scholarly journals Translation Invariant Spaces and Asymptotic Properties of Variational Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-36 ◽  
Author(s):  
Adina Luminiţa Sasu ◽  
Bogdan Sasu
Keyword(s):  
Control Systems ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Invariant Function ◽  
Function Spaces ◽  
Skew Product ◽  
Translation Invariant ◽  
Variational Equations ◽  
Skew Product Flows ◽  
New Perspective

We present a new perspective concerning the study of the asymptotic behavior of variational equations by employing function spaces techniques. We give a complete description of the dichotomous behaviors of the most general case of skew-product flows, without any assumption concerning the flow, the cocycle or the splitting of the state space, our study being based only on the solvability of some associated control systems between certain function spaces. The main results do not only point out new necessary and sufficient conditions for the existence of uniform and exponential dichotomy of skew-product flows, but also provide a clear chart of the connections between the classes of translation invariant function spaces that play the role of the input or output classes with respect to certain control systems. Finally, we emphasize the significance of each underlying hypothesis by illustrative examples and present several interesting applications.

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

scholarly journals On Exponential Dichotomy of Variational Difference Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Bogdan Sasu
Keyword(s):  
Difference Equations ◽  
Exponential Dichotomy ◽  
New Method ◽  
Skew Product ◽  
Skew Product Flows

We give very general characterizations for uniform exponential dichotomy of variational difference equations. We propose a new method in the study of exponential dichotomy based on the convergence of some associated series of nonlinear trajectories. The obtained results are applied to difference equations and also to linear skew-product flows.

scholarly journals Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kerboua ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Control Systems ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Dynamic ◽  
Deterministic Control ◽  
Stochastic Dynamic Systems

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

scholarly journals Approximate controllability of delayed semilinear control systems

2005 ◽  
Vol 2005 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Lianwen Wang
Keyword(s):  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Sufficient Conditions ◽  
Semilinear Control Systems

We deal with the approximate controllability of control systems governed by delayed semilinear differential equations y˙(t)=Ay(t)+A1y(t−Δ)+F(t,y(t),yt)+(Bu)(t). Various sufficient conditions for approximate controllability have been obtained; these results usually require some complicated and limited assumptions. Results in this paper provide sufficient conditions for the approximate controllability of a class of delayed semilinear control systems under natural assumptions.

scholarly journals Invariant Bipartite Random Graphs on Rd

2014 ◽  
Vol 51 (3) ◽  
pp. 769-779
Author(s):  
Fabio Lopes
Keyword(s):  
Point Processes ◽  
Random Number ◽  
Probability Distributions ◽  
Sufficient Conditions ◽  
Stable Marriage ◽  
Simple Point ◽  
Stable Marriage Problem ◽  
Blue Point ◽  
Translation Invariant ◽  
Positive Integers

Suppose that red and blue points occur in Rd according to two simple point processes with finite intensities λR and λB, respectively. Furthermore, let ν and μ be two probability distributions on the strictly positive integers with means ν̅ and μ̅, respectively. Assign independently a random number of stubs (half-edges) to each red (blue) point with law ν (μ). We are interested in translation-invariant schemes for matching stubs between points of different colors in order to obtain random bipartite graphs in which each point has a prescribed degree distribution with law ν or μ depending on its color. For a large class of point processes, we show that such translation-invariant schemes matching almost surely all stubs are possible if and only if λRν̅ = λBμ̅, including the case when ν̅ = μ̅ = ∞ so that both sides are infinite. Furthermore, we study a particular scheme based on the Gale-Shapley stable marriage problem. For this scheme, we give sufficient conditions on ν and μ for the presence and absence of infinite components. These results are two-color versions of those obtained by Deijfen, Holroyd and Häggström.

Approximate controllability of non-instantaneous impulsive semilinear measure driven control system with infinite delay via fundamental solution

2020 ◽  
Author(s):  
Surendra Kumar ◽  
Syed Mohammad Abdal
Keyword(s):  
Fundamental Solution ◽  
Differential Equations ◽  
Control Systems ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Existence Of A Solution ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
New Class

Abstract This article investigates a new class of non-instantaneous impulsive measure driven control systems with infinite delay. The considered system covers a large class of the hybrid system without any restriction on their Zeno behavior. The concept of measure differential equations is more general as compared to the ordinary impulsive differential equations; consequently, the discussed results are more general than the existing ones. In particular, using the fundamental solution, Krasnoselskii’s fixed-point theorem and the theory of Lebesgue–Stieltjes integral, a new set of sufficient conditions is constructed that ensures the existence of a solution and the approximate controllability of the considered system. Lastly, an example is constructed to demonstrate the effectiveness of obtained results.

Event-triggered H∞ control for networked control systems under denial-of-service attacks

2020 ◽  
pp. 014233122096641
Author(s):  
Liruo Zhang ◽  
Sing Kiong Nguang ◽  
Shen Yan
Keyword(s):  
Control Systems ◽  
Networked Control Systems ◽  
Denial Of Service ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Linear Matrix ◽  
Dos Attacks ◽  
Network Resources ◽  
Zigbee Protocol ◽  
Event Triggered

This paper investigates the event-triggered H∞ control for networked control systems under the denial-of-service (DoS) attacks. First, a novel system model is established considering random, time-constraint DoS attacks. Second, an event-triggered scheme including an off-time is proposed to reduce the unnecessary occupation of network resources, with which a prescribed minimum inter-triggering time is guaranteed and Zeno problem is avoided. Third, sufficient conditions for the existence of an event-triggered controller which ensures the exponential stability of the closed-loop system with desired H∞ performance are formulated in linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed method is examined by two illustrative examples, where a real communication network based on the ZigBee protocol is utilized.

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