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1
Content available Window of Visibility in the Display and Capture Process
Xiong F., Zhai G., Zhang Y.
International Journal of Electronics and Telecommunications
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2018
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Vol. 64, No. 3
315--320
EN
In normal conditions, the Critical Flicker Frequency is usually 60Hz. But in some special conditions, such as low spatial frequency and high contrast between frames, these special conditions have high probability to occur in some TPVM-based applications. So it’s extremely important to verify if a visual signal with a combination of temporal and spatial frequency can be recognize by human eyes. Based on the research in the last paper ’ ’Window of Visibility’ inspired security lighting system’, this paper introduces the measuring method of WoV of human eyes. In this paper we will measure critical flicker frequency in low spatial frequency and high contrast conditions, and we can witness a different conclusion from the normal conditions.
2
Content available Quadratic performance analysis of switched affine time-varying systems
Li W., Huang C., Zhai G.
International Journal of Applied Mathematics and Computer Science
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2018
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Vol. 28, no. 3
429--440
EN
We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2 gain analysis problem for the switched affine time-varying systems under state feedback.
3
Content available A generalization of the graph Laplacian with application to a distributed consensus algorithm
Zhai G.
International Journal of Applied Mathematics and Computer Science
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2015
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Vol. 25, no. 2
353--360
EN
In order to describe the interconnection among agents with multi-dimensional states, we generalize the notion of a graph Laplacian by extending the adjacency weights (or weighted interconnection coefficients) from scalars to matrices. More precisely, we use positive definite matrices to denote full multi-dimensional interconnections, while using nonnegative definite matrices to denote partial multi-dimensional interconnections. We prove that the generalized graph Laplacian inherits the spectral properties of the graph Laplacian. As an application, we use the generalized graph Laplacian to establish a distributed consensus algorithm for agents described by multi-dimensional integrators.
4
Content available Decentralized design of interconnected H infinity feedback control systems with quantized signals
Zhai G., Chen N., Gui W.
International Journal of Applied Mathematics and Computer Science
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2013
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Vol. 23, no. 2
317--325
EN
In this paper, we consider the design of interconnected H infinity feedback control systems with quantized signals. We assume that a decentralized dynamic output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H infinity disturbance attenuation level is achieved, and that the subsystem measurement outputs are quantized before they are passed to the local controllers. We propose a local-output-dependent strategy for updating the parameters of the quantizers, so that the overall closed-loop system is asymptotically stable and achieves the same H infinity disturbance attenuation level. Both the pre-designed controllers and the parameters of the quantizers are constructed in a decentralized manner, depending on local measurement outputs.
5
Content available remote A unified approach to stability analysis of switched linear descriptor systems under arbitrary switching
Zhai G., Xu X.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 2
249-259
EN
We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switched system is stable under arbitrary switching. The analysis results are natural extensions of the existing results for switched linear state space systems.
6
Content available remote Effect of growth time on the morphologies of vapour grown carbon fibres and a suggested mechanism of growth
Zhang H., Shi J., Song Y., Zhao J., Wang K., Guo Q., Zhai G., Liu L.
Materials Science Poland
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2009
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Vol. 27, No. 3
885--890
EN
The microstructure of vapour grown carbon fibres is two-double layered. This paper addresses the question of morphology transformation of vapour grown carbon fibres. Special attention is given to developing understanding of the growth mechanism of the outer layer of the fibres. The influence of growth time on the morphologies of as-prepared carbon fibres was investigated using scanning electron microscopy. Results showed that with the prolongation of reaction time, their morphology changed from linear fibres to carbon micro-bead chains and then again to thicker linear fibres, which led to the increase of the carbon fibres diameters from 200 nm to several micrometers. Furthermore, several kinds of carbon fibres with special morphology such as carbon micro-beads, chains, etc., could be obtained by adjusting the growth time. A growth mechanism, henceforth referred to as fibre-bead-thicker fibre, for the outer layer of vapour grown carbon fibres is proposed.
7
Content available remote A matrix inequality based design method for consensus problems in multi-agent systems
Zhai G., Okuno S., Imae J., Kobayashi T.
International Journal of Applied Mathematics and Computer Science
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2009
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Vol. 19, no 4
639-646
EN
In this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus problem at hand to the solving of a strict matrix inequality with respect to a Lyapunov matrix and a controller gain matrix, and we propose two algorithms for solving the matrix inequality. It turns out that this method includes the existing Laplacian based method as a special case and can deal with various additional control requirements such as the convergence rate and actuator constraints.
8
Content available remote Extended Lie algebraic stability analysis for switched systems with continuous-time and discrete–time subsystems
Zhai G., Xu X., Lin H., Liu D.
International Journal of Applied Mathematics and Computer Science
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2007
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Vol. 17, no 4
447-454
EN
We analyze stability for switched systems which are composed of both continuous-time and discrete-time subsystems. By considering a Lie algebra generated by all subsystem matrices, we show that if all subsystems are Hurwitz/Schur stable and this Lie algebra is solvable, then there is a common quadratic Lyapunov function for all subsystems and thus the switched system is exponentially stable under arbitrary switching. When not all subsystems are stable and the same Lie algebra is solvable, we show that there is a common quadratic Lyapunov-like function for all subsystems and the switched system is exponentially stable under a dwell time scheme. Two numerical examples are provided to demonstrate the result.
9
Content available remote Hybrid stabilization of discrete-time LTI systems with two quantized signals
Zhai G., Matsumoto Y., Chen X., Imae J., Kobayashi T.
International Journal of Applied Mathematics and Computer Science
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2005
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Vol. 15, no 4
509-516
EN
We consider stabilizing a discrete-time LTI (linear time-invariant) system via state feedback where both the quantized state and control input signals are involved. The system under consideration is stabilizable and stabilizing state feedback has been designed without considering quantization, but the system’s stability is not guaranteed due to the quantization effect. For this reason, we propose a hybrid quantized state feedback strategy asymptotically stabilizing the system, where the values of the quantizer parameters are updated at discrete time instants. We also extend the result to the case of static output feedback.
10
Content available remote Generalized practical stability analysis of discontinuous dynamical systems
Zhai G., Michel A. N.
International Journal of Applied Mathematics and Computer Science
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2004
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Vol. 14, no 1
5-12
EN
In practice, one is not only interested in the qualitative characterizations provided by the Lyapunov stability, but also in quantitative information concerning the system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner using the concept of practical stability. In the present paper, we give a new definition of generalized practical stability (abbreviated as GP-stability) and establish some sufficient conditions concerning GP-stability for a wide class of discontinuous dynamical systems. As in the classical Lyapunov theory, our results constitute a Direct Method, making use of auxiliary scalar-valued Lyapunov-like functions. These functions, however, have properties that differ significantly from the usual Lyapunov functions. We demonstrate the applicability of our results by means of several specific examples.
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