ℋ index for continuous time stochastic systems with markov jump and multiplicative noise this paper investigates the problem of index for stochastic linear continuous time systems involving markov jump and multiplicative noise a set of generalized differential riccati equations gdres are presented and it is shown that the solvability of gdres is necessary and sufficient for the feasibility of an index larger than 0 our results extend the corresponding deterministic cases to stochastic systems furthermore the infinite horizon index problem for square systems is considered finally the effectiveness of the obtained results is tested by two examples

stabilization of networked control systems with both network induced delay and packet dropout this paper is concerned with the mean square stabilization problem for discrete time networked control systems ncss it is assumed that control signal is sent to plant over a lossy communication channel where network induced delay and packet dropout occur simultaneously a necessary and sufficient stabilizing condition is developed in terms of the unique positive definite solutions to some coupled algebraic riccati equations cares the contributions of this paper are twofold first an existence theorem of the maximum packet dropout rate is proposed second for one dimensional single input system and the decoupled multi input system it is shown that the ncs is stabilizable iff the network induced delay and the packet dropout rate satisfy some simple algebraic inequalities if the network induced delay is known a priori the maximum packet dropout rate is given explicitly in terms of network induced delay and unstable eigenvalues of the system matrix if the packet dropout rate is known a priori the maximum allowable delay bound is also given explicitly

variational problems with two phases and their free boundaries the problem of minimizing vu 2 q2 x 2 v dx in an appropriate class of functions v is considered here q x 0 and a2 t x2 if v 0 any minimizer u is harmonic in u 0 and vu 2 has a jump a2 x 22 across the free boundary u 0 regularity and various properties are established for the minimizer u and for the free boundary introduction in this paper we consider the problem of minimizing j v f vv 2 q2 x x2 v dx vgk where q2 x 0 a22 ifu 0 and x2 u is lower semicontinuous at v 0 it is assumed that a2 0 and a a2 a22 0 the class k consists of all functions v in l loc s2 with vu g l2 i2 such that v u on a given open subset s of 3i2 and s is a domain in r the analogous problem for functions in k v k v 0 a e was studied in 1 in that paper it was proved that any local minimizer of j v in k is lipschitz continuous and if n 2 the free boundary 8 w 0 is analytic if q x is analytic the present variational problem is motivated by applications to the now of two liquids in models of jets and cavities these applications will be studied in other forthcoming papers 5 6 the present work is aimed at extending results of 1 in particular we shall establish nondegeneracy theorems the lipschitz continuity of the solution and some properties of the free boundary for n 2 the free boundary is proved to be continuously differentiable a new and rather powerful tool introduced in this paper is the monotonicity formula lemma 5 1 asserting that for a minimizer u if u x0 0 then

the obstacle problem for the fractional laplacian with critical drift we study the obstacle problem for the fractional laplacian with drift min vardelta su b cdot nabla u u varphi 0 in mathbb r n in the critical regime s frac 1 2 our main result establishes the c 1 alpha regularity of the free boundary around any regular point x 0 with an expansion of the form open image in new window where e in mathbb s n 1 is the normal vector to the free boundary sigma 0 and c 0 0 we also establish an analogous result for more general nonlocal operators of order 1 in this case the exponent tilde gamma x 0 also depends on the operator

a geometric approach to generalized stokes conjectures we consider the stokes conjecture concerning the shape of extreme 2 dimensional water waves by new geometric methods including a non linear frequency formula we prove the stokes conjecture in the original variables our results do not rely on structural assumptions needed in previous results such as isolated singularities symmetry and monotonicity part of our results extends to the mathematical problem in higher dimensions

quantized output feedback control for networked control systems this paper addresses the problem of output feedback control for networked control systems ncss with limited communication capacity firstly we propose a new model to describe the non ideal network conditions and the input output state quantization of the ncss in a unified framework secondly based on our newly proposed model and an improved separation lemma the observer based controller is developed for the asymptotical stabilization of the ncss which are shown in terms of nonlinear matrices inequalities the nonlinear problems can be computed through solving a convex optimization problems and the observed and controller gains could be derived by solving a set of linear matrix inequalities thirdly two simulation examples are given to demonstrate the effectiveness of the proposed method

