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An Duong, Vietnam

Nam P.T.,Quynhon University | Pathirana P.N.,Deakin University | Trinh H.,Deakin University
Journal of the Franklin Institute | Year: 2015

In this paper, we derive a new inequality, which encompasses the discrete Jensen inequality. The new inequality is applied to analyze stability of linear discrete systems with an interval time-varying delay and a less conservative stability condition is obtained. Two numerical examples are given to show the effectiveness of the obtained stability condition. © 2015 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. Source


Thuan M.V.,Thainguyen University of science | Trinh H.,Deakin University | Huong D.C.,Quynhon University
International Journal of Systems Science | Year: 2016

In this paper, we address the problem of finding outer bound of forward reachable sets and inter-bound of backward reachable sets of switched systems with an interval time-varying delay and bounded disturbances. By constructing a flexible Lyapunov–Krasovskii functional combining with some recent refined integral-based inequalities, some sufficient conditions are derived for the existence of (1) the smallest possible outer bound of forwards reachable sets; and (2) the largest possible inter-bound of backward reachable sets. These conditions are delay dependent and in the form of linear matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. A constructive geometric design of switching laws is also presented. Two numerical examples with simulation results are provided to demonstrate the effectiveness of our results. © 2016 Informa UK Limited, trading as Taylor & Francis Group Source


Phan T.H.,University of Bonn | Phan T.H.,Quynhon University | Wandelt K.,University of Bonn | Wandelt K.,Wroclaw University
Surface Science | Year: 2013

Combined Cyclic Voltammetry (CV) and in-situ Electrochemical Scanning Tunneling Microscopy (EC-STM) studies were employed to compare the self-assembly of redox-active 5,10,15,20-Tetrakis (4-trimethyl ammonium phenyl) porphyrin tetra (p-toluenesulfonate), abbreviated as [H 2TTMAPP] + 4 on Cu(100) and Cu(111) electrode surfaces in 10 mM HCl solution. Under these conditions, both surfaces are chloride pre-covered with a c(2 × 2) Cl- and cp×3 Cl-layer on Cu(100) and Cu(111), respectively. On both surfaces highly ordered [H 2TTMAPP] + 4 layers are spontaneously formed. The short range molecular arrangement is quadratic in nature on both surfaces which can be described by a 58×58 R23° unit cell on the c(2 × 2) Cl-Cu(100), and a (3 × 4) unit cell on the cp×3 Cl-Cu(111) substrate. Large scale domains are formed on both surfaces the orientation of which reflects the symmetry of the substrate, namely on Cu(100) [Cu(111)] equivalent domains are rotated by 90° [120°], respectively. Thus, the different symmetry of the respective substrate surface has an influence on the otherwise self-assembled organic molecules. © 2012 Elsevier B.V. All rights reserved. Source


Nam P.,Quynhon University | Pathirana P.N.,Deakin University | Trinh H.,Deakin University
IET Control Theory and Applications | Year: 2015

This study considers linear systems with state/input time-varying delays and bounded disturbances. The authors study a new problem of designing a static output feedback controller which guarantees that the state vector of the closedloop system converges within a pre-specified polyhedron. Based on the Lyapunov-Krasovskii method combining with the free-weighting matrix technique, a new sufficient condition for the existence of a static output feedback controller is derived. The author's condition is expressed in terms of linear matrix inequalities with two parameters need to be tuned and therefore can be efficiently solved by using a two-dimensional search method combining with convex optimisation algorithms. To be able to obtain directly an output feedback control matrix from the derived condition, they propose an appropriate combination between a state transformation with a choice of a special form of the free-weighting matrices. The feasibility and effectiveness of the derived results are illustrated through five numerical examples. © The Institution of Engineering and Technology 2015. Source


Nam P.T.,Quynhon University | Pathirana P.N.,Deakin University
Automatica | Year: 2011

The problem of reachable set estimation of linear uncertain polytopic time-varying delay systems subject to bounded peak inputs is studied in this paper. The delays considered in this paper are assumed to be non-differentiable and vary within an interval where the lower and upper bounds are known. Based on the LyapunovKrasovskii method and delay decomposition technique, a sufficient condition for the existence of a ball that bounds the reachable set of the system is proposed in terms of matrix inequalities containing only one scalar which can be solved by using an one-dimensional search method and Matlab's LMI Toolbox and allow us to find the smallest radius. A numerical example is given to illustrate the effectiveness of the proposed result. © 2011 Elsevier Ltd. All rights reserved. Source

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