enriched stick breaking processes for functional data in many applications involving functional data prior information is available about the proportion of curves having different attributes it is not straightforward to include such information in existing procedures for functional data analysis generalizing the functional dirichlet process fdp we propose a class of stick breaking priors for distributions of functions these priors incorporate functional atoms drawn from constrained stochastic processes the stick breaking weights are specified to allow user specified prior probabilities for curve attributes with hyperpriors accommodating uncertainty compared with the fdp the random distribution is enriched for curves having attributes known to be common theoretical properties are considered methods are developed for posterior computation and the approach is illustrated using data on temperature curves in menstrual cycles

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

multiple solutions to some degenerate quasilinear equation with variable exponents via perturbation method abstract in this paper we prove the existence of signed and sign changing solutions to some degenerate quasilinear and elliptic equation containing a gradient term and involving a variable exponent our main idea is to make use of the perturbation method together with invariant sets of descending flow the fact that the exponent is not constant plays an important role

multiple solutions for quasilinear elliptic equations with a finite potential well abstract we consider multiplicity of solutions for a class of quasilinear problems which has received considerable attention in the past including the so called modified nonlinear schrodinger equations by combining a new variational approach via q laplacian regularization and the compactness arguments from 4 we establish infinitely many bound state solutions for the quasilinear schrodinger type equations extending the earlier work of 4 for semilinear equations

admissible consensus and consensualization of high order linear time invariant singular swarm systems abstract admissible consensus analysis and consensualizing controller design problems for high order linear time invariant singular swarm systems are investigated firstly by projecting the state of a singular swarm system onto a consensus subspace and a complement consensus subspace a necessary and sufficient condition for admissible consensus is presented in terms of linear matrix inequalities lmis an approach to decrease the calculation complexity is proposed by which only three lmis independent of the number of agents need to be checked then by using the changing variable method sufficient conditions for admissible consensualization are shown an explicit expression of the consensus function is given and it is shown that the modes of the consensus function can be arbitrarily placed if each agent is r controllable and impulse controllable and the interaction topology has a spanning tree finally theoretical results are applied to deal with cooperative control problems of multi agent supporting systems

technical communique delay dependent output feedback guaranteed cost control for uncertain time delay systems this paper considers the problem of output feedback guaranteed cost controller design for uncertain time delay systems by representing the time delay system in the descriptor form and using a recent result on bounding of cross products of vectors we obtain new delay dependent sufficient conditions for the existence of the guaranteed cost output feedback controller in terms of matrix inequalities a numerical algorithm is proposed to construct a full order output feedback controller achieving a suboptimal guaranteed cost such that the system can be stabilized for all admissible uncertainties an example is presented which shows that the proposed method can produce a lower guaranteed cost than the delay independent method

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

infinitely many sign changing solutions for a quasilinear elliptic equation in r n abstract in this paper by using the methods of perturbation and invariant sets of descending flow we obtain the existence of infinitely many sign changing solutions of a quasilinear elliptic equation in r n

average consensus in networks of multi agents with both switching topology and coupling time delay abstract this paper is devoted to the study of the average consensus problem in directed networks of agents with both switching topology and time delay the stability analysis is performed based on a proposed lyapunov krasovskii function sufficient conditions in terms of linear matrix inequalities lmis are given to guarantee the average consensus under arbitrary switching of the network topology even if the time delay is time varying numerical simulations show the effectiveness of our theoretical results

robust stability and stabilization for singular systems with state delay and parameter uncertainty considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay the parametric uncertainty is assumed to be norm bounded the purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular impulse free and stable for all admissible uncertainties while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed loop system is robustly stable these problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization respectively necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived a strict linear matrix inequality lmi design approach is developed an explicit expression for the desired robust state feedback control law is also given finally a numerical example is provided to demonstrate the application of the proposed method

