towards a matrix theory for unbounded operator matrices sur l espace produit r l 2 r on considere l operateur 7b a a 0 ou d d dx est defini sur d a w 1 r 0 est la mesure de dirac en 0 c l 2 r est un operateur de r dans l 2 r et 7b a a un domaine d 7b a r w 1 r on introduit une fonction caracteristique non commutative donnant une facon efficace pour calculer le spectre de 7b a on obtient des resultats sur la generation de semi groupes par des matrices operateur

controllability and observability of systems of linear delay differential equations via the matrix lambert w function during recent decades controllability and observability of linear time delay systems have been studied including various definitions and corresponding criteria however the lack of an analytical solution approach has limited the applicability of the existing theory recently the solution to systems of linear delay differential equations has been derived in the form of an infinite series of modes written in terms of the matrix lambert w function the solution form enables one to put the results for point wise controllability and observability of systems of delay differential equations to practical use we derive the criteria for point wise controllability and observability obtain the analytical expressions for their gramians in terms of the parameters of the system and develop a method to approximate them for the first time using the matrix lambert w function based solution form

constrained polynomial approximation of quadric surfaces quadric surfaces are one of the geometric elements most commonly used for shape expression and mechanical accessory cartography in three dimensions since quadric surfaces cannot be represented exactly using polynomials it is not suitable to deal with most problems encountered in engineering application for this reason we present a new method for polynomial approximation of quadric surfaces the approximation tensor product surface obtained by the proposed method has no limit on its degree i e arbitrary degree it has c k h k h 0 1 2 continuity at four corners with the original quadric surface meanwhile the method has an optimal approximation result in the l2 norm and it can also be applied to piecewise continuous quadric surface patches or a quadric surface patch combined with surface subdivision scheme and the resulting piecewise approximation patches are globally c0 continuous finally error estimation for the approximation method is given and numerical examples are presented to validate the feasibility and effectiveness of our method

a new approach to state observation of nonlinear systems with delayed output the article presents a new approach for the construction of a state observer for nonlinear systems when the output measurements are available for computations after a nonnegligible time delay the proposed observer consists of a chain of observation algorithms reconstructing the system state at different delayed time instants chain observer conditions are given for ensuring global exponential convergence to zero of the observation error for any given delay in the measurements the implementation of the observer is simple and computer simulations demonstrate its effectiveness

robust stability analysis of linear time delay systems by lambert w function some extreme point results robust stability conditions are derived for linear time delay systems using lambert w function the characteristic quasi polynomials of the systems are assumed to be factorized it is proven that if uncertainties in the coefficients of the quasi polynomial are set in appropriate regions in the complex plane we can enjoy extreme point results finite number of stability checks at some points of the boarder of the regions suffice the strength of lambert w function approach lies in the fact that the function is implemented on some standard software packages such as mathematica maple or matlab which afford to compute the function value very easily the above two points make the stability test for the class of uncertain time delay systems quite practical

approximation of circular arcs and offset curves by bezier curves of high degree in this paper we present an exact error analysis for circle approximation by bezier curve the approximation method is a special case of floater s conic approximation method comput aided geom design 8 1991 135 using this we propose an approximation method of the offset curve of given plane bezier curve by bezier curve of the same degree

control of systems with i o delay via reduction to a one block problem in this paper the standard four block h sup spl infin control problem for systems with a single delay in the feedback loop is studied a simple procedure of the reduction of the problem to an equivalent one block problem having particularly simple structure is proposed the one block problem is then solved by the j spectral factorization approach resulting in the so called dead time compensator dtc form of the controller the advantages of the proposed procedure are its simplicity intuitively clear derivation of the dtc form of the h sup spl infin controller and extensibility to the multiple delay case

finite spectrum assignment of unstable time delay systems with a safe implementation the instability mechanisms related to the implementation of distributed delay controllers in the context of finite spectrum assignment were studied in detail in the past few years in this note we introduce a distributed delay control law that assigns a finite closed loop spectrum and whose implementation with a sum of point wise delays is safe this property is obtained by implicitly including a low pass filter in the control loop this leads to a closed loop characteristic quasipolynomial of retarded type and not one of neutral type which was shown to be a cause of instability in previous schemes

truncated predictor feedback control for exponentially unstable linear systems with time varying input delay abstract the stabilization of exponentially unstable linear systems with time varying input delay is considered in this paper we extend the truncated predictor feedback tpf design method which was recently developed for systems with all poles on the closed left half plane to be applicable to exponentially unstable linear systems assuming that the time varying delay is known and bounded the design approach of a time varying state feedback controller is developed based on the solution of a parametric lyapunov equation an explicit condition is derived for which the stability of the closed loop system with the proposed controller is guaranteed it is shown that for the stability of the closed loop system the maximum allowable time delay in the input is inversely proportional to the sum of the unstable poles in the plant the effectiveness of the proposed method is demonstrated through numerical examples

periodic solutions for some nonautonomous semilinear boundary evolution equations abstract in this work we study the massera problem for the existence of a periodic mild solution of a class of nonautonomous semilinear boundary evolution equations 0 1 x t a m t x t f t x t t 0 l t x t t x t g t x t t 0 x 0 x 0 first we prove the existence of a periodic solution for nonhomogeneous boundary evolution equations under the existence of a bounded solution on the right half real line next by using a fixed point theorem we investigate the existence of periodic solutions in the semilinear case we end with an application to a periodic heat equation with semilinear boundary conditions

on nonautonomous functional differential equations abstract in this paper we prove a theorem on boundary perturbation of nonautonomous cauchy problems and then apply this result to show the existence and uniqueness of classical solutions of the nonautonomous banach space valued functional differential equation formula

approximating conic sections by constrained bezier curves of arbitrary degree in this paper an algorithm for approximating conic sections by constrained bezier curves of arbitrary degree is proposed first using the eigenvalues of recurrence equations and the method of undetermined coefficients some exact integral formulas for the product of two bernstein basis functions and the denominator of rational quadratic form expressing conic section are given then using the least squares method a matrix based representation of the control points of the optimal bezier approximation curve is deduced this algorithm yields an explicit arbitrary degree bezier approximation of conic sections which has function value and derivatives at the endpoints that match the function value and the derivatives of the conic section up to second order and is optimal in the l 2 norm to reduce error the method can be combined with a curve subdivision scheme computational examples are presented to validate the feasibility and effectiveness of the algorithm for a whole curve or its part generated by a subdivision

high order parametric polynomial approximation of quadrics in rd abstract in this paper an approximation of implicitly defined quadrics in r d by parametric polynomial hypersurfaces is considered the construction of the approximants provides the polynomial hypersurface in a closed form and it is based on the minimization of the error term arising from the implicit equation of a quadric it is shown that this approach also minimizes the normal distance between the quadric and the polynomial hypersurface furthermore the asymptotic analysis confirms that the distance decreases at least exponentially as the polynomial degree grows numerical experiments for spatial quadrics illustrate the obtained theoretical results

on computing the maximal delay intervals for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems the authors consider delay systems of both retarded and neutral types expressed in state space forms the author s main goal is to provide a computation oriented method for computing the maximal delay intervals over which the systems under consideration maintain stability the author s results show that this can be accomplished by computing the generalized eigenvalues of certain frequency dependent matrices based on these results the author also states a necessary and sufficient condition concerning stability independent of delay for each of the retarded and neutral systems the author s results can be readily implemented and appear suitable for analyzing systems with high dimensions and many delay units

an observer for a class of nonlinear systems with time varying observation delay abstract this paper presents a state observer for drift observable nonlinear systems when output measurements are affected by a known and bounded time varying delay the structure of the proposed observer is very simple and it is a generalization of an existing observer for undelayed systems the observer exhibits good performance in estimating the system state also in the presence of significant measurement delays the technique used to prove the asymptotical convergence to zero of the observation error based on the lyapunov razumikhin approach does not require any assumption about the dependence of the delay on the time

stability robustness of retarded lti systems with single delay and exhaustive determination of their imaginary spectra in this paper we consider the stability robustness of the general class of vector lti linear time invariant equations with a single delay dot bf x t bf a bf x t bf b bf x t tau bf x in bf r n the robustness is against the uncertain but constant delay tau in bf r we first present a set of novel propositions and state that the solution must start from the complete knowledge of imaginary spectra of the system and the corresponding delays the propositions claim that such spectra form a set of manageably small number of members and this number is upper bounded by n 2 regardless of the composition of bf a and bf b matrices they also claim that the infinite dimensional system at hand has an outstanding discipline regarding these imaginary spectra this discipline invites the recently developed concept called the cluster treatment of characteristic roots ctcr the ctcr procedure requires a complete and precise determination of the imaginary spectra of the system there are many procedures in the literature to achieve this they are in fact some variations of the five main methods of different levels of precision and complexity there is however no study known to the authors for presenting a comparison among these methods this paper addresses this need we first offer an overview of each of the five methods and then compare their numerical performances over an example case study

prediction based control for lti systems with uncertain time varying delays and partial state knowledge abstractthe stability of a prediction based controller for linear time invariant lti systems is studied in the presence of time varying input and output delays the uncertain delay case is treated as well as the partial state knowledge case the reduction method is used in order to prove the convergence of the closed loop system including the state observer the predictor and the plant explicit conditions that guarantee the closed loop stability are given thanks to a lyapunov razumikhin analysis simulations illustrate the theoretical results

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

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

approximation of circular arcs by bezier curves abