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Stability and Robust Stability of Switched Positive Linear Systems With All Modes Unstable

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IEEE/CAA Journal of Automatica Sinica 2019年第1期6卷 167-176页

作者： Shaoxia Feng Juan Wang Jun Zhao Shanxi Institute of Mechanical and Electrical Engineering the College of Information Scienceand Engineering Northeastern University the Faculty of Information and Control Engineering Shenyang Jianzhu University the State Key Laboratory of Synthetical Automationfor Process Industries (Northeastern University) the Collegeof Information Science and Engineering Northeastern University

This paper is concerned with the stability and robust stability of switched positive linear systems(SPLSs) whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions, some stability conditions of switched positive linear systems with all modes unstable are derived in both the continuous-time and the discrete-time cases, respectively. The copositive Lyapunov functions constructed in this paper are timevarying during the dwell time and time-invariant afterwards. In addition, the above approach is extended to the switched interval positive systems. A numerical example is proposed to illustrate our approach.

关键词： discretized co-positive Lyapunov functions mode-dependent dwell time robust stability switched positive linear systems (SPLSs) unstable subsystem

Switching-based stabilization of aperiodic sampled-data Boolean control networks with all subsystems unstable

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Frontiers of Information Technology & Electronic Engineering 2020年第2期21卷 260-267页

作者： Liang-jie SUN Jian-quan LU Wai-Ki CHING School of Mathematics Southeast UniversttyNanjing 210096China Department of Mathematics The University of Hong KongHong KongChina

We aim to further study the global stability of Boolean control networks(BCNs)under aperiodic sampleddata control(ASDC).According to our previous work,it is known that a BCN under ASDC can be transformed into a switched Boolean network(SBN),and further global stability of the BCN under ASDC can be obtained by studying the global stability of the transformed SBN.Unfortunately,since the major idea of our previous work is to use stable subsystems to offset the state divergence caused by unstable subsystems,the SBN considered has at least one stable subsystem.The central thought in this paper is that switching behavior also has good stabilization;i.e.,the SBN can also be stable with appropriate switching laws designed,even if all subsystems are unstable.This is completely different from that in our previous work.Specifically,for this case,the dwell time(DT)should be limited within a pair of upper and lower bounds.By means of the discretized Lyapunov function and DT,a sufficient condition for global stability is obtained.Finally,the above results are demonstrated by a biological example.

关键词： Aperiodic sampled-data control Boolean control networks Unstable subsystem discretized Lyapunov function Dwell time

Simplified Integral Calculations for Radial Fin with Temperature-Dependent Thermal Conductivity

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Journal of Applied Mathematics and Physics 2019年第3期7卷 513-526页

作者： Okey Oseloka Onyejekwe Computational Science Program Addis Ababa University Arat Kilo Campus Addis Ababa Ethiopia

Numerical solution of a radiative radial fin with temperature-dependent thermal conductivity is presented. Calculations are implemented along the lines of a boundary integral technique coupled with domain discretization. Localized solutions of the nonlinear governing differential equation are sought on each element of the problem domain after enforcing inter-nodal connectivity as well as the boundary conditions for the dependent variables. A finite element-type assembly of the element equations and matrix solution yield the scalar profile. Comparison of the numerical results with those found in literature validates the formulation. The effects of such problem parameters as radiation-sink temperature, thermal conductivity, radiation-conduction fin parameter, volumetric heat generation, on the scalar profile were found to be in conformity with the physics of the problem. We also observed from this study that the volumetric heat generation plays a significant role in the overall heat transfer activity for a fin. For relatively high values of internal heat generation, a situation arises where a greater percentage of this energy can not escape to the environment and the fin ends up gaining energy instead of losing it. And the overall fin performance deteriorates. The same can also be said for the radiation-conduction parameter , whose increases can only give physically realistic results below a certain threshold value.

关键词： Radiative Radial Fin Temperature-Dependent Thermal Conductivity discretized Problem Domain Boundary Integral Technique Generic Elements Assembly of Element Equations

The Mixture of New Integral Transform and Homotopy Perturbation Method for Solving Discontinued Problems Arising in Nanotechnology

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Open Journal of Applied Sciences 2015年第11期5卷 688-695页

作者： Kunjan Shah Twinkle Singh Applied Mathematics and Humanities Department S. V. National Institute of Technology Surat India

In this paper, a reliable algorithm based on mixture of new integral transform and homotopy perturbation method is proposed to solve a nonlinear differential-difference equation arising in nanotechnology. Continuum hypothesis on nanoscales is invalid, and a differential-difference model is considered as an alternative approach to describing discontinued problems. The technique finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. Comparison of the approximate solution with the exact one reveals that the method is very effective. It provides more realistic series solutions that converge very rapidly for nonlinear real physical problems.

关键词： New Integral Transform Homotopy Perturbation Method He’s Polynomials discretized mKDV Lattice Equation Nanotechnology

Arnold Tongues for Discrete Hill’s Equation

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Applied Mathematics 2017年第12期8卷 1859-1882页

作者： José Guillermo Rodríguez Servín M. Joaquin Collado Automatic Control Departament CINVESTAV-IPN Mexico City Mexico

In this work we study two types of Discrete Hill’s equation. The first comes from the discretization process of a Continuous-time Hill’s equation, we called discretized Hill’s equation. The Second is a naturally obtained in Discrete-Time and will be called Discrete-time Hill’s equation. The objective of discretization is preserving the continuous-time behavior and we show this property. On the contrary a completely different dynamic property was found for the Discrete-Time Hill’s equation. At the end of the paper is shown that both types share the nonoscillatory behavior of solutions in the 0-th Arnold Tongue.

关键词： Arnold Tongues Discrete Hill’s Equation Monodromy Matrix discretized Hamiltonian