A sufficient and necessary condition for stabilization of zeros in discrete-time multirate sampled systems

2017 ◽  
Vol 51 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Cheng Zeng ◽  
Yingying Su ◽  
Shan Liang
Keyword(s):  
Discrete Time ◽  
Necessary Condition ◽  
Sampled Systems ◽  
Sufficient And Necessary Condition

Robust Distributed Filters Design for Discrete-time Spatially Interconnected Systems with LFT Uncertainties

2020 ◽  
pp. 2150159
Author(s):  
Hongyan Feng ◽  
Wenhui Liu ◽  
Hui Chen
Keyword(s):  
Discrete Time ◽  
Interconnected Systems ◽  
Necessary Condition ◽  
Well Posedness ◽  
Bilinear Transformation ◽  
Quadratic Stability ◽  
Vehicle Platoon ◽  
Spatially Interconnected Systems ◽  
Well Posed ◽  
Sufficient And Necessary Condition

In this paper, we investigate discrete-time uncertain spatially interconnected systems (USISs), where uncertainties are modeled by linear fractional transformation (LFT). First, the well-posedness, quadratic stability and contractiveness of discrete-time USISs are introduced. Second, a sufficient condition is proposed to guarantee that discrete-time USISs are well-posed, quadratically stable and contractive. Then, a more tractable condition is derived to check the well-posedness, quadratic stability and contractiveness of discrete-time USISs via a modified bilinear transformation. Besides, the robust distributed filters which inherit the structure of the plants are designed. A sufficient and necessary condition is presented to guarantee the existence of the robust distributed filters. Finally, a vehicle platoon model demonstrates the effectiveness of the proposed scheme.

Optimality of a Linear Decision Rule in Discrete Time AK Model

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Myungkyu Shim
Keyword(s):  
Utility Function ◽  
Decision Rule ◽  
Discrete Time ◽  
Pareto Optimality ◽  
Continuous Time ◽  
Formal Proof ◽  
Necessary Condition ◽  
Linear Decision Rule ◽  
Ak Model ◽  
Sufficient And Necessary Condition

Abstract Surprisingly, formal proof on the optimality of a linear decision rule in the discrete time AK model with a CRRA utility function has not been established in the growth literature while that in the continuous time counterpart is well-established. This note fills such a gap: I provide a formal proof that consumption being linearly related to investment is a sufficient and necessary condition for Pareto optimality in the discrete time AK model.

scholarly journals Cauchy matrix and Liouville formula of quaternion impulsive dynamic equations on time scales

2020 ◽  
Vol 18 (1) ◽  
pp. 353-377 ◽  
Author(s):  
Zhien Li ◽  
Chao Wang
Keyword(s):  
Time Scales ◽  
Quaternion Algebra ◽  
Matrix Exponential ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Quaternion Matrix ◽  
Exponential Functions ◽  
Cauchy Matrix ◽  
Adjoint Matrix ◽  
Sufficient And Necessary Condition

Abstract In this study, we obtain the scalar and matrix exponential functions through a series of quaternion-valued functions on time scales. A sufficient and necessary condition is established to guarantee that the induced matrix is real-valued for the complex adjoint matrix of a quaternion matrix. Moreover, the Cauchy matrices and Liouville formulas for the quaternion homogeneous and nonhomogeneous impulsive dynamic equations are given and proved. Based on it, the existence, uniqueness, and expressions of their solutions are also obtained, including their scalar and matrix forms. Since the quaternion algebra is noncommutative, many concepts and properties of the non-quaternion impulsive dynamic equations are ineffective, we provide several examples and counterexamples on various time scales to illustrate the effectiveness of our results.

scholarly journals Sufficient and necessary conditions for oscillation of linear fractional-order delay differential equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qiong Meng ◽  
Zhen Jin ◽  
Guirong Liu
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Necessary Condition ◽  
Multiple Delays ◽  
All Solutions ◽  
Sufficient And Necessary Conditions ◽  
Delay Differential ◽  
T Tau ◽  
Sufficient And Necessary Condition

AbstractThis paper studies the linear fractional-order delay differential equation $$ {}^{C}D^{\alpha }_{-}x(t)-px(t-\tau )= 0, $$ D − α C x ( t ) − p x ( t − τ ) = 0 , where $0<\alpha =\frac{\text{odd integer}}{\text{odd integer}}<1$ 0 < α = odd integer odd integer < 1 , $p, \tau >0$ p , τ > 0 , ${}^{C}D_{-}^{\alpha }x(t)=-\Gamma ^{-1}(1-\alpha )\int _{t}^{\infty }(s-t)^{- \alpha }x'(s)\,ds$ D − α C x ( t ) = − Γ − 1 ( 1 − α ) ∫ t ∞ ( s − t ) − α x ′ ( s ) d s . We obtain the conclusion that $$ p^{1/\alpha } \tau >\alpha /e $$ p 1 / α τ > α / e is a sufficient and necessary condition of the oscillations for all solutions of Eq. (*). At the same time, some sufficient conditions are obtained for the oscillations of multiple delays linear fractional differential equation. Several examples are given to illustrate our theorems.

