almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

periodicity in a delayed ratio dependent predator prey system abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a delayed ratio dependent predator prey system in a periodic environment

permanence and extinction in nonlinear single and multiple species system with diffusion in this paper we consider the effect of diffusion on the permanence and extinction of single and multiple endangered species that live in changing patch environments average conditions are obtained for the permanence and extinction of the systems considered the results obtained in this paper generalize the main results of cui and chen the effect of diffusion on the time varying logistic population growth comput math appl 36 3 1998 1 9 permanence and extinction in logistic and lotka volterra systems with diffusion j math anal appl 258 2 2001 512 535

permanence for a two species gause type ratio dependent predator prey system with time delay in a two patch environment this paper is devoted to a two species periodic gause type ratio dependent predator prey system with time delay in a two patch environment by using the comparison theorem of differential equations we establish sufficient conditions for the permanence of the system as corollaries some applications are listed in particular our results generalize and improve some known ones

effect of weak prey in leslie gower predator prey model a leslie gower prey predator model incorporating partial prey protection is proposed prey densities are divided into two groups strong and weak the special dynamic of each group is considered the condition of existence and uniqueness of the equilibrium point in the positive octant is determined and by constructing a suitable lyapunov function it is shown that the unique equilibrium point is stable in the positive octant the effects of strong prey becoming weak prey is studied and it is shown that it has no influence on the persistent property of the system and can enhance the co existence of the prey predator

harmonic analysis on nilpotent groups and singular integrals ii singular kernels supported on submanifolds on etudie des operateurs de convolution singuliers sur des groupes de lie nilpotents generaux et plus specifiquement des operateurs dont les noyaux ont pour supports des varietes de faible dimension et qui peuvent aussi contenir des facteurs polynomiaux exponentiels oscillatoires

a rough hypersingular integral operator with an oscillating factor abstract we study certain hypersingular integrals t f defined on all test functions f s r n where the kernel of the operator t has a strong singularity y n 0 at the origin an oscillating factor e i y 0 and a distribution h r s n 1 0 r 1 we show that t extends to a bounded linear operator from the sobolev space l p l p to the lebesgue space l p for p if the distribution is in the hardy space h r s n 1 with 0 r n 1 n 1 0 and 2 0

global stability for a class of predator prey systems this paper deals with the question of global stability of the positive locally asymptotically stable equilibrium in a class of predator prey systems the dulac s criterion is applied and liapunov functions are constructed to establish the global stability

global periodic solutions of a generalized n species gilpin ayala competition model abstract in this paper we investigate a generalized n species gilpin ayala competition system with several deviating arguments in periodic environment which is more general and more realistic than the classical lotka volterra competition systems by using the method of coincidence degree a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive componentwise periodic solution some new results are obtained as applications we also apply our main results to some special cases of the system we consider here including the classical n species lotka volterra competition systems and n species gilpin ayala competition model which have been studied extensively in the literature some known results are improved and generalized the examples show that our criteria are new general and easily verifiable

weighted weak 1 1 and weighted estimates for oscillating kernels weak type 1 1 and strong type p p inequalities are proved for operators defined by oscillating kernels the techniques are sufficiently general to derive versions of these inequalities using weighted norms 0 introduction given a positive real number a o a 7 1 define the oscillating kernel ka by ka x 1 x leilxla and consider the convolution operator ka f in an earlier paper 2 we studied the boundedness properties of such operators on weighted lp spaces 1 1 we define l p f 1l p w a e f x lpw x dx r and say f e lp r if llfllp w 1 the multiplier operator t associated to ka is defixled by t d 0 1 l e 1tl f where 0 is a c function defined by i 0 4 0 if 1 when p 0

nonlinear h sub spl infin control and its application to rigid spacecraft the problem of h sub spl infin control of a rigid spacecraft with three control torques and disturbances is addressed the hamilton jacobi isaacs inequality for h sub spl infin feedback design is solved an h sub spl infin suboptimal feedback is given and the stability properties of the closed loop system are studied