existence of non trivial solution for a class of modified schrodinger poisson equations via perturbation method abstract in this paper by using the methods of perturbation and the mountain pass theorem we prove the existence of non trivial solution to a class of modified schrodinger poisson equations

soliton solutions for quasilinear schrodinger equations ii abstract for a class of quasilinear schrodinger equations we establish the existence of ground states of soliton type solutions by a variational method

delay dependent admissible consensualization for singular time delayed swarm systems abstract admissible consensus analysis and design problems for high order linear time invariant singular swarm systems with time delays are investigated firstly by state decomposition the admissible consensus problem is transformed into admissible problems of multiple singular subsystems with lower dimensions then linear matrix inequality lmi criteria for admissible consensualization are presented which only involve eight lmi constraints independent of the number of agents moreover an explicit expression of the consensus function which is independent of time delays is presented and the impacts of protocol states and interaction topologies on the consensus function are revealed finally a numerical example is given to illustrate the effectiveness of theoretical results

output feedback stabilization for a discrete time system with a time varying delay this study employs the free weighting matrix approach to investigate the output feedback control of a linear discrete time system with an interval time varying delay first the delay dependent stability is analyzed using a new method of estimating the upper bound on the difference of a lyapunov function without ignoring any terms and based on the results a design criterion for a static output feedback sof controller is derived since the conditions thus obtained for the existence of admissible controllers are not expressed strictly in terms of linear matrix inequalities a modified cone complementarity linearization algorithm is employed to solve the nonconvex feasibility sof control problem furthermore the problem of designing a dynamic output feedback controller is formulated as one of designing an sof controller numerical examples demonstrate the effectiveness of the method and its advantage over existing methods

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

existence of multiple solutions for modified schrdingerkirchhoffpoisson type systems via perturbation method with sign changing potential in this paper we prove the existence of positive solutions and negative solutions for the following modified schrdingerkirchhoffpoisson type systems a br3u2 u v x u u12u u2 f x u inr3 u2 inr3 where a 0 b0 v and f are continuous functions and v x is allowed to be sign changing under some certain assumptions on v and f we prove the existence of nontrivial nonnegative solutions nontrivial nonpositive solutions and sequence of high energy solutions via the perturbation method

solutions for a quasilinear schrodinger equation a dual approach abstract we consider quasilinear stationary schrodinger equations of the form 1 u u 2 u g x u x r n introducing a change of unknown we transform the search of solutions u x of 1 into the search of solutions v x of the semilinear equation 2 v 1 1 2f 2 v g x f v x r n where f is suitably chosen if v is a classical solution of 2 then u f v is a classical solution of 1 variational methods are then used to obtain various existence results

infinitely many sign changing solutions to some quasilinear equation involving exponential term abstract in this paper we prove the existence of infinitely many sign changing solutions to some quasilinear and elliptic equation whose divergence part contains exponential term our main idea consists of the use of the perturbation method together with invariant sets of descending flow in the framework of classical critical point theory

consensus analysis and design for high order linear swarm systems with time varying delays abstract consensus analysis and design problems for high order linear time invariant swarm systems with time varying delays are dealt with first a consensus subspace and a complement consensus subspace are introduced by the state projection onto the two subspaces consensus problems are converted into simultaneous stabilization problems of multiple time delayed subsystems with low dimensions and a method to analyze and design the consensus function is given then sufficient conditions for consensus and consensualization are presented which include only four linear matrix inequality constraints finally theoretical results are applied to deal with cooperative control problems of multi agent supporting systems

consensus problems for high order linear time invariant swarm systems abstract consensus problems for high order continuous time linear time invariant swarm systems with directed interaction topologies are investigated a new method to deal with consensus problems is proposed based on state space decomposition two subspaces of a complex space are introduced namely a consensus subspace and a complement consensus subspace based on this decomposition necessary and sufficient conditions for consensus and consensualizability are presented respectively an approach for determining and designing the consensus function which may be time varying is shown the applications of theoretical results in multi agent supporting systems are studied