brief paper a way to stabilize linear systems with delayed state a simple method is proposed for stabilizing linear systems with delayed state using linear feedback the method requires checking the negativity of a matrix containing two free parameters and solving a matrix lyapunov equation with these parameters a known stabilizability criterion and a simple stability theorem for the open loop system are obtained as special cases of the main result

control of an unstable reaction diffusion pde with long input delay abstract a smith predictor like design for compensation of arbitrarily long input delays is available for general controllable possibly unstable lti finite dimensional systems such a design has not been proposed previously for problems where the plant is a pde we present a design and stability analysis for a prototype problem where the plant is a reaction diffusion parabolic pde with boundary control the plant has an arbitrary number of unstable eigenvalues and arbitrarily long delay with an unbounded input operator the predictor based feedback design extends fairly routinely within the framework of infinite dimensional backstepping however the stability analysis contains interesting features that do not arise in predictor problems when the plant is an ode the unbounded character of the input operator requires that the stability be characterized in terms of the h 1 rather than the usual l 2 norm of the actuator state the analysis involves an interesting structure of interconnected pdes of parabolic and first order hyperbolic types where the feedback gain kernel for the undelayed problem becomes an initial condition in a pde arising in the compensator design for the problem with input delay space and time variables swap their roles in an interesting manner throughout the analysis

mixed discontinuous galerkin analysis of thermally nonlinear coupled problem abstract a stabilized mixed discontinuous galerkin smdg method based on brezzi hughes marini masud f brezzi t j r hughes l d marini a masud mixed discontnuous galerkin methods for darcy flow j sci comput 22 2005 119 145 is proposed to solve a thermally coupled nonlinear elliptic system modeling a large class of engineering problems a fixed point algorithm is adopted to solve the nonlinear systems convergence analysis and error estimates are presented for equal order linear or bilinear discontinuous lagrangian finite element interpolations for all fields numerical results are presented confirming the predicted convergence rates and illustrating the performance of the proposed formulation solving problems with globally stable and blowing up solutions

unified hybridization of discontinuous galerkin mixed and continuous galerkin methods for second order elliptic problems we introduce a unifying framework for hybridization of finite element methods for second order elliptic problems the methods fitting in the framework are a general class of mixed dual finite element methods including hybridized mixed continuous galerkin nonconforming and a new wide class of hybridizable discontinuous galerkin methods the distinctive feature of the methods in this framework is that the only globally coupled degrees of freedom are those of an approximation of the solution defined only on the boundaries of the elements since the associated matrix is sparse symmetric and positive definite these methods can be efficiently implemented moreover the framework allows in a single implementation the use of different methods in different elements or subdomains of the computational domain which are then automatically coupled finally the framework brings about a new point of view thanks to which it is possible to see how to devise novel methods displaying very localized and simple mortaring techniques as well as methods permitting an even further reduction of the number of globally coupled degrees of freedom

an observer of systems with delays in state variables the paper is concerned with the design of an observer of systems with delays in state variables and control it is shown on the basis of the finite spectrum assignment theory that if the system is spectrally observable there exists an observer which can estimate the state variables of the system as fast as desired a systematic design procedure of the observer is presented the advantage of the proposed method is that the observer is constructed without preliminary knowledge of the open loop spectrum in contrast with the design method based on the spectral decomposition

formulas on preview and delayed h infty control a generalized hinfin control problem which covers preview and delayed control strategies is discussed based on a state space approach by introducing a hamiltonian matrix which is associated with a delay free generalized plant the analytic solution to the corresponding operator riccati equation is newly established based on the result obtained here the hinfin control problem is solved and for typical control problems e g hinfin and linear quadratic lq control for multiple input delay systems hinfin preview control some interpretations are provided on the resulting control system

robust guaranteed cost control for uncertain linear differential systems of neutral type in this paper the robust guaranteed cost control problem for a class of uncertain linear differential systems of neutral type with a given quadratic cost functions is investigated the uncertainty is assumed to be norm bounded and time varying nonlinear the problem is to design a state feedback control laws such that the closed loop system is robustly stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay a criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the lyapunov method a parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities a numerical example is given to illustrate the proposed method

on the existence of finite dimensional compensators for retarded and neutral systems in this paper we study a large class of neutral systems containing the class of retarded systems a necessary and sufficient condition is given for the existence of a finite dimensional compensator achieving exponential stability

time stepping along characteristics with incomplete iteration for a galerkin approximation of miscible displacement in porous media miscible displacement of one incompressible fluid by another in a porous medium is modeled by a nonlinear coupled system of two partial differential equations the pressure equation is elliptic while the concentration equation is parabolic but normally convection dominated a sequential backward difference time stepping scheme is defined it approximates the pressure by a standard galerkin procedure and the concentration by a combination of a galerkin method and the method of characteristics optimal convergence rates in l 2 and h 1 are demonstrated for this scheme and for a modified version in which the algebraic equations at each time step are solved approximately by a limited number of preconditioned conjugate gradient iterations time stepping along the characteristics of the hyperbolic part of the concentration equation is shown to result in smaller time truncation errors than those of standard methods numerical results published elsewhere have confirmed that larger time steps are appropriate

central limit theorems for elliptic curves and modular forms with smooth weight functions abstract in 11 the second and third named authors established a central limit theorem for the error term in the sato tate law for families of modular forms this method was adapted to families of elliptic curves in 3 by the first and second named authors in this context a central limit theorem was established only under a strong hypothesis going beyond the riemann hypothesis in the present paper we consider a smoothed version of the sato tate conjecture which allows us to overcome several limitations in particular for the smoothed version we are able to establish a central limit theorem for much smaller families of modular forms and we succeed in proving a theorem of this type for families of elliptic curves under the riemann hypothesis for l functions associated to hecke eigenforms for the full modular group

cross term forwarding for systems with time delay this paper presents a lyapunov based control design method for nonlinear systems with time delay the key step is construction of a composite lyapunov functionalv for a stable cascade this functional consists of lyapunov functionals for the subsystems and a cross term defined by an infinite integral the ldquol g v typerdquo control law is then employed to achieve global asymptotic stability the design procedure can be applied recursively to stabilize complex feedforward structures when applied to a linear cascade it gives a formula for the control law even if some parts of the system can only be stabilized through channels with multiple non commensurate or distributed delays

on the design of observer based controller of linear neutral delay differential systems in this note the observer based control problem for a class of linear delay differential systems of neutral type is investigated using the lyapunov method a criterion for asymptotic stability is derived in terms of matrix inequalities which solved by convex optimization algorithms a numerical example is given to illustrate the proposed method

the sato tate distribution in thin parametric families of elliptic curves we obtain new results concerning the sato tate conjecture on the distribution of frobenius traces over single and double parametric families of elliptic curves we consider these curves for values of parameters having prescribed arithmetic structure product sets geometric progressions and most significantly prime numbers in particular some families are much thinner than the ones previously studied

paper linear optimal control of systems with state and control variable delays in this paper we announce a new rigorous state space formulation for systems with delays in state and control variables this is used to solve the linear quadratic optimal control problem over both finite and infinite time horizons in each case abstract operational riccati equations are derived to characterize the feedback gains this paper extends recent results of vinter and kwong

a combined mixed and discontinuous galerkin method for compressible miscible displacement problem in porous media in this paper we present a numerical scheme for solving the coupled system of compressible miscible displacement problem in porous media the flow equation is solved by the mixed finite element method and the transport equation is approximated by a discontinuous galerkin method the scheme is continuous in time and a priori hp error estimates is presented