positive periodic solution of two species ratio dependent predator prey system with time delay in two patch environment in this paper we are concerned with the existence of positive periodic solution to a class of two species ratio dependent predator prey diffusion model with time delay by using the continuation theorem of coincidence degree theory we transform this problem into a problem of calculating the topological degree of a continuous mapping and then some sufficient conditions of the existence of positive periodic solution is established for the system

weighted boundedness for rough marcinkiewicz integrals with different weights in this paper the authors give the weighted boundedness of the marcinkiewicz integral operators for different weight functions where the kernel functions of the operators discussed here are without smoothness not only on the sphere but also in the radial direction

cooperative systems of differential equations with concave nonlinearities on considere le systeme dynamique discret engendre par une application monotone concave t r n r n on etudie ensuite des systemes d equations differentielles cooperatifs periodiques x f t x a non linearites concaves

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

robust stabilization of the angular velocity of a rigid body the problem of robust control for the angular velocity of a rigid body subject to external disturbances is addressed it is shown that if the disturbances are matched there exists a control law attenuating the effect of the disturbances whereas in the case of non matched disturbances no such a feedback law generically exists hence a new concept of disturbance attenuation is introduced and it is proved that the aforementioned problem is solvable in this weaker sense explicit expressions of the control laws solving the proposed robust stabilization problems are given

brief trading robustness with optimality in nonlinear control the mixed h 2 h control problem is studied for a class of nonlinear systems a procedure providing a sub optimal solution to this problem is discussed and analyzed in detail the sub optimal state feedback control law can be obtained solving two hamilton jacobi equations and a simple one parameter static minimization problem a simple one dimensional example is discussed in detail and applications to the optimal robust stabilization of the angular velocities of a rigid body are included

on a periodic multi species ecological model a periodic predator prey model with m predators and n preys is proposed in this paper which can be seen as the modification of the traditional lotka volterra model by using comparison theorem the ultimately bounded region of the system is obtained by using comparison theorem and brouwer fixed point theorem sufficient conditions with guarantee the existence of a positive periodic solution of the system is obtained finally by constructing a suitable lyapunov function some sufficient conditions are obtained for the existence of a unique globally attractive periodic solution of system the results obtained here generalized the main results of j d zhao w c chen global asymptotic stability of a periodic ecological model applied mathematics and computation 147 3 2004 881 892

hilbert integrals singular integrals and radon transforms i on introduit deux nouvelles classes d operateurs on etudie leur relation et on montre comment on peut les appliquer a l etude des problemes aux valeurs limites

the effect of dispersal on permanence in a predator prey population growth model abstract in this paper we consider a periodic predator prey system where the prey can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation we assume a volterra within patch dynamic under the assumption that the average of dispersal rate from patch 1 to patch 2 is less than that of the intrinsic growth rate of prey in patch 1 we provide a sufficient and necessary condition to guarantee the prey and predator species to be permanent by using the main techniques in 1

the effect of diffusion on the time varying logistic population growth abstract in this paper we consider the effect of diffusion on the species that live in changing patches environment different from the former studies 1 4 we pay attention to the more important situation in conservation biology that species live in a weak patches environment in the sense that species in some of the isolated patches will be extinct without the contribution from other patches we obtain an interesting result the identical species can persist for some diffusion rates and can also vanish for another set of restriction on diffusion rates

rough singular integrals supported on submanifolds abstract in this paper the authors study the boundedness of the singular integral operators associated to submanifolds on triebel lizorkin spaces and besov spaces moreover the authors also establish an l q valued inequality for the maximal operators associated to submanifolds in this paper

persistence and stability for a two species ratio dependent predator prey system with time delay in a two patch environment abstract a two species ratio dependent predator prey diffusion model with time delay is investigated it is shown that the system is permanent under some appropriate conditions and sufficient conditions are obtained for the local and global stability of the positive equilibrium of the system

existence uniqueness and stability of positive periodic solution for a nonlinear prey competition model with delays a nonlinear periodic predator prey model with m preys and n m predators and delays is proposed in this paper which can be seen as the modification of the traditional lotka volterra prey competition model sufficient conditions which guarantee the existence of a unique globally attractive positive periodic solution of the system are obtained

