Anti-parity-time topologically undefined state

We constructed an anti-parity-time-symmetric photonic lattice by using perturbations. The results show the topological state will appear when the waveguide coupling constants $\kappa_1<\kappa_2$; Interestingly, a state with undefined winding numbers occurs when $\kappa_1=\kappa_2$, in which the light distributes only in the wide waveguides with equal magnitude distribution. Further studies show that the edge state will be strengthened by introducing defect for the topologically non-trivial case, while it will not affect the equal intensity transmission for the topologically undefined state. Our work provides a new way to realize the topological state and equally divided light transmission and might be applicable in optical circuits and optical interconnect

ROBUST OUTPUT STABILITY PROPERTIES FOR NONLINEAR DELAY SYSTEMS

Motivated by the regulator theory and adaptive controls, several notions on output stability in the framework of input-to-state stability (iss) were introduced for finite-dimensional systems. It turned out that these output stability notions are intrinsically different, reflecting different manners of how state variables may affect the transient be-havior of output variables. In this work, we consider these output stability properties for delay systems. Our main objective is to illustrate how the various notions are related for delay systems and to provide Razumikhin criteria for the output stability properties. The main results are also critical in developing the converse Lyapunov theorems of the output stability properties for delay systems

Remarks on Lyapunov-Krasovskii Functionals with Weak Decay Rates

In the existing Lyapunov literature, the decay rate of a Lyapunov-Krasovskii functional along trajectories is commonly required to be comparable to the norm of the state variables (or output variables) over the delay interval. In this work we consider a class of Lyapunov-Krasovskii functionals whose decay rates along trajectories depend only on the current values of the state or output variables. We show that for one type of input-to-output stability property (which leads to input-to-state stability when the output and the state variables are the same), a Lyapunov-Krasovskii functional with the weaker decay rate will still be sufficient for the corresponding stability property

Recent Results on Lyapunov-Theoretic Techniques for Nonlinear Stability

This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unified and natural manner, it (1) includes arbitrary bounded disturbances acting on the system, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets. As a corollary of the obtained Converse Theorem, we show that the well-known Lyapunov sufficient condition for &quot;input-to-state stability&quot; is also necessary, settling positively an open question raised by several authors during the past few years

ROBUST OUTPUT STABILITY PROPERTIES FOR NONLINEAR DELAY SYSTEMS

Motivated by the regulator theory and adaptive controls, several notions on output stability in the framework of input-to-state stability (iss) were introduced for finite-dimensional systems. It turned out that these output stability notions are intrinsically different, reflecting different manners of how state variables may affect the transient be-havior of output variables. In this work, we consider these output stability properties for delay systems. Our main objective is to illustrate how the various notions are related for delay systems and to provide Razumikhin criteria for the output stability properties. The main results are also critical in developing the converse Lyapunov theorems of the output stability properties for delay systems

A Smooth Converse Lyapunov Theorem for Robust Stability

. This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded time-varying parameters in the system description, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets. 1. Introduction. This work is motivated by problems of robust nonlinear stabilization. One of our main contributions is to provide a statement and proof of a Converse Lyapunov Function Theorem which is in a form particularly useful for the study of such feedback control analysis and design problems. We provide a single (and natural) unified result that: 1. applies to stability with respect to not necessarily compact invariant sets; 2. deals with global (as opposed to merely loca..

Input to State Stabilizability for Parameterized Families of Systems

This paper studies various stability issues for parameterized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications. A Lyapunov-theoretic necessary and sufficient characterization is obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc conditions found in the literature by more conceptual stability notions. We then use these techniques to establish a result linking state space stability to &quot;input to state&quot; (bounded-input bounded-state) stability. In addition, the preservation of stabilizability under certain types of cascade interconnections is analyzed

Test analysis on influence of welding defects on fatigue life of aluminum alloy plate frames

[Objectives] This paper aims to study the influence of welding defects on fatigue life of aluminum alloy plate frame.[Methods] Firstly,use X-ray to detect the welds of the test aluminum alloy plate frames with two gusset joints,and then select two plate frames with and without welding defects respectively. Then obtain main types of the welding defects through the analysis on the X-ray images. Then,carry out fatigue tests for these two plate frames with and without welding defects under different loads,so as to obtain the fatigue life of the plate frames. Finally,establish local FE models for the test plate frames with three types of welding defects by using ABAQUS software,and analyze and reveal the failure mechanism of the plate frames with welding defects.[Results] The test results show that,the failure of the test plate frame with welding defects is caused by the fracture on the longitudinal web due to the extension of the crack in the welding defect at the end of the weld;the failure of the test plate frame without welding defects,which is related to the gusset joint,is caused by the fracture on the longitudinal web due to the extension of the fatigue crack generated under the cyclic loads on the longitudinal web.[Conclusions] This study results can provide a reference for the assessment of the fatigue life and for the influence of the welding defects on the fatigue life