impulse responses are shown to belong to Banach spaces. Further on, by demonstrating that the set of all bounded-input bounded-output (BIBO) stable discrete-time LTV systems is a Banach space, the system representation problem is shown to be reducible to the linear approximation problem in the Banach space setting, with the approximation errors converging to zero as the number of terms in the representation increases. Three types of LTV system representation, based on the input-side, the output-side, and the input-output transformations, are developed and the suitability of each representation for matching a particular type of the LTV system behavior is indicated.

scholarly journals Existence of Periodic Solutions for Integrodifferential Impulsive Periodic System on Banach Space

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
JinRong Wang ◽  
X. Xiang ◽  
W. Wei
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Periodic System ◽  
Evolution Operator ◽  
Mild Solutions ◽  
Periodic Systems ◽  
Gronwall Lemma ◽  
Existence Of Periodic Solutions

This paper deals with a class of integrodifferential impulsive periodic systems on Banach space. Using impulsive periodic evolution operator given by us, theT0-periodicPC-mild solution is introduced and suitablePoincaréoperator is constructed. By virtue of the generalized new Gronwall lemma with impulse andB-norm, the estimate on thePC-mild solutions is derived. Showing the continuity and compactness of thePoincaréoperator, we utilize Horn's fixed point theorem to prove the existence ofT0-periodicPC-mild solutions when thePC-mild solutions are bounded and ultimate bounded. This extends the study of periodic solutions of integrodifferential periodic system without impulse to integrodifferential periodic system with impulse on general Banach spaces. At last, an example is given for demonstration.

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