the qualitative analysis of n species nonlinear prey competition systems in this paper we consider an n species nonlinear prey competition system using the differential inequality theorem and the v function method we obtain some sufficient conditions for the permanence and global asymptotic stability of the system

passivity based adaptive attitude control of a rigid spacecraft an adaptive control scheme for the attitude control of a rigid spacecraft is derived using a linear parameterization of the equation of motion the tracking error is described with the euler parameter vector global convergence of the tracking error to zero is shown using passivity theory this allows for the use of time varying positive definite feedback gain matrices and the results can easily be extended to other passive parameter update laws

comments on the attitude control problem the commenter refers to above paper by wen and kreutz delgado ibid vol 36 no 10 p 1148 62 1991 and points out that there are some errors in the proof of theorem 1 as a result of this the final expression in theorem 1 and 2 together with the table in theorem 2 should be modified

inverse optimal adaptive control for attitude tracking of spacecraft the attitude tracking control problem of a rigid spacecraft with external disturbances and an uncertain inertia matrix is addressed using the adaptive control method the adaptive control laws proposed in this paper are optimal with respect to a family of cost functionals this is achieved by the inverse optimality approach without solving the associated hamilton jacobi isaacs partial differential hjipd equation directly the design of the optimal adaptive controllers is separated into two stages by means of integrator backstepping and a control lyapunov argument is constructed to show that the inverse optimal adaptive controllers achieve h sub spl infin disturbance attenuation with respect to external disturbances and global asymptotic convergence of tracking errors to zero for disturbances with bounded energy the convergence of adaptive parameters is also analyzed in terms of invariant manifold numerical simulations illustrate the performance of the proposed control algorithms

brief paper a discrete time observer design for spacecraft attitude determination using an orthogonality preserving algorithm this paper studies a nonlinear discrete time partial state observer design problem for rigid spacecraft systems particularly for spacecraft attitude estimation the construction is inspired by an orthogonality preserving numerical algorithm and it yields a semiglobal practical asymptotic observer we show that the separation principle holds and hence stabilization using output feedback is possible an example is provided to illustrate the usefulness of our results in a sampled data implementation of an attitude control for a rigid spacecraft using output feedback and to illustrate the advantages of the proposed observer design especially compared to a sample and hold version of a similar type observer designed in continuous time

global set stabilisation of the spacecraft attitude using finite time control technique in this article we revisit the classical problem of attitude stabilisation for a rigid spacecraft with external disturbances a global set stabilisation method using finite time control technique is proposed in the absence of disturbances the states of the closed loop system will be stabilised in finite time to a set consisting of two equilibria in the presence of disturbances the states will be stabilised to a neighbourhood of this set by constructing a particular lyapunov function it is proved that the closed loop system satisfies global set stability the control method in this article is based on set control idea and thus is more natural and energy efficient numerical simulation results show the effectiveness of the method

rough maximal singular integral and maximal operators supported by subvarieties on triebel lizorkin spaces abstract in this paper our object of investigation is the maximal singular integrals with rough kernels associated to polynomial mapping p as well as the corresponding compound submanifolds which is defined by t h p f x sup 0 y f x p y h y y y n d y we show that the operator t h p is bounded on triebel lizorkin spaces and besov spaces when the rough kernel l log l s n 1 for some 0 1 similar results can be extended to hardy littlewood maximal operators with rough kernels associated to the mapping p

on a nonlinear nonautonomous predator prey model with diffusion and distributed delay in this paper a nonlinear nonautonomous predator prey model with diffusion and continuous distributed delay is studied where all the parameters are time dependent the system which is composed of two patches has two species the prey can diffuse between two patches but the predator is confined to one patch we first discuss the uniform persistence and global asymptotic stability of the model after that by constructing a suitable lyapunov functional some sufficient conditions for the existence of a unique almost periodic solution of the system are obtained an example shows the feasibility of our main results

