This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno（T-S）fuzzy systems.New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapu...This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno（T-S）fuzzy systems.New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used.Through the staircase membership functions approximating the continuous membership functions of the given fuzzy model,the information of the membership functions can be brought into the stabilization design of the fuzzy systems,thereby significantly reducing the conservativeness in the existing stabilization conditions of the T-S fuzzy systems.Unlike some previous fuzzy Lyapunov function approaches reported in the literature,the proposed stabilization conditions do not depend on the time-derivative of the membership functions that may be the main source of conservatism when considering fuzzy Lyapunov functions analysis.Moreover,conditions for the solvability of the controller design are written in the form of linear matrix inequalities,but not bilinear matrix inequalities,which are easier to be solved by convex optimization techniques.A simulation example is given to demonstrate the validity of the proposed approach.展开更多
A sequence of periodic attractors has been observed in a two-dimensional discontinuous map, which canbe considered as a model of impact oscillator. The so-called 'transfer number', which is defined as the mean...A sequence of periodic attractors has been observed in a two-dimensional discontinuous map, which canbe considered as a model of impact oscillator. The so-called 'transfer number', which is defined as the mean numberof transfer from non-impact state to impact state per iteration, is locked onto a lot of rational values to form a curveconsisting of many steps. Our numerical investigation confirms that every step is confined by conditions created by thecollision between the periodic orbit and the discontinuous boundary of the system. After the last collision the systemshows a chaotic motion with intermittent characteristics. Therefore the staircase can be addressed as a 'prelude staircaseto type V intermittency'. The similar phenomenon has also been observed in a model of electric circuit. These resultsof our study suggest that this kind of staircases is common in two (or even higher) dimensional discontinuous maps.展开更多
The RGB2GRAY conversion model is the most popular and classical tool for image decolorization. A recent study showed that adapting the three weighting parameters in this first-order linear model with a discrete search...The RGB2GRAY conversion model is the most popular and classical tool for image decolorization. A recent study showed that adapting the three weighting parameters in this first-order linear model with a discrete searching solver has a great potential in its c6nversion ability. In this paper, we present a two-step strategy to efficiently extend the parameter searching solver to a two-order multivariance polynomial model, as a sum of three subspaces. We show that the first subspace in the two-order model is the most important and the second one can be seen as a refinement. In the first stage of our model, the gradient correlation similarity （Gcs） measure is used on the first subspace to obtain an immediate grayed image. Then, Gcs is applied again to select the optimal result from the immettiate grayed image plus the second subspace-induced candidate images. Experimental results show the advantages of the proposed approach in terms of quantitative evaluation, qualitative evaluation, and algorithm complexity.展开更多
基金The National Natural Science Foundation of China(No.60764001,60835001,60875035,61004032)the Postdoctoral Research Fund of Southeast Universitythe Natural Science Foundation of Jiangsu Province(No.BK2008294)
文摘This paper deals with the problem of stabilization design for a class of continuous-time Takagi-Sugeno（T-S）fuzzy systems.New stabilization conditions are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used.Through the staircase membership functions approximating the continuous membership functions of the given fuzzy model,the information of the membership functions can be brought into the stabilization design of the fuzzy systems,thereby significantly reducing the conservativeness in the existing stabilization conditions of the T-S fuzzy systems.Unlike some previous fuzzy Lyapunov function approaches reported in the literature,the proposed stabilization conditions do not depend on the time-derivative of the membership functions that may be the main source of conservatism when considering fuzzy Lyapunov functions analysis.Moreover,conditions for the solvability of the controller design are written in the form of linear matrix inequalities,but not bilinear matrix inequalities,which are easier to be solved by convex optimization techniques.A simulation example is given to demonstrate the validity of the proposed approach.
文摘A sequence of periodic attractors has been observed in a two-dimensional discontinuous map, which canbe considered as a model of impact oscillator. The so-called 'transfer number', which is defined as the mean numberof transfer from non-impact state to impact state per iteration, is locked onto a lot of rational values to form a curveconsisting of many steps. Our numerical investigation confirms that every step is confined by conditions created by thecollision between the periodic orbit and the discontinuous boundary of the system. After the last collision the systemshows a chaotic motion with intermittent characteristics. Therefore the staircase can be addressed as a 'prelude staircaseto type V intermittency'. The similar phenomenon has also been observed in a model of electric circuit. These resultsof our study suggest that this kind of staircases is common in two (or even higher) dimensional discontinuous maps.
基金Project supported by the National- Basic Research Program （973） of China （No. 2013CB035600）, the National Natural Science Foundation of China （Nos. 61261010, 61362001, and 61503176）, Jiangxi Provincial Advanced Projects for Post-Doctoral Research Funds of China （No. 2014KY02）, the International Postdoctoral Exchange Fellowship Program, and the International Scientific and Technological Cooperation Projects of Jiangxi Province, China （No. 20141BDH80001）
文摘The RGB2GRAY conversion model is the most popular and classical tool for image decolorization. A recent study showed that adapting the three weighting parameters in this first-order linear model with a discrete searching solver has a great potential in its c6nversion ability. In this paper, we present a two-step strategy to efficiently extend the parameter searching solver to a two-order multivariance polynomial model, as a sum of three subspaces. We show that the first subspace in the two-order model is the most important and the second one can be seen as a refinement. In the first stage of our model, the gradient correlation similarity （Gcs） measure is used on the first subspace to obtain an immediate grayed image. Then, Gcs is applied again to select the optimal result from the immettiate grayed image plus the second subspace-induced candidate images. Experimental results show the advantages of the proposed approach in terms of quantitative evaluation, qualitative evaluation, and algorithm complexity.
