negative holomorphic curvature and positive canonical bundle in this note we show that if a projective manifold admits a kahler metric with negative holomorphic sectional curvature then the canonical bundle of the manifold is ample this confirms a conjecture of the second author

correspondence comments on robust stabilization of mimo nonlinear time varying mismatched uncertain systems the main false conclusion wang soh chai automatica 33 1997 2197 was pointed out by a simple counterexample

reduction of manifolds with semi negative holomorphic sectional curvature in this note we continue the investigation of a projective kahler manifold m of semi negative holomorphic sectional curvature h we introduce a new differential geometric numerical rank invariant which measures the number of linearly independent truly flat directions of h in the tangent spaces we prove that this invariant is bounded above by the nef dimension and bounded below by the numerical kodaira dimension of m we also prove a splitting theorem for m in terms of the nef dimension and under some additional hypotheses in terms of the new rank invariant

on h div conforming methods for double diffusion equations in porous media a stationary navier stokes brinkman problem coupled to a system of advection diffusion equations serves as a model for so called double diffusive viscous flow in porous media in which both heat a

robust output tracking control of nonlinear mimo systems via sliding mode technique abstract the robust output tracking control problem of general nonlinear multi input multi output mimo systems is discussed the robustness against parameter uncertainties and unknown disturbances is considered a second order sliding mode control smc technique is used to establish the desired tracking input output i o linearization relative degree minimum phase and matching condition concepts are reviewed some earlier smc strategies which are restricted to the systems in canonical form are extended to a much broader class of nonlinear dynamics it is also shown that for unperturbed dynamics the sliding phase of the smc applications have a direct correspondence to the i o linearization operations interesting parametric flexibilities emanate within the formation of the second order smc designating the s dynamics and the error dynamics segments as frequency domain filters however a critical impasse is posed in the off line selections of the design parameters a set of example cases is presented for a spacecraft attitude control problem these examples manifest that the proposed control strategy is tunable to a desired response despite the disturbances and uncertainties

robust output tracking for nonlinear uncertain systems abstract the problem of robust output tracking for nonlinear systems in the presence of uncertainties is further studied by extending the results of behtash 1990 to systems with mismatched uncertainties a new design method which is called the stable combined variable perturbation method scvpm is proposed and a robust controller is presented using high gain feedback our results are compatible with those of behtash 1990 in a sense that the new controller will degenerate to the one of behtash 1990 if the so called generalized matching condition is satisfied simulation results verified the effectiveness of the newly proposed method and controller

hermitian metrics of positive holomorphic sectional curvature on fibrations the main result of this note essentially is that if the base and fibers of a compact fibration carry hermitian metrics of positive holomorphic sectional curvature then so does the total space of the fibration the proof is based on the use of a warped product metric as in the work by cheung in case of negative holomorphic sectional curvature but differs in certain key aspects e g in that it does not use the subadditivity property for holomorphic sectional curvature due to grauert reckziegel and wu

almost disturbance decoupling for single input single output nonlinear systems the almost disturbance decoupling problem for nonlinear single input single output systems is addressed by using singular perturbation methods and high gain feedback sufficient conditions and the explicit high gain nonlinear state feedback in solvable cases are given they generalize both previous almost results for linear systems and exact ones for nonlinear systems the necessity of the conditions is discussed in particular an example is given where the main structural condition is not satisfied and the high gain control designed on the basis of linear approximations fails to achieve almost disturbance decoupling for the original system

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

globally stable robust tracking of nonlinear systems using variable structure control and with an application to a robotic manipulator the globally stable robust output tracking for a class of nonlinear systems is considered based only on the knowledge of the bounds on the uncertainties a variable structure control vsc law is developed under the structure matching assumption it is shown that the outputs of the closed loop system asymptotically track given output trajectories despite the uncertainties while maintaining the boundedness of all signals inside the loop all signals inside the loop are shown to be bounded for all time to illustrate the efficiency of the controller the approach is applied to the case of a two degree of freedom dof robotic manipulator with variable payload numerical simulation results are also provided

robustness of uncertain systems in the absence of matching assumptions abstract we consider a class of uncertain dynamical systems containing uncertain elements these may be due to model parameter uncertainty input disturbance and measurement noise we require no a priori information on the uncertain elements except that their restraint sets are assumed to be known and compact this paper describes a general approach for designing controls to assure practical stability in the absence of matching assumptions which most previous results have needed the result is applicable to non linear systems a specialization to linear systems is then given and a comparison is made with previous work

output tracking control of nonlinear systems with mismatched uncertainties abstract this paper addresses the output tracking problem of a class of nonlinear systems given input output linearizability of the class of nonlinear systems a robust output tracking controller derived via a lyapunov based approach is proposed here the model uncertainties do not need to satisfy the conventional matching condition but states and tracking error remain bounded furthermore the magnitude of the tracking error will bear dominant dependence on the magnitude of the mismatched uncertainties

stationary solutions for generalized boussinesq models abstract we study the existence regularity and conditions for uniqueness of solutions of a generalized boussinesq model for thermally driven convection the model allows temperature dependent viscosity and thermal conductivity

