This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of...This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of coordinate transformation and orthogonal decomposition of vector fields.Then,based on the equivalent form,some delay-dependent results are derived for the stability analysis of the systems by constructing a novel Lyapunov functional.Thirdly,the authors use the equivalent form and the obtained stability results to investigate the H_∞ control problem for a class of nonhnear time-delay control systems,and present a control design procedure.Finally,an illustrative example is given to show the effectiveness of the results obtained in this paper.It is shown that the main results of this paper are easier to check than some existing ones,and have less conservatism.展开更多
This paper considers uncontrollable control systems, and gives the definition of the canonical form for such systems. Necessary and sufficient conditions for the existence of the canonical form are derived.
X-ray photoelectron spectroscopy (XPS) and automatic titrimeter were nsed to study the relation be-tween pH and the transformation of the coordinate forms of P on goethite surfaces. The results showed thatfor a given ...X-ray photoelectron spectroscopy (XPS) and automatic titrimeter were nsed to study the relation be-tween pH and the transformation of the coordinate forms of P on goethite surfaces. The results showed thatfor a given P concentration, increasing the pH of suspension could cause a fast transformation of monodentatecomplexes of phosphate ions on goethite surfaces to binuclear ones. When lowering the PH, additional adsorp-tion of P occurred and the binuclear complexes reverted slowly to the monodentate ones. The dissociationand association of protons of the sorbed P caused by PH changes was considered to be a major reason lewtingto the transformation of the coordinate forms of P on the surfaces. The stability of binuclear surface complexof P was greater than that of monodentate complex. The possible reactions on the interface of goethite andsolutions with pH changes, and the reasons causing the different stabilities of the two coordinate P complexesare discussed in the paper.展开更多
A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitude and latitude was proposed.The vertical and horizontal geodesic coordinates measured with length were defined as coor...A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitude and latitude was proposed.The vertical and horizontal geodesic coordinates measured with length were defined as coordinate parameters,but the two families of coordinate curves were still meridians and parallel circles.The first fundamental form on the ellipsoidal surface and its three coefficients were deduced by the geodesic coordinate.The formula for the latitudinal scale factor of length for geodetic parallel lines was derived,by which the obtained result conformed to that standard value calculated from geodetic latitude,and it is applicable in the range of 400 km from north to south.Therefore,it lays the foundation for establishing the differential equation and differential relationship based on this type of coordinate parameters;and consequently,it is convenient and accurate enough to operate on the ellipsoidal surface in this new form of geodetic coordinate system.展开更多
Various transforms of the indeterminate forms are presented in this part, which include simplification in spherical coordinates, origin translation, axis alteration, transformation of limit conservation and applicatio...Various transforms of the indeterminate forms are presented in this part, which include simplification in spherical coordinates, origin translation, axis alteration, transformation of limit conservation and application of Xh?K0. Fundamental factors for numerical simplification are provided respectively for bi-variable indeterminate forms, tri-variable indeterminate forms and the universal extending multiplier.展开更多
Let [z^0, z^1…, z^n] be the homogeneous coordinate of CP^n. We take a local coordinate neighbourhood U={z^0= 1} of CP^n. In the local coordinate Z=(z^1,…,z^n), the Fubini-Study metric is given
For the controllable linear time-invariant system, we can change the original system into canonical form by choosing a suitable coordinate transformation, e.g. the Luenberger canonical form. If it is not clear beforeh...For the controllable linear time-invariant system, we can change the original system into canonical form by choosing a suitable coordinate transformation, e.g. the Luenberger canonical form. If it is not clear beforehand whether the system is completely controllable, it can be turned into the Yokoyama controllable展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.G60774009,61074068,61034007,61374065,and 61304033the Research Fund for the Doctoral Program of Chinese Higher Education under Grant No.200804220028+1 种基金the Natural Science Foundation of Shandong Province under Grant Nos.ZR2013ZEM006,ZR2011EL021,BS2011ZZ012,2013ZRB01873Colleges and Universities in Shandong Province Science and Technology Project under Grant Nos.J13LN37 and J12LN29
文摘This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of coordinate transformation and orthogonal decomposition of vector fields.Then,based on the equivalent form,some delay-dependent results are derived for the stability analysis of the systems by constructing a novel Lyapunov functional.Thirdly,the authors use the equivalent form and the obtained stability results to investigate the H_∞ control problem for a class of nonhnear time-delay control systems,and present a control design procedure.Finally,an illustrative example is given to show the effectiveness of the results obtained in this paper.It is shown that the main results of this paper are easier to check than some existing ones,and have less conservatism.
基金Project supported by the National Natural Science Foundation of China
文摘This paper considers uncontrollable control systems, and gives the definition of the canonical form for such systems. Necessary and sufficient conditions for the existence of the canonical form are derived.
文摘X-ray photoelectron spectroscopy (XPS) and automatic titrimeter were nsed to study the relation be-tween pH and the transformation of the coordinate forms of P on goethite surfaces. The results showed thatfor a given P concentration, increasing the pH of suspension could cause a fast transformation of monodentatecomplexes of phosphate ions on goethite surfaces to binuclear ones. When lowering the PH, additional adsorp-tion of P occurred and the binuclear complexes reverted slowly to the monodentate ones. The dissociationand association of protons of the sorbed P caused by PH changes was considered to be a major reason lewtingto the transformation of the coordinate forms of P on the surfaces. The stability of binuclear surface complexof P was greater than that of monodentate complex. The possible reactions on the interface of goethite andsolutions with pH changes, and the reasons causing the different stabilities of the two coordinate P complexesare discussed in the paper.
基金supported by the National Natural Science Foundation of China(Grant No.40471114).
文摘A new form of geodetic coordinate system based on geodesic coordinates instead of geodetic longitude and latitude was proposed.The vertical and horizontal geodesic coordinates measured with length were defined as coordinate parameters,but the two families of coordinate curves were still meridians and parallel circles.The first fundamental form on the ellipsoidal surface and its three coefficients were deduced by the geodesic coordinate.The formula for the latitudinal scale factor of length for geodetic parallel lines was derived,by which the obtained result conformed to that standard value calculated from geodetic latitude,and it is applicable in the range of 400 km from north to south.Therefore,it lays the foundation for establishing the differential equation and differential relationship based on this type of coordinate parameters;and consequently,it is convenient and accurate enough to operate on the ellipsoidal surface in this new form of geodetic coordinate system.
文摘Various transforms of the indeterminate forms are presented in this part, which include simplification in spherical coordinates, origin translation, axis alteration, transformation of limit conservation and application of Xh?K0. Fundamental factors for numerical simplification are provided respectively for bi-variable indeterminate forms, tri-variable indeterminate forms and the universal extending multiplier.
文摘Let [z^0, z^1…, z^n] be the homogeneous coordinate of CP^n. We take a local coordinate neighbourhood U={z^0= 1} of CP^n. In the local coordinate Z=(z^1,…,z^n), the Fubini-Study metric is given
文摘For the controllable linear time-invariant system, we can change the original system into canonical form by choosing a suitable coordinate transformation, e.g. the Luenberger canonical form. If it is not clear beforehand whether the system is completely controllable, it can be turned into the Yokoyama controllable