scholarly journals Research on the Relationship between Shared Leadership and Individual Creativity-Qualitative Comparative Analysis on the Basis of Clear Set

2021 ◽  
Vol 13 (10) ◽  
pp. 5445
Author(s):  
Muyun Sun ◽  
Jigan Wang ◽  
Ting Wen
Keyword(s):  
Comparative Analysis ◽  
Environmental Factors ◽  
Shared Leadership ◽  
Management Practices ◽  
Qualitative Comparative Analysis ◽  
Necessary Condition ◽  
The Individual ◽  
The Impact ◽  
The Relationship ◽  
Sufficient And Necessary Condition

Creativity is the key to obtaining and maintaining competitiveness of modern organizations, and it has attracted much attention from academic circles and management practices. Shared leadership is believed to effectively influence team output. However, research on the impact of individual creativity is still in its infancy. This study adopts the qualitative comparative analysis method, taking 1584 individuals as the research objects, underpinned by a questionnaire-based survey. It investigates the influence of the team’s shared leadership network elements and organizational environmental factors on the individual creativity. We have found that there are six combination of conditions of shared leadership and organizational environmental factors constituting sufficient combination of conditions to increase or decrease individual creativity. Moreover, we have noticed that the low network density of shared leadership is a sufficient and necessary condition of reducing individual creativity. Our results also provide management suggestions for practical activities during the team management.

scholarly journals A nonlocal game for witnessing quantum networks

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Ming-Xing Luo
Keyword(s):  
Computational Complexity ◽  
Main Idea ◽  
Bell Inequalities ◽  
Theoretical Computer Science ◽  
Graph Representation ◽  
Necessary Condition ◽  
Quantum Networks ◽  
Theoretical Computer ◽  
Sufficient And Necessary Condition ◽  
Unified Method

Abstract Nonlocal game as a witness of the nonlocality of entanglement is of fundamental importance in various fields. The well-known nonlocal games or equivalent linear Bell inequalities are only useful for Bell networks consisting of single entanglement. Our goal in this paper is to propose a unified method for constructing cooperating games in network scenarios. We propose an efficient method to construct multipartite nonlocal games from any graphs. The main idea is the graph representation of entanglement-based quantum networks. We further specify these graphic games with quantum advantages by providing a simple sufficient and necessary condition. The graphic games imply a linear Bell testing of the nonlocality of general quantum networks consisting of EPR states. It also allows generating new instances going beyond CHSH game. These results have interesting applications in quantum networks, Bell theory, computational complexity, and theoretical computer science.

New characterizations of g-frames and g-Riesz bases

2018 ◽  
Vol 16 (06) ◽  
pp. 1850053 ◽  
Author(s):  
Dongwei Li ◽  
Jinsong Leng ◽  
Tingzhu Huang
Keyword(s):  
Riesz Basis ◽  
Riesz Bases ◽  
Gram Matrix ◽  
Necessary Condition ◽  
Topological Properties ◽  
Bessel Sequence ◽  
Bessel Sequences ◽  
Sufficient And Necessary Condition

In this paper, we give some new characterizations of g-frames, g-Bessel sequences and g-Riesz bases from their topological properties. By using the Gram matrix associated with the g-Bessel sequence, we present a sufficient and necessary condition under which the sequence is a g-Bessel sequence (or g-Riesz basis). Finally, we consider the excess of a g-frame and obtain some new results.

A SUFFICIENT AND NECESSARY CONDITION FOR CREDIBILITY MEASURES

2006 ◽  
Vol 14 (05) ◽  
pp. 527-535 ◽  
Author(s):  
XIANG LI ◽  
BAODING LIU
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Extension Theorem ◽  
The Self ◽  
Necessary Condition ◽  
Self Duality ◽  
Duality Property ◽  
Sufficient And Necessary Condition

Possibility measures and credibility measures are widely used in fuzzy set theory. Compared with possibility measures, the advantage of credibility measures is the self-duality property. This paper gives a relation between possibility measures and credibility measures, and proves a sufficient and necessary condition for credibility measures. Finally, the credibility extension theorem is shown.

scholarly journals Formation behaviors of networks with antagonistic interactions of agents

2017 ◽  
Vol 13 (8) ◽  
pp. 155014771772629 ◽  
Author(s):  
Wen-Lu Zou ◽  
Gun Li
Keyword(s):  
Time Delay ◽  
Frequency Domain Analysis ◽  
Necessary Condition ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Formation Behavior ◽  
Multi Agent ◽  
Group Form ◽  
Sufficient And Necessary Condition ◽  
Antagonistic Interactions

In this study, a new formation behavior problem for second-order multi-agent systems with time delay is investigated in the presence of antagonistic interactions. We first proposed a formation behavior protocol with time delay for each agent in the antagonistic network. Then, by a frequency-domain analysis, a sufficient and necessary condition is derived to guarantee the consensus stability of the multi-agent system. It is shown that the agents in the same group form their own desired formation while keeping a desired relative position with other groups. Finally, numerical simulations are provided to illustrate the obtained results.

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