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

on the evolution of a hermitian metric by its chern ricci form we consider the evolution of a hermitian metric on a compact complex manifold by its chern ricci form this is an evolution equation first studied by m gill and coincides with the kahler ricci flow if the initial metric is kahler we find the maximal existence time for the flow in terms of the initial data we investigate the behavior of the flow on complex surfaces when the initial metric is gauduchon on complex manifolds with negative first chern class and on some hopf manifolds finally we discuss a new estimate for the complex monge ampere equation on hermitian manifolds

holomorphic sectional curvature nefness and miyaoka yau type inequality on a compact kahler manifold we introduce a notion of almost nonpositivity for the holomorphic sectional curvature which by definition is weaker than the existence of a kahler metric with semi negative holomorphic sectional curvature we prove that a compact kahler manifold of almost nonpositive holomorphic sectional curvature has a nef canonical line bundle contains no rational curves and satisfies some miyaoka yau type inequalities in the course of the discussions we attach a real value to any fixed kahler class which up to a constant factor depending only on the dimension of manifold turns out to be an upper bound for the nef threshold

robust output tracking for non linear systems the problem of output tracking for a single input single output non linear system in the presence of uncertainties is studied the notions relative degree and minimum phase for non linear systems are reviewed given a bounded desired tracking signal with bounded derivatives a control law is designed for minimum phase non linear systems which results in tracking of this signal by the output this control law is modified in the presence of uncertainties associated with the model vector fields to reduce the effects of these uncertainties on the tracking errors two types of uncertainties are considered those satisfying a generalized matching condition but otherwise unstructured and linear parametric uncertainties it is shown that for systems with the first type of uncertainty high gain control laws can result in small tracking errors of o where e is a small design parameter an alternative scheme based on variable structure control strategy is shown to yield zero tracking errors adaptive control te

robust stabilization of mimo nonlinear time varying mismatched uncertain systems abstract this paper considers the problem of robust stabilization of multi input multi output mimo nonlinear systems in the presence of mismatched time varying uncertainties combining the differential geometric feedback linearization with the deterministic approach it derives two robust stabilizing controllers i e the high gain feedback controller and the variable structure controller these two controllers only require the knowledge of the nominal system and the bounds of the uncertainties therefore they are more feasible to be implemented both controllers reduce the effects of arbitrarily large bounded mismatched uncertainties successfully to achieve uniform ultimate boundedness stabilization of the mimo nonlinear timevarying uncertain systems

local curvature estimates of long time solutions to the kahler ricci flow abstract we study the local curvature estimates of long time solutions to the normalized kahler ricci flow on compact kahler manifolds with semi ample canonical line bundle using these estimates we prove that on such a manifold the set of singular fibers of the semi ample fibration on which the riemann curvature blows up at time infinity is independent of the choice of the initial kahler metric moreover when a regular fiber of the semi ample fibration is not a finite quotient of a torus we determine the exact curvature blow up rate of the kahler ricci flow near the regular fiber

an extension of a theorem of wu yau we show that a compact kahler manifold with nonpositive holomorphic sectional curvature has nef canonical bundle if the holomorphic sectional curvature is negative then it follows that the canonical bundle is ample confirming a conjecture of yau the key ingredient is the recent solution of this conjecture in the projective case by wu yau

robust control of non linear affine systems issue of robust control for non linear affine systems with uncertainties appearing in both drift and non drift terms are presented based on lyapunov function approach control laws are proposed to guarantee uniformly asymptotic stability of the equilibrium point to facilitate the design and simplify the checking procedure stabilization control for the uncertain systems possess asymptotic stabilizable nominal time invariant driftness terms are proposed for the demonstration of robust design

robust control of nonlinear uncertain systems without generalized matching conditions a novel procedure called recursive interlacing procedure is proposed for designing globally stabilizing robust control the procedure introduces new interlacing steps and combines them with the existing recursive or backstepping design it is shown by examining all possible third order vector systems that the procedure is applicable to systems not satisfying any of the existing structural conditions that is to systems in which uncertainties are potentially anywhere and of any bounding function by its nature the procedure is not limited to systems of any specific order it either produces stabilizing control or reveals certain measure of unstabilizability and it includes recursive design as a special case

the uniformization theorem for compact kahler manifolds of nonnegative holomorphic bisectional curvature soit x h une variete de kahler compacte a n dimensions de courbure bisectionnelle holomorphe non negative et soit x h son espace de recouvrement universel alors il existe des entiers non negatifs k n 1 n l et des espaces symetriques hermitiens compacts ineductibles m 1 m k de rang 2 tels que x h est isometriquement bi holomorphe a c k g 0 p nu 1 1 p nu l l m 1 g 1 m p g p ou g 0 est la metrique euclidienne sur c k g 1 g p sont des metriques canoniques sur m 1 m p et i 1 i l est une metrique de kahler sur p nu i portant une courbure bisectionnelle holomorphe non negative

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions