an inverse problem for a semi linear elliptic equation in riemannian geometries abstract we study the inverse problem of unique recovery of a complex valued scalar function v m c c defined over a smooth compact riemannian manifold m g with smooth boundary given the dirichlet to neumann map in a suitable sense for the elliptic semi linear equation g u v x u 0 we show that uniqueness holds for a large class of non linearities when the manifold is conformally transversally anisotropic the proof is constructive and is based on a multiple fold linearization of the semi linear equation near complex geometric optic solutions for the linearized operator and the resulting non linear interactions these interactions result in the study of a weighted integral transform along geodesics that we call the jacobi weighted ray transform

stability and stabilization of switched linear time invariant systems with saddle points and switching delays this paper addresses global asymptotic stability gas and stabilization issues of switched linear time invariant lti systems with saddle points and time varying switching delays firstly two criteria of gas are proposed for such switched systems with all subsystems sharing a common unique saddle point under arbitrary periodic quasi periodic switching paths psp qsp secondly by using our stability results we design global asymptotic stabilizing controls gasc periodic quasi periodic stabilizing switching paths pssp qssp and an algorithm of gasc and pssp qssp for the switched systems finally we present a numerical example of a switching multi agent system to illustrate the effectiveness and practicality of our new results

the calderon problem with partial data in this paper we improve an earlier result by bukhgeim and uhlmann 1 by showing that in dimension n 3 the knowledge of the cauchy data for the schr nodinger equation measured on possibly very small subsets of the boundary determines uniquely the potential we follow the general strategy of 1 but use a richer set of solutions to the dirichlet problem this implies a similar result for the problem of electrical impedance tomography which consists in determining the conductivity of a body by making voltage and current measurements at the boundary

co positive lyapunov functions for the stabilization of positive switched systems in this paper exponential stabilizability of continuous time positive switched systems is investigated for two dimensional systems exponential stabilizability by means of a switching control law can be achieved if and only if there exists a hurwitz convex combination of the metzler system matrices in the higher dimensional case it is shown by means of an example that the existence of a hurwitz convex combination is only sufficient for exponential stabilizability and that such a combination can be found if and only if there exists a smooth positively homogeneous and co positive control lyapunov function for the system in the general case exponential stabilizability ensures the existence of a concave positively homogeneous and co positive control lyapunov function but this is not always smooth the results obtained in the first part of the paper are exploited to characterize exponential stabilizability of positive switched systems with delays and to provide a description of all the switched equilibrium points of an affine positive switched system

rapid stabilisation of multi dimensional schrodinger equation with the internal delay control abstractin this paper we are concerned with the controller design for multi dimensional schrodinger equation with the internal delay control we introduce a new approach to design the feedback con

inverse problems for lorentzian manifolds and non linear hyperbolic equations we study two inverse problems on a globally hyperbolic lorentzian manifold m g the problems are 1 passive observations in spacetime consider observations in an open set v subset m the light observation set corresponding to a point source at q in m is the intersection of v and the light cone emanating from the point q let w subset m be an unknown open relatively compact set we show that under natural causality conditions the family of light observation sets corresponding to point sources at points q in w determine uniquely the conformal type of w 2 active measurements in spacetime we develop a new method for inverse problems for non linear hyperbolic equations that utilizes the non linearity as a tool this enables us to solve inverse problems for non linear equations for which the corresponding problems for linear equations are still unsolved to illustrate this method we solve an inverse problem for semilinear wave equations with quadratic non linearities we assume that we are given the neighborhood v of the time like path mu and the source to solution operator that maps the source supported on v to the restriction of the solution of the wave equation to v when m is 4 dimensional we show that these data determine the topological differentiable and conformal structures of the spacetime in the maximal set where waves can propagate from mu and return back to mu

asynchronously switched control of discrete impulsive switched systems with time delays this paper is concerned with the stabilization problem for a class of uncertain discrete impulsive switched delay systems under asynchronous switching the so called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous by using the average dwell time adt approach sufficient conditions for the existence of an asynchronously switched controller is derived such that the resulting closed loop system is exponentially stable the desired controller gains and the admissible switching signals are obtained in terms of a set of matrix inequalities a numerical example is given to illustrate the effectiveness of the proposed method

