On the Final States of Shallow Arches on Elastic Foundations Subjected to Dynamical Loads

1968 ◽  
Vol 35 (4) ◽  
pp. 713-723 ◽  
Author(s):  
C. S. Hsu ◽  
C. T. Kuo ◽  
S. S. Lee
Keyword(s):  
Sufficient Conditions ◽  
Spatial Distributions ◽  
Time Varying ◽  
Final State ◽  
Shallow Arches ◽  
Elastic Foundations ◽  
Linear Elastic ◽  
Wide Range ◽  
Sinusoidal Shape ◽  
Necessary And Sufficient

Given in this paper is a nonlinear analysis of snap-through problems of shallow arches on linear elastic foundations subjected to time-varying loads which have a time-independent character as τ → ∞. Specific problems studied in detail are simply supported sinusoidal arches under impulsive loads, under time-varying loads with asymptotic spatial distributions of sinusoidal shape, and under time-varying loads with uniform asymptotic spatial distributions. It is found that for a very wide range of the foundation modulus a necessary and sufficient condition for stability against snap-through can be established and the final state of the arch predicted. Outside this range and when the loads are timewise step loads, useful sufficient conditions for instability and sufficient conditions for stability can be found separately. The nonlinear treatment presented here is exact in the sense that no approximation is made or is required in the mathematical analysis.

scholarly journals MUTUAL INFORMATION OF BIPARTITE STATES AND QUANTUM DISCORD IN TERMS OF COHERENCE INFORMATION

2005 ◽  
Vol 03 (04) ◽  
pp. 691-728 ◽  
Author(s):  
FEDOR HERBUT
Keyword(s):  
Quantum Discord ◽  
Information Gain ◽  
Sufficient Conditions ◽  
Quantum Correlations ◽  
Global State ◽  
Final State ◽  
Global Coherence ◽  
State Formula ◽  
Necessary And Sufficient ◽  
Bipartite States

In relation to an observable and quantum state, the entity IC from previous work quantifies simultaneously coherence, incompatibility and quantumness. In this paper, its application to quantum correlations in bipartite states is studied. It is shown that Zurek's quantum discord can always be expressed as excess coherence information (global minus local). Strong and weak zero-discord cases are distinguished and investigated in terms of necessary and sufficient and sufficient conditions respectively. A unique string of relevant subsystem observables, each a function of the next, for "interrogating" the global state about the state of the opposite subsystem is derived with detailed entropy and information gain discussion. The apparent disappearance of discord in measurement is investigated, and it is shown that it is actually shifted from between subsystems 1 and 2 to between subsystems 1 and (2 + 3), where 3 is the measuring instrument. Finally, it is shown that the global coherence information IC(A2, ρ12) is shifted into the global coherence information [Formula: see text] in the final state [Formula: see text] of the measurement interaction.

scholarly journals Minimum Energy Control of 2D Positive Continuous-Discrete Linear Systems

2014 ◽  
Vol 8 (3) ◽  
pp. 165-168
Author(s):  
Tadeusz Kaczorek
Keyword(s):  
Linear Systems ◽  
Minimum Energy ◽  
Sufficient Conditions ◽  
Existence Of Solution ◽  
Energy Control ◽  
Final State ◽  
Discrete Linear Systems ◽  
Minimum Energy Control ◽  
One Step ◽  
Necessary And Sufficient

Abstract The minimum energy control problem for the 2D positive continuous-discrete linear systems is formulated and solved. Necessary and sufficient conditions for the reachability at the point of the systems are given. Sufficient conditions for the existence of solution to the problem are established. It is shown that if the system is reachable then there exists an optimal input that steers the state from zero boundary conditions to given final state and minimizing the performance index for only one step (q = 1). A procedure for solving of the problem is proposed and illustrated by a numerical example.

scholarly journals Positive time-varying continuous-time linear systems and electrical circuits

2015 ◽  
Vol 63 (4) ◽  
pp. 837-842 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Large Class ◽  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Electrical Circuits ◽  
Time Varying Parameters ◽  
Positive Time ◽  
Necessary And Sufficient ◽  
Time Linear

AbstractThe positivity of time-varying continuous-time linear systems and electrical circuits are addressed. Necessary and sufficient conditions for the positivity of the systems and electrical circuits are established. It is shown that there exists a large class of positive electrical circuits with time-varying parameters. Examples of positive electrical circuits are presented.

Consensus and Consensualization of High-Order Swarm Systems With Time Delays and External Disturbances

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Jianxiang Xi ◽  
Zongying Shi ◽  
Yisheng Zhong
Keyword(s):  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
External Disturbances ◽  
Consensus Function ◽  
Design Problems ◽  
Consensus Analysis ◽  
Analysis And Design ◽  
Time Varying Delay ◽  
Necessary And Sufficient

By using dynamic output feedback consensus protocols, consensus analysis, and design, problems for swarm systems with external disturbances and time-varying delays are dealt with. First, two subspaces, namely, a consensus subspace and a complement consensus subspace, are defined. Based on the state projection onto the two subspaces, L2-consensus and L2-consensualization problems are introduced. Then, a necessary and sufficient condition for consensus is presented and an explicit expression of the consensus function is given. Especially, it is shown that the time-varying delay does not influence the consensus function. Finally, in terms of linear matrix inequalities, sufficient conditions for L2-consensus and L2-consensualization are presented, respectively, which possess less calculation complexity, since they are independent of the number of agents, and numerical simulations are shown to demonstrate theoretical results.

scholarly journals New approach to asymptotic stability: time-varying nonlinear systems

1997 ◽  
Vol 20 (2) ◽  
pp. 347-366 ◽  
Author(s):  
L. T. Grujić
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Sufficient Conditions ◽  
Stability Domain ◽  
Time Varying ◽  
Uniform Asymptotic Stability ◽  
Stability Time ◽  
Necessary And Sufficient

The results of the paper concern a broad family of time-varying nonlinear systems with differentiable motions. The solutions are established in a form of the necessary and sufficient conditions for: 1) uniform asymptotic stability of the zero state, 2) for an exact single construction of a system Lyapunov function and 3) for an accurate single determination of the (uniform) asymptotic stability domain. They permit arbitrary selection of a functionp(⋅)from a defined functional family to determine a Lyapunov functionv(⋅),[v(⋅)], by solvingv′(⋅)=−p(⋅){or equivalently,v′(⋅)=−p(⋅)[1−v(⋅)]}, respectively. Illstrative examples are worked out.

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