singularities in axisymmetric free boundaries for electrohydrodynamic equations we consider singularities in the electrohydrodynamic equations in a regime where we are allowed to neglect surface tension and assuming that the free surface is given by an injective curve and that either the fluid velocity or the electric field satisfies a certain non degeneracy condition we prove that either the fluid region or the gas region is asymptotically a cusp our proofs depend on a combination of monotonicity formulas and a non vanishing result by caffarelli and friedman as a by product of our analysis we also obtain a special solution with convex conical air phase which we believe to be new

a new approach for numerical identification of free boundary this paper studies a stefan problem with a forcing term in identifying the free boundary we propose a parameter estimation technique function space parameter estimation convergence is proved and numerical simulations are performed

higher regularity of the free boundary in the obstacle problem for the fractional laplacian abstract we prove a higher regularity result for the free boundary in the obstacle problem for the fractional laplacian via a higher order boundary harnack estimate

the structure of the free boundary for lower dimensional obstacle problems we study the regularity of the free surface in boundary obstacle problems we show that near a non degenerate point the free boundary is a c 1 a n 2 dimensional surface in r n 1

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

linear quadratic regulation for discrete time systems with input delay and colored multiplicative noise abstract this paper is concerned with the linear quadratic regulation lqr problem for discrete time systems involving input delay and colored multiplicative noise due to the correlation of the adjoining state this problem will be more complicated than the case of white noise in this paper the necessary and sufficient condition for the solvability of optimal control problem is presented by solving the forward and backward stochastic difference equations fbsdes moreover the optimal lqr controller is given in terms of the coupled difference equations developed in this paper

modeling and control of ito stochastic networked control systems with random packet dropouts subject to time varying sampling in this note we discuss the modeling and control of a class of ito stochastic networked control systems ncss with packet dropouts that are subject to time varying sampling the system under consideration is first modeled as a continuous time system with input delay that is subject to double randomness via the input delay approach then by assuming the packet drop rate and recurring to the celebrated formula of total probability an equivalent model which takes full advantage of probability distribution characteristics of both packet dropouts and sampling periods is established in particular the probability distribution values of the stochastic delay taking values in two given intervals can be explicitly obtained which is of crucial importance to model and analyze the actual problem in ncss based on that robustly exponentially mean square stability of the system with an h infty performance is guaranteed an h infty controller design procedure is then proposed finally a numerical simulation example is exploited to show the effectiveness and applicability of the results derived and some less conservative results are obtained

brief paper robust sampled data h control with stochastic sampling in this paper the problem of robust h control is investigated for sampled data systems with probabilistic sampling the parameter uncertainties are time varying norm bounded and appear in both the state and input matrices for the simplicity of technical development only two different sampling periods are considered whose occurrence probabilities are given constants and satisfy bernoulli distribution which can be further extended to the case with multiple stochastic sampling periods by applying an input delay approach the probabilistic sampling system is transformed into a continuous time delay system with stochastic parameters in the system matrices by linear matrix inequality lmi approach sufficient conditions are obtained which guarantee the robust mean square exponential stability of the system with an h performance moreover an h controller design procedure is then proposed an illustrative example is included to demonstrate the effectiveness of the proposed techniques

obstacle problems for integro differential operators higher regularity of free boundaries abstract we study the higher regularity of free boundaries in obstacle problems for integro differential operators our main result establishes that once free boundaries are c 1 then they are c this completes the study of regular points initiated in 5 in order to achieve this we need to establish optimal boundary regularity estimates for solutions to linear nonlocal equations in c k domains these new estimates are the core of our paper and extend previously known results by grubb for k and by the second author and serra for k 1

sampled data synchronization control of dynamical networks with stochastic sampling this technical note is concerned with the sampled data synchronization control problem for a class of dynamical networks the sampling period considered here is assumed to be time varying that switches between two different values in a random way with given probability the addressed synchronization control problem is first formulated as an exponentially mean square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays mpids and the sector bounded nonlinearities sbns then a novel lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean square stable both gronwall s inequality and jenson integral inequality are utilized to substantially simplify the derivation of the main results subsequently a set of sampled data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software finally a numerical simulation example is employed to show the effectiveness of the proposed sampled data synchronization control scheme

stabilization of sampled data control systems with control inputs missing this note is concerned with the stabilization problem for sampled data control systems with control inputs missing a sufficient condition is derived for the existence of exponentially stabilizing state feedback controllers via the switched system approach the obtained condition establishes several quantitative relations among some system parameters such as the sampling period and the exponential decay rate the actual data missing rate and the admissible data missing rate bound two illustrative examples are given to show the effectiveness of the proposed results

higher regularity of the free boundary in the elliptic signorini problem abstract in this paper we study the higher regularity of the free boundary for the elliptic signorini problem by using a partial hodograph legendre transformation we show that the regular part of the free boundary is real analytic the first complication in the study is the invertibility of the hodograph transform which is only c 0 1 2 which can be overcome by studying the precise asymptotic behavior of the solutions near regular free boundary points the second and main complication in the study is that the equation satisfied by the legendre transform is degenerate however the equation has a subelliptic structure and can be viewed as a perturbation of the baouendi grushin operator by using the l p theory available for that operator we can bootstrap the regularity of the legendre transform up to real analyticity which implies the real analyticity of the free boundary

new monotonicity formulas and the optimal regularity in the signorini problem with variable coefficients abstract we study the interior signorini or lower dimensional obstacle problem for a uniformly elliptic divergence form operator l div a x with lipschitz continuous coefficients our main result states that similarly to what happens when l the variational solution has the optimal interior regularity c loc 1 1 2 m when m is a codimension one flat manifold which supports the obstacle we achieve this by proving some new monotonicity formulas for an appropriate generalization of the celebrated almgren s frequency functional

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

regularity estimates for the solution and the free boundary of the obstacle problem for the fractional laplacian we use a characterization of the fractional laplacian as a dirichlet to neumann operator for an appropriate differential equation to study its obstacle problem we write an equivalent characterization as a thin obstacle problem in this way we are able to apply local type arguments to obtain sharp regularity estimates for the solution and study the regularity of the free boundary

a homogeneity improvement approach to the obstacle problem this paper contains a new approach to regularity and singularity of the obstacle problem by means of an epiperimetric inequality and a monotonicity formula an energy decay estimate is derived as a consequence the increase in the solution s homogeneity when passing to a smaller ball can be estimated this leads to uniqueness of blow up limits and regularity in that order

the structure of the free boundary in the fully nonlinear thin obstacle problem abstract we study the regularity of the free boundary in the fully nonlinear thin obstacle problem our main result establishes that the free boundary is c 1 near any regular point this extends to the fully nonlinear setting the celebrated result of athanasopoulos caffarelli salsa 1 the proofs we present here are completely independent from those in 1 and do not rely on any monotonicity formula furthermore an interesting and novel feature of our proofs is that we establish the regularity of the free boundary without classifying blow ups a priori they could be non homogeneous and or non unique we do not classify blow ups but only prove that they are 1d on x n 0

a necessary and sufficient rhc stabilizability condition for stochastic control with delayed input abstract we study the mean square stabilizability of ito stochastic systems with delayed input in contrast to most previous results where only sufficient condition was derived this paper proposes a necessary and sufficient stabilization condition by exploring the receding horizon control rhc and the coupled riccati equations it is shown that the system controlled by rhc is stabilizable if and only if the two coupled lyapunov type inequalities are satisfied the key is to design a novel cost function based on the optimal cost of finite horizon optimization problem

global regularity for the free boundary in the obstacle problem for the fractional laplacian we study the regularity of the free boundary in the obstacle problem for the fractional laplacian under the assumption that the obstacle varphi satisfies delta varphi leq 0 near the contact region our main result establishes that the free boundary consists of a set of regular points which is known to be a n 1 dimensional c 1 alpha manifold by the results obtained by caffarelli salsa and silvestre it invent math 2008 and a set of singular points which we prove to be contained in a union of k dimensional c 1 submanifold k 0 ldots n 1 such a complete result on the structure of the free boundary proved by l a caffarelli it acta math 1977 and it j fourier anal appl 1998 was known only in the case of the classical laplacian and it is new even for the signorini problem which corresponds to the particular case of the 1 over 2 fractional laplacian a key ingredient behind our results is the validity of a new non degeneracy condition sup b r x 0 u varphi geq c r 2 valid at all free boundary points x 0

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

unique continuation for elliptic operators a geometric variational approach dans un sous ensemble connexe ouvert de r n n 3 on considere l equation d ordre 2 lu div a x u b x u v x u 0 ou a x a id j x est une matrice symetrique reelle on etudie les proprietes d unicite de l operateur

network based fuzzy control for nonlinear markov jump systems subject to quantization and dropout compensation abstract this paper focuses on the issue of network based fuzzy control for nonlinear markov jump systems with unreliable communication links the nonlinear system under consideration is described by a takagi sugeno t s fuzzy model through corresponding fuzzy rules the control signals are quantized by a logarithmic quantizer before they are transmitted to the network and in case quantized control signals lose intermittently when being passed to the actuator a compensation strategy is implemented to deal with the packet dropout based on a novel lyapunov function which is both fuzzy basis dependent and mode dependent the existence criterion for the desired controller is established to ensure the stochastic stability as well as a predefined h performance index of the resulting closed loop system a bench mark example of robot arm is presented to demonstrate the validity of the proposed design technique

on the fine structure of the free boundary for the classical obstacle problem in the classical obstacle problem the free boundary can be decomposed into regular and singular points as shown by caffarelli in his seminal papers caffarelli in acta math 139 155 184 1977 j fourier anal appl 4 383 402 1998 regular points consist of smooth hypersurfaces while singular points are contained in a stratified union of c 1 manifolds of varying dimension in two dimensions this c 1 result has been improved to c 1 alpha by weiss invent math 138 23 50 1999 in this paper we prove that for n 2 singular points are locally contained in a c 2 curve in higher dimension n ge 3 we show that the same result holds with c 1 1 manifolds or with countably many c 2 manifolds up to the presence of some anomalous points of higher codimension in addition we prove that the higher dimensional stratum is always contained in a c 1 alpha manifold thus extending to every dimension the result in weiss 1999 we note that in terms of density decay estimates for the contact set our result is optimal in addition for n ge 3 we construct examples of very symmetric solutions exhibiting linear spaces of anomalous points proving that our bound on their hausdorff dimension is sharp

singularities of steady axisymmetric free surface flows with gravity we consider a steady axisymmetric solution of the euler equations describing the irrotational flow without swirl of an incompressible inviscid fluid acted on by gravity and with a free surface we analyze stagnation points as well as points on the axis of symmetry at points on the axis of symmetry that are not stagnation points constant velocity motion is the only blowup profile consistent with the invariant scaling of the equation this suggests the presence of downward pointing cusps at those points at stagnation points on the axis of symmetry the unique blowup profile consistent with the invariant scaling of the equation is the garabedian pointed bubble solution with water above air thus at stagnation points on the axis of symmetry with no water above the stagnation point the invariant scaling of the equation cannot be the right scaling a finer blowup analysis of the velocity field yields that in the case when the surface is described by an injective curve the velocity field scales almost like and is asymptotically given by with a nonzero constant c0 the last result relies on a frequency formula in combination with a concentration compactness result for the axially symmetric euler equations by delort while the concentration compactness result alone does not lead to strong convergence in general we prove the convergence to be strong in our application 2014 wiley periodicals inc

a new method for stabilization of networked control systems with random delays we consider the stabilization problem for a class of networked control systems in the discrete time domain with random delays the sensor to controller and controller to actuator delays are modeled as two markov chains and the resulting closed loop systems are jump linear systems with two modes the necessary and sufficient conditions on the existence of stabilizing controllers are established it is shown that state feedback gains are mode dependent an iterative linear matrix inequality lmi approach is employed to calculate the state feedback gains

the variable coefficient thin obstacle problem carleman inequalities abstract in this article we present a new strategy of addressing the variable coefficient thin obstacle problem our approach is based on a variable coefficient carleman estimate this yields semi continuity of the vanishing order lower and uniform upper growth bounds of solutions and sufficient compactness properties in order to carry out a blow up procedure moreover the carleman estimate implies the existence of homogeneous blow up limits along certain sequences and ultimately leads to an almost optimal regularity statement as it is a very robust tool it allows us to consider the problem in the setting of sobolev metrics i e working on the upper half ball b 1 r n 1 the coefficients are only w 1 p regular for some p n 1 these results provide the basis for our further analysis of the free boundary the optimal regularity of solutions and a first order asymptotic expansion of solutions at the regular free boundary which is carried out in a follow up article 21 in the framework of w 1 p p 2 n 1 regular coefficients and w 2 p p 2 n 1 regular non zero obstacles