sums of euler products and statistics of elliptic curves we present several results related to statistics for elliptic curves over a finite field mathbb f p as corollaries of a general theorem about averages of euler products that we demonstrate in this general framework we can reprove known results such as the average lang trotter conjecture the average koblitz conjecture and the vertical sato tate conjecture even for very short intervals not accessible by previous methods we also compute statistics for new questions such as the problem of amicable pairs and aliquot cycles first introduced by silverman and stange our technique is rather flexible and should be easily applicable to a wide range of similar problems the starting point of our results is a theorem of gekeler which gives a reinterpretation of deuring s theorem in terms of an euler product involving random matrices thus making a direct connection between the conjectural horizontal distributions and the vertical distributions our main technical result then shows that under certain conditions a weighted average of euler products is asymptotic to the euler product of the average factors

feedback controllers for a wind tunnel model involving a delay analytical design and numerical simulation an application of a finite spectrum assignment method for time delay systems to a feedback control of mach number in a wind tunnel is presented the linearized model of mach number control is a system of three state equations with a delay in one of the state variables the proposed feedback is a linear combination of state variables and weighted integrals of some of the state variables over a period equal to time delay the spectrum of the closed loop system is finite and consists of three eigenvalues that can be placed arbitrarily four possible variants of the feedback control law are presented the calculation of feedback coefficients is very simple which makes it possible to update the controller s parameters on line with the changes of the operating point an extensive numerical simulation of the system dynamics and the feedback controllers was done and led to several conclusions in particular a very good settling time under problem constraints has been obtained and several nice features of the proposed feedback controller have been demonstrated

linear systems with commensurate time delays stability and stabilization independent of delay notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays constructive methods for determining a stabilizing feedback are also presented the last part of the paper deals with a standard type of observer and regulator with the requirement that the closed loop system be stable independent of delay

the sato tate conjecture on average for small angles we obtain average results on the sato tate conjecture for elliptic curves for small angles

linear quadratic optimal control of hereditary differential systems infinite dimensional riccati equations and numerical approximations recent theory of infinite dimensional riccati equations is applied to the linear quadratic optimal control problem for hereditary differential systems and it is shown that for most such problems the operator solutions of the riccati equations are of trace class i e nuclear with special attention to trace norm convergence an abstract approximation theory is developed and applied to a particular approximation scheme numerical examples are given problems on both finite and infinite time intervals are studied for both the hereditary system and the approximating systems in the infinite time problem characteristic equations are derived for the closed loop eigenvalues and formulas for the corresponding eigenvectors are given

a combined discontinuous galerkin finite element method for miscible displacement problem a new combined method is constructed for solving incompressible miscible displacement in porous media in this procedure a hybrid mixed element method is constructed for the pressure and velocity equation while a symmetric discontinuous galerkin finite element method is proposed for the concentration equation the introduction of these two numerical methods not only makes the coefficient matrixes symmetric positive definite but also conserves the local mass balance the stability and consistency of the method are analyzed and the optimal error estimate in l l 2 for velocity and concentration and the super convergence in l h 1 for pressure are derived finally some numerical results are presented

asymptotic stability of impulsive control neutral type systems in this paper we consider a delay control system of neutral type applying lyapunov functions and razumikhin technique combining with an impulsive feedback control we established some criteria for asymptotic stability of the system an example is also discussed to illustrate the main results we show that by means of appropriate impulsive perturbations we can control the stability behaviour of the system

vibrational control of linear time lag systems with arbitrarily large but bounded delays it is shown that vibrational stabilization can be effective for linear systems with large bounded delays theorems are given that define the procedures for the search of the stabilizing vibrations robust oscillatory stabilization insensitive to the delay size is also shown to take place for some classes of systems

on the stabilization of linear neutral delay differential systems feedback feedforward stabilizers for linear neutral delay differential systems are proposed explicit conditions under which an adequate compensator yields a desired closed loop characteristic polynomial are given the relation between realizability properties such as causality of the compensator and structural properties of the system are also described an example is provided to illustrate the design technique

stabilization of time delay systems using finite dimensional compensators for linear time invariant systems with one or more noncommensurate time delays necessary and sufficient conditions are given for the existence of a finite dimensional stabilizing feedback compensator in particular it is shown that a stabilizable time delay system can always be stabilized using a finite dimensional compensator the problem of explicitly constructing finite dimensional stabilizing compensators is also considered

delay dependent guaranteed cost stabilization criterion for neutral delay differential systems matrix inequality approach abstract in this paper we address the problem of the guaranteed cost stabilization for a class of neutral delay differential systems with a given quadratic cost function based on the lyapunov method delay dependent criteria which are expressed in terms of matrix inequalities are proposed to guarantee the asymptotic stability of the system the matrix inequalities can be easily solved by various efficient optimization algorithms

memoryless stabilization of linear delay differential systems sufficient conditions for memoryless feedback stabilization of linear time invariant delay differential systems are derived for both constant and time dependent delays

feedback stabilization of linear autonomous time lag systems a stabilization theory which employs well established finite dimensional control system tools is developed for the stabilization of linear autonomous time lag systems the main ideas include 1 a set whose elements are matrices each of which is a left zero of the system characteristic quasi polynomial matrix and 2 a linear transformation which reduces the delay system to a delay free system whose state matrix is a direct sum of n elements of the matrix set where n is some positive integer from the definition of this matrix set it is shown that each of its elements inherits its spectrum from that of the delay system so that by design the system unstable poles may be embedded in the spectrum of the delay free system under the assumption of spectral stabilizability it is then shown how to obtain a stabilizing feedback control law on the basis of the delay free system numerical examples are presented to confirm the theory

an internal state decomposition approach to a discrete time h2 control problem with irrational input non minimum phase property abstract an internal state decomposition approach to a class of discrete time h 2 control problems with irrational non minimum phase property at the control input is proposed this is a generalization of the state variable transformation to derive the discrete time smith predictor for a single input delay system the h 2 optimal controller is derived using the orthogonality principle in h 2 space as a direct consequence of the state decomposition the characterization of the optimal cost by the previous and alternative truncation operators is also discussed

a coupling of hybrid mixed and continuous galerkin finite element methods for poroelasticity abstract a coupling finite element method for biot s model in poroelasticity is considered the method is based on a coupling of a hybrid mixed finite element method for the pressure and velocity of the fluid phase with a continuous galerkin finite element method for the displacement of the solid phase the subproblem for pressure and darcy velocity are solved at element level and these variables are eliminated in favor of the lagrange multiplier identified as pressure trace at the element interfaces the method is consistent and locally mass conservative by introducing the energy norm we can obtain the stability of this system the optimal error estimates are derived for both semi discrete and fully discrete schemes finally numerical results illustrate the accuracy of the method

input delay compensation of linear systems with both state and input delays by nested prediction abstract in this paper we consider the input delay compensation of linear systems with both state and input delays under the condition that the open loop time delay systems in the absence of input delay can be stabilized by delayed state feedback a nested predictor based approach is established to predict the future states so that the delays in the input are compensated it is shown that the compensated closed loop system in the presence of input delay possesses the same characteristic equation as the closed loop system in the absence of input delay the proposed approach can be generalized to general linear systems having multiple state delays and or multiple input delays to implement the nested predictor based controllers by applying numerical integration approaches an augmented nested predictor based approach by adding input filters is proposed two numerical examples are worked out to show the effectiveness of the proposed approach

on stability independent of delay for linear systems a new criterion for asymptotic stability of solutions of certain linear differential difference equations independent of the delay duration is given in terms of solutions of a complex lyapunov matrix equation

adaptive sinusoidal disturbance cancellation for unknown lti systems despite input delay solutions exist for the problems of canceling sinusoidal disturbances and compensating input delays in this paper two problems are considered simultaneously and an adaptive controller is designed to cancel unknown sinusoidal disturbances forcing an unknown linear time invariant system in controllable canonical form despite input delay the design is based on three steps 1 parametrization of the sinusoidal disturbance as the output of a known feedback system with an unknown output vector that depends on unknown disturbance parameters 2 representation of the delay as a transport pde 3 design of the adaptive controller by using the backstepping boundary control technique for pdes it is proven that the equilibrium of the closed loop system is stable and the state of the considered system converges to zero as t with perfect disturbance estimation the effectiveness of the controller is illustrated with a simulation example of a second order system