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

output feedback control of markovian jump repeated scalar nonlinear systems this paper is concerned with the induced l2 dynamic output feedback controller dofc design problem for discrete time markovian jump repeated scalar nonlinear systems by employing both the switching sequence dependent lyapunov function approach and the positive definite diagonally dominant lyapunov function technique a sufficient condition is first established which guarantees the underlying system to be stochastically stable with an induced l2 disturbance attenuation performance then the desired full or reduced order dofcs are designed by using projection approach cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem finally a numerical example is presented to show the effectiveness of the proposed methods

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks in this paper we consider in a bounded and smooth domain the wave equation with a delay term in the boundary condition we also consider the wave equation with a delayed velocity term and mixed dirichlet neumann boundary condition in both cases under suitable assumptions we prove exponential stability of the solution these results are obtained by introducing suitable energies and by using some observability inequalities if one of the above assumptions is not satisfied some instability results are also given by constructing some sequences of delays for which the energy of some solutions does not tend to zero

two examples of ill posedness with respect to small time delays in stabilized elastic systems two examples of elastic control systems that are uniformly stabilized by feedback controls on their boundaries for which divergence rates can be obtained when small time delays are introduced into their feedbacks are presented

stabilization of an euler bernoulli beam with input delay in the boundary control abstract in this paper we consider a cantilever euler bernoulli beam with controller delay suppose that the output of the boundary controller is of the form u t u t where u t is the controller input it is well known that a system with a collocated feedback control law is exponentially stable if 0 and it is unstable with the same control law when 0 in the present paper we shall design a dynamic controller that makes the system stabilize exponentially for any and 0 furthermore we discuss the stability of the system for

riesz basis property of serially connected timoshenko beams in this paper we study the riesz basis property of serially connected timoshenko beams with joint and boundary feedback controls suppose that the left end of the whole beam is clamped and the right end is free at intermediate nodes the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be discontinuous the collocated velocity feedback of the beams at intermediate nodes and the right end are used to stabilize the system we prove that the operator determined by the closed loop system has compact resolvent and generates a c 0 semigroup in an appropriate hilbert space we also show that there is a sequence of the generalized eigenvectors of the operator that forms a riesz basis with parentheses hence the spectrum determined growth condition holds therefore if the imaginary axis is not an asymptote of the spectrum then the closed loop system is exponentially stable finally we give a conclusion remark to explain that our result can be applied not

delay dependent exponential stabilization of positive 2d switched state delayed systems in the roesser model this paper deals with the controller synthesis for a class of positive two dimensional 2d switched delay systems described by the roesser model this kind of systems has the property that the states take nonnegative values whenever the initial boundaries are nonnegative some delay dependent sufficient conditions for the exponential stability of positive 2d switched systems with state delays are given furthermore the design of positive state feedback controller under which the resulting closed loop system meets the requirements of positivity and exponential stability is presented in terms of linear matrix inequalities lmis an example is included to illustrate the effectiveness of the proposed approach

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

distributed control of a class of flexible mechanical systems with global constraint in this paper the constrained problem is investigated for both flexible string model and euler bernoulli beam model with the tip payload based on an infinite dimensional generalisation of a distributed control method the control objectives are to develop the control law so that the motion of flexible mechanical systems can track a desired reference signal and ensure that the string or beam remain in a constrained space we prove that with the proposed control the tracking error is exponentially stable without violation of the constraint the proof of convergence is based on an integral barrier lyapunov function iblf and extensive simulations are provided to illustrate the performance of the control system

controllability and stability of a second order hyperbolic system with collocated sensor actuator a second order hyperbolic system with collocated sensor actuator is considered the semigroup generation is shown for the closed loop system under the feedback of a generic unbounded observation operator the equivalence between the exponential stability of the closed loop system and exact controllability of the open loop system is established in the general framework of well posed linear systems finally the conditions are weakened for the diagonal semigroups with finite dimensional inputs example of beam equation is presented to display the application

determining anisotropic real analytic conductivities by boundary measurements if an electrical potential is applied to the surface of a solid body the current flux across the surface depends on the conductivity in the interior of the body we want to consider the inverse problem of determining the conductivity by these boundary measurements

brief paper stability of switched positive linear systems with average dwell time switching in this paper the stability analysis problem for a class of switched positive linear systems splss with average dwell time switching is investigated a multiple linear copositive lyapunov function mlclf is first introduced by which the sufficient stability criteria in terms of a set of linear matrix inequalities are given for the underlying systems in both continuous time and discrete time contexts the stability results for the splss under arbitrary switching which have been previously studied in the literature can be easily obtained by reducing mlclf to the common linear copositive lyapunov function used for the system under arbitrary switching those systems finally a numerical example is given to show the effectiveness and advantages of the proposed techniques