periodic solutions and permanence for a delayed nonautonomous ratio dependent predator prey model with holling type functional response by using the continuation theorem of coincidence degree theory the existence of positive periodic solutions for a delayed ratio dependent predator prey model with holling type iii functional response x t x t a t b t t k t s x s ds c t x2 t y t m2y2 t x2 t y t y t e t x2 t m2y2 t x2 t d t is established where a t b t c t e t and d t are all positive periodic continuous functions with period 0 m 0 and k s is a measurable function with period is a nonnegative constant the permanence of the system is also considered in particular if k s 0 s where 0 s is the dirac delta function at s 0 our results show that the permanence of the above system is equivalent to the existence of positive periodic solution

on a delayed nonautonomous ratio dependent predator prey model with holling type functional response and diffusion abstract a two species periodic ratio dependent predator prey model with holling type functional response and diffusion is investigated three different sets of sufficient conditions one set is diffusive independent and the other two sets are diffusive dependent which ensure the permanence of the system and a set of sufficient condition which ensure the extinction of the predator species are obtained examples together with their numeric simulations show the feasibility of the main results

permanence and extinction of a three species ratio dependent food chain model with delay and prey diffusion abstract in this paper we study a diffusive three species ratio dependent food chain model using differential inequality to obtain sufficient conditions that ensure the permanence of the system and the extinction of predator species our results reinforce the main result of sun wen shihua chen and huihai mei positive periodic solution of a more realistic three species lotka volterra model with delay and density regulation chaos solitons and fractals in press

inverse optimal stabilization of a rigid spacecraft the authors present an approach for constructing optimal feedback control laws for regulation of a rotating rigid spacecraft they employ the inverse optimal control approach which circumvents the task of solving a hamilton jacobi equation and results in a controller optimal with respect to a meaningful cost functional the inverse optimality approach requires the knowledge of a control lyapunov function and a stabilizing control law of a particular form for the spacecraft problem they are both constructed using the method of integrator backstepping the authors give a characterization of nonlinear stability margins achieved with the inverse optimal control law

state feedback spl hscr sub spl infin suboptimal control of a rigid spacecraft a state feedback spl hscr sub spl infin suboptimal control problem on tso 3 for a rigid spacecraft with three control torques and disturbances is addressed the hamilton jacobi inequality associated with a corresponding state feedback spl hscr sub spl infin suboptimal control problem on ts sup 3 is solved globally the spl hscr sub spl infin suboptimal state feedback on ts sup 3 involves the euler parameters and solves the original problem on tso 3 when the initial values of the euler parameters are appropriately chosen

the attitude control problem a general framework for the analysis of the attitude tracking control problem for a rigid body is presented a large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body the controllers share the common structure of a proportional derivative feedback plus some feedforward which can be zero the model independent case the coriolis torque compensation or an adaptive compensation these controller structures are compared in terms of the requirement on the a priori model information guaranteed transient performance and robustness the global stability of the luh walker paul robot end effector controller is also analyzed in this framework

harmonic analysis on nilpotent groups and singular integrals i oscillatory integrals abstract this paper is devoted to the study of the operator given by where k is a standard calderon zygmund kernel and p is a real polynomial on r n r n we show t is bounded on lp to itself when 1

existence of four periodic solutions for a generalized delayed ratio dependent predator prey system in this paper by using the continuation theorem of coincidence degree theory we obtain the existence condition of at least four periodic solutions for a delayed ratio dependent predator prey system an example is represented to illustrate the feasibility of our main result

periodicity in a logistic type system with several delays with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of the following several delays logistic type system du t dt u t a t j 1mb j t u t t j t q j where a t b j t are positive periodic continuous functions with periodic w 0 t j t are nonnegative continuous periodic functions with periodic w 0 after that by constructing a suitable lyapunov functional some sufficient conditions which guarantee the stability of the positive periodic solutions are obtained

singular integrals related to the radon transform and boundary value problems abstract two classes of integral operators are introduced that combine features of calderon zygmund singular integrals the hilbert integral and the radon transform examples and applications arising from integral geometry and several complex variables are discussed