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

forwarding backstepping and finite spectrum assignment for time delay systems the nonlinear control ideas and results of forwarding and backstepping have been recently extended to systems with time delay in this paper we discuss how to apply these tools to design robust controls for linear delay systems we first show that the integral cross term forwarding produces a feedback law that achieves finite spectrum of the closed loop system combining it with backstepping provides a structured design method for a large class of systems with time delay robustness of the controller to uncertainties including uncertain time delay is illustrated by an example

output feedback stabilization of delay systems via generalization of the transformation method the left characteristic matrix equation l c m e of a delay system has been employed to develop a state feedback stabilization theory for delay systems analogously the right characteristic matrix equation r c m e has led to the development of an observer theory for this class of systems the characteristic matrix equation approach however only permits the relocation of integral multiples of n poles where n represents the system order this restriction is removed in this work through a generalization of the l c m e and r c m e in a manner which permits the stabilization of an arbitrary but finite number of unstable modes the resulting state feedback controller and state estimator permit the output feedback stabilization of the most general linear autonomous delay system under the minimal assumptions of spectral stabilizability and detectability

feedback stabilization of neutral systems via the transformation technique within the class of delay systems a neutral system may be distinguished by the possible presence of a neutral root chain an infinite chain of eigenvalues in a vertical strip of the complex plane assuming that such a neutral root chain if it exists is stable this work shows how our method of transformation can be extended to obtain feedback controllers for this class of neutral systems

guaranteed cost stabilization of neutral differential systems with parametric uncertainty in this paper we address the problem of the guaranteed cost stabilization for a class of neutral systems with parametric uncertainties and a given quadratic cost function the parametric uncertainties are real time varying norm bounded and state delay is a constant the problem is to design the state feedback control laws such that the closed loop system is asymptotically stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainty and delay two criteria for the existence of such controllers are derived based on the matrix inequality approach combined with the lyapunov method the developed guaranteed cost controllers can be synthesized in terms of the feasible solutions to the certain matrix inequalities

stability analysis and observer design for neutral delay systems this paper deals with the observer design problem for a class of linear delay systems of the neutral type the problem addressed is that of designing a full order observer that guarantees the exponential stability of the error dynamic system an effective algebraic matrix equation approach is developed to solve this problem in particular both the observer analysis and design problems are investigated by using the singular value decomposition technique and the generalized inverse theory sufficient conditions for a neutral type delay system to be exponentially stable are first established then an explicit expression of the desired observers is derived in terms of some free parameters furthermore an illustrative example is used to demonstrate the validity of the proposed design procedure

convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics abstract a nonlinear system of two coupled partial differential equations models miscible displacement of one incompressible fluid by another in a porous medium conservation of mass for the mixture leads to an elliptic equation for pressure and conservation for the displacing fluid yields a convectiondominated parabolic equation for the concentration of that fluid a sequential implicit time stepping procedure is defined in which the pressure and darcy velocity of the mixture are approximated simultaneously by a mixed finite element method and the concentration is approximated by a combination of a galerkin finite element method and the method of characteristics optimal order convergence in l2 is proved time truncation errors of standard procedures are reduced by time stepping along the characteristics of the hyperbolic part of the concentration equation temporal and spatial errors are lessened by direct computation of the velocity in the mixed method as opposed to differentiation of the pressure several extensions of these results are outlined