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

regularity of the obstacle problem for a fractional power of the laplace operator given a function and s 0 1 we will study the solutions of the following obstacle problem u in r n s u 0i nr n s u x 0 for those x such that u x x lim x u x 0 we show that when is c 1 s or smoother the solution u is in the space c 1 for every s in the case where the contact set u is convex we prove the optimal regularity result u c 1 s when is only c 1 for a s we prove that our solution u is c 1 for every c 2006 wiley periodicals inc

obstacle problems for integro differential operators regularity of solutions and free boundaries we study the obstacle problem for integro differential operators of order 2s with s in 0 1 our main result establish that the free boundary is c 1 gamma and u in c 1 s near all regular points namely we prove the following dichotomy at all free boundary points x 0 in partial u varphi i either u x varphi x c d 1 s x o x x 0 1 s alpha for some c 0 ii or u x varphi x o x x 0 1 s alpha where d is the distance to the contact set u varphi moreover we show that the set of free boundary points x 0 satisfying i is open and that the free boundary is c 1 gamma and u in c 1 s near those points these results were only known for the fractional laplacian 2 and are completely new for more general integro differential operators the methods we develop here are purely nonlocal and do not rely on any monotonicity type formula for the operator thanks to this our techniques can be applied in the much more general context of fully nonlinear integro differential operators we establish similar regularity results for obstacle problems with convex operators

robust stability with structured real parameter perturbations this paper considers the problem of robust stabilization of a linear time invariant system subject to variations of a real parameter vector for a given controller the radius of the largest stability hypersphere in this parameter space is calculated this radius is a measure of the stability margin of the closed loop system the results developed are applicable to all systems where the closed loop characteristic polynomial coefficients are linear functions of the parameters of interest in particular this always occurs for single input multioutput or single output multiinput systems where the transfer function coefficients are linear or affine functions of the parameters many problems with transfer function coefficients which are nonlinear functions of physical parameters can be cast into this mathematical framework by suitable weighting and redefinition of functions of physical parameters as new parameters the largest stability hyperellipsoid for the case of weighted perturbations and a stability polytope in parameter space are also determined based on these calculations a design procedure is proposed to robustify a given stabilizing controller this algorithm iteratively enlarges the stability hypersphere or hyperellipsoid in parameter space and can be used to design a controller io stabilize a plant subject to given ranges of parameter excursions these results are illustrated by an example

output feedback stabilization of networked control systems with packet dropouts in this paper we discuss the modeling and control of a class of networked control systems ncss with packet dropouts for the cases that there may be packet dropouts in both the backward and the forward channels in the communication network and that the network induced delays are shorter than one sampling period the closed loop ncs is modeled as a discrete time switched system with four subsystems by using the asynchronous dynamical systems approach and the average dwell time method sufficient conditions for the exponential stability of the closed loop ncs are presented in terms of nonlinear matrix inequalities and the relation between the packet dropout rate and the stability of the closed loop ncs is explicitly established a procedure involving an iterative algorithm is proposed to design the observer based output feedback controllers lastly an illustrative example is given to demonstrate the effectiveness of the proposed results

mixed finite element method for a single phase quasi linear stefan problem with a forcing term in non divergence form abstract based on coordinate transformation a mixed finite element method is proposed and analyzed for a single phase quasi linear stefan problem with forcing term in non divergence form a better rate of convergence for the flux in l 2 norm is derived using h 1 galerkin mixed method in one space dimension

some new monotonicity formulas and the singular set in the lower dimensional obstacle problem we construct two new one parameter families of monotonicity formulas to study the free boundary points in the lower dimensional obstacle problem the first one is a family of weiss type formulas geared for points of any given homogeneity and the second one is a family of monneau type formulas suited for the study of singular points we show the uniqueness and continuous dependence of the blowups at singular points of given homogeneity this allows to prove a structural theorem for the singular set our approach works both for zero and smooth non zero lower dimensional obstacles the study in the latter case is based on a generalization of almgren s frequency formula first established by caffarelli salsa and silvestre