dynamic feedback control and exponential stabilization of a compound system abstract we studied the exponential stabilization problem of a compounded system composed of a flow equation and an euler bernoulli beam which is equivalent to a cantilever euler bernoulli beam with a delay controller we designed a dynamic feedback controller that stabilizes exponentially the system provided that the eigenvalues of the free system are not the zeros of controller in this paper we described the design detail of the dynamic feedback controller and proved its stabilization property

not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks we present two examples of hyperbolic partial differential equations which are stabilized by boundary feedback controls and then destabilized by small delays in these controls we show that in a general case when the controls are distributed stabilized hyperbolic systems possess nontrivial periodic solutions if small time delays are introduced into their feedbacks we also indicate by means of an example that the general case of this phenomenon is harder to demonstrate for boundary control problems

rapid stabilisation of an euler bernoulli beam with the internal delay control in this paper we are concerned with rapid stabilisation of an euler bernoulli beam with internal delayed control herein we introduce a new approach of the feedback control design from the system

inverse problems in quasilinear anisotropic media we consider the question of whether one can determine the anisotropic quasilinear conductivity of a medium by making voltage and current measurements at the boundary we prove that all the known results for the linear case also hold in the quasilinear case

control of planar networks of timoshenko beams the present study is concerned with the questions of controllability and stabilizability of planar networks of vibrating beams consisting of several timoshenko beams connected to each other by rigid joints at all interior nodes of the system some of the exterior nodes are either clamped or free controls may be applied at the remaining exterior nodes and or at interior joints in the form of forces and or bending moments for a given configuration is it at all possible to drive all vibrations to the rest configuration in a given finite time interval by means of controls acting at some or all of the available nonclamped nodes of the network and if so where should such controls be placed alternatively a control objective is to construct energy absorbing boundary feedback controls that will guarantee uniform energy decay it is demonstrated that if such a network does not contain closed loops and if at most one of the exterior nodes is clamped exact controllability and uniform stabilizability of the

the inverse problem for the local geodesic ray transform under a convexity assumption on the boundary we solve a local inverse problem namely we show that the geodesic x ray transform can be inverted locally in a stable manner one even has a reconstruction formula we also show that under an assumption on the existence of a global foliation by strictly convex hypersurfaces the geodesic x ray transform is globally injective in addition we prove stability estimates and propose a layer stripping type algorithm for reconstruction

stabilization of planar switched systems this paper considers the problem of stabilization of single input planar switched systems we assume the switching law is observable a formula is presented which provides a necessary and sufficient condition for the system to be quadratically stabilizable a set of linear inequalities are given to describe the set of all quadratic lyapunov functions the solvability and the control design technique are clearly described in a straightforward computation algorithm

stability and l2 gain analysis for switched delay systems a delay dependent method in this paper we study stability and l 2 gain for a class of switched systems with time varying delays sufficient conditions for exponential stability and weighted l 2 gain are developed for a class of switching signals with average dwell time these conditions are delay dependent and are given in the form of linear matrix inequalities lmis as a special case of such switching signals we can obtain exponential stability and normal l 2 gain under arbitrary switching signals the state decay estimate is explicitly given two examples illustrate the effectiveness and applicability of the proposed method

stabilisation of timoshenko beam system with delay in the boundary control in this paper we consider the exponential stabilisation problem of a timoshenko beam with delay in boundary control suppose that the controller outputs of the forms 1u1 t 1u1 t and 2u2 t 2u2 t where u1 t and u2 t are the inputs of boundary controllers in the past most of the stabilisation results are required j j 0 j 1 2 in the present paper we shall give a new dynamic feedback control law that makes the system exponential stabilisation 0 provided that j j j 1 2 the exponential stabilisation result is proved via test of exact observability of the system

non dissipative boundary feedback for rayleigh and timoshenko beams abstract we show that a non dissipative feedback that has been shown in the literature to exponentially stabilize an euler bernoulli beam makes a rayleigh beam and a timoshenko beam unstable

dissipativity based sliding mode control of switched stochastic systems this technical brief is concerned with dissipativity analysis and dissipativity based sliding mode control smc of continuous time switched stochastic systems firstly a sufficient condition is proposed to guarantee the mean square exponential stability and strict dissipativity for the switched stochastic system then an integral type sliding surface function is designed for establishing a sliding mode dynamics which can be formulated by a switched stochastic system with an external disturbance uncertainty dissipativity analysis and synthesis are both investigated for the sliding mode dynamics and consequently sufficient conditions are derived which pave the way for solving the dissipativity analysis and control problems moreover a smc law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time finally the efficiency of the theoretical findings is demonstrated by an illustrative example

limiting carleman weights and anisotropic inverse problems in this article we consider the anisotropic calderon problem and related inverse problems the approach is based on limiting carleman weights introduced in kenig et al ann math 165 567 591 2007 in the euclidean case we characterize those riemannian manifolds which admit limiting carleman weights and give a complex geometrical optics construction for a class of such manifolds this is used to prove uniqueness results for anisotropic inverse problems via the attenuated geodesic ray transform earlier results in dimension n 3 were restricted to real analytic metrics

the exponential stability region of timoshenko beam with interior delays and boundary damping abstractin this paper we investigate the exponential stability of a timoshenko beam with interior time delays and boundary damping at first we show that the system is well posed by the semigroup method next we construct an appropriate functional to study the exponential stability we transform the exponential stability into the solvability of inequality equations and then by analysing the relationship between delays parameters 1 2 and damping parameters 1 2 we describe the 1 2 region for which the system is exponentially stable

robust control on saturated markov jump systems with missing information in this paper a robust h controller is designed for saturated markov jump systems with uncertainties and time varying transition probabilities the time varying transition probability uncertainty is described as a polytope set stochastic stability is analyzed for the underlying systems by lyapunov function approach and a sufficient condition is derived to design controllers such that the resulting closed loop system is stochastically stable and a prescribed h performance is also achieved furthermore the attraction domain of this markov jump system is estimated and evaluated a simulation example is given to show the effectiveness of the developed techniques

model approximation for fuzzy switched systems with stochastic perturbation in this paper the model approximation problem is investigated for a takagi sugeno fuzzy switched system with stochastic disturbance for a high order considered system our attention is focused on the construction of a reduced order model which not only approximates the original system well with a hankel norm performance but translates it into a lower dimensional fuzzy switched system as well by using the average dwell time approach and the piecewise lyapunov function technique a sufficient condition is first proposed to guarantee the mean square exponential stability with a hankel norm error performance for the error system the model approximation is then converted into a convex optimization problem by using a linearization procedure finally simulations are provided to illustrate the effectiveness of the proposed theory

inverse spectral problems on hyperbolic manifolds and their applications to inverse boundary value problems in euclidean space we propose a new approach to solve the inverse boundary value problems in the euclidean space the idea consists of embedding the problem into hyperbolic manifolds and using their spectral properties as a by product one can discuss the reconstruction of local conformal deformation of the metric of hyperbolic manifolds from the spectral data at infinity we also propose a new spectral data observed from the cusp neighborhood at infinity

boundary control of a timoshenko beam system with input dead zone in this paper boundary control is designed for a timoshenko beam system with the input dead zone by the hamilton s principle the dynamics of the timoshenko beam system is represented by a distributed parameter model with two partial differential equations and four ordinary differential equations the bounded part is separated from the input dead zone and then forms the disturbance like term together with the boundary disturbance which finally acts on the timoshenko beam system boundary control based on the lyapunov s direct method is proposed to ensure the timoshenko beam converge into a small neighbourhood of zero where stability of the system is also analysed besides the existence and uniqueness of the solution of the timoshenko beam system are proved simulations are provided to reveal the applicability and effectiveness of the proposed control scheme

stochastic boundary control design for timoshenko beams with large motions abstract this paper considers modeling and boundary control of timoshenko beams with large motions under both deterministic and stochastic external loads the original nonlinear partial differential equations governing motion of the beams are derived and used in the control design the control design is based on the lyapunov direct method the proposed controllers guarantee globally practically k exponentially p stability of the beam motions at the reference state well posedness and stability are analyzed based on a lyapunov type theorem developed to study well posedness and stability for a class of stochastic evolution systems in hilbert space simulation results are included to illustrate the effectiveness of the proposed control design

a stability result of a timoshenko system with a delay term in the internal feedback abstract in this paper we consider a timoshenko system with a delay term in the feedback and prove a stability result the beam is clamped at the endpoints and has in addition to an internal damping a feedback with a delay under an appropriate assumption on the weights of the two feedbacks we prove the well posedness of the system and establish an exponential decay result for the case of equal speed wave propagation

stabilization of exact nonlinear timoshenko beams in space by boundary feedback abstract boundary feedback controllers are designed to stabilize timoshenko beams with large translational and rotational motions in space under external disturbances the exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design the designed controllers guarantee globally practically asymptotically and locally practically exponentially stability of the beam motions at the reference state the control design well posedness and stability analysis are based on various relationships between the earth fixed and body fixed coordinates sobolev embeddings and a lyapunov type theorem developed to study well posedness and stability for a class of evolution systems in hilbert space simulation results are included to illustrate the effectiveness of the proposed control design

stabilisation of timoshenko beam system with a tip payload under the unknown boundary external disturbances this paper is concerned with the boundary stabilisation of a timoshenko beam with a tip payload under the boundary external disturbances nonlinear feedback control laws are designed to reduce the effects of the external disturbances since the controlled system is nonlinear the well posedness of the nonlinear closed loop system is investigated using the theory of nonlinear maximal monotone operators and the variational principle in addition we show the exponential stability of the nonlinear controlled system using the lyapunov direct method in the end the numerical simulations are displayed to illustrate the effectiveness of the proposed boundary controls

global uniqueness for a two dimensional inverse boundary value problem we show that the coefficient y x of the elliptic equation vie qyvu 0 in a two dimensional domain is uniquely determined by the corresponding dirichlet to neumann map on the boundary and give a reconstruction pro

stabilization for switched stochastic neutral systems under asynchronous switching in this paper the mean square exponential stability of switched stochastic neutral systems with time varying delay under asynchronous switching is investigated a new lyapunov function dependent on the controllers switching signal is constructed which can counteract the difficulty of controller design to stabilize the system under asynchronous switching moreover the value of the lyapunov function is allowed to increase during mismatched periods based on the average dwell time approach a sufficient condition expressed by a set of linear matrix inequalities lmis is derived to guarantee the mean square exponential stability for the closed loop system and the controllers with asynchronous switching are designed finally a numerical example illustrates the effectiveness of the results

dynamic domain decomposition of optimal control problems for networks of strings and timoshenko beams we consider general networks of strings and or timoshenko beams we apply controls at boundary nodes of the network and want to minimize some cost function along part of the structure optimality systems for the entire structure are far too complex to compute in reasonable time in particular in real time applications one wants to reduce the size of the problem thus dynamic decomposition into its physical elements appears to be a natural approach we show how to iteratively decompose the global optimality system into a system related to a substructure then we interpret the local system as an optimality system corresponding to an optimal control problem for the substructure and finally we show convergence of the outer iteration

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

boundary feedback exponential stabilization of a timoshenko beam with both ends free in the present paper we consider the boundary feedback stabilization of a timoshenko beam with both ends free we propose boundary feedback control law that makes the closed loop system dissipative using asymptotic analysis techniques we give explicit asymptotic formula of eigenvalues of the closed loop system and prove the riesz basis property of eigenvectors and generalized eigenvectors by a detailed analysis of spectrum of the closed loop system we show that the closed system is exponentially stable

global uniqueness for a two dimensional semilinear elliptic inverse problem for a general class of nonlinear schrodinger equations au a x u 0 in a bounded planar domain 2 we show that the function a x u can be recovered from knowledge of the corresponding dirichlet to neumann map on the boundary dq

an example on the effect of time delays in boundary feedback stabilization of wave equations this note is concerned with the erect of time delays in boundary feedback stabilization schemes for wave equations the question to be addressed is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays

exponential stability of descriptor systems with large delay period based on a switching method this paper addresses the problem of exponential stability for a class of descriptor systems with interval time varying delays the time varying delays contain a large delay period ldp which is often present in practical control systems such descriptor system with ldp has been modeled as a switched descriptor system with delay which may include an unstable subsystem caused by large delay bound by adopting the switching technique and constructing a novel lyapunov krasovskii functional stability criteria are proposed under the restriction frequency and the rate of ldp to ensure that the descriptor system is regular impulse free and exponentially stable finally an integrated circuit example and a numerical simulation are given to illustrate the effectiveness and applicability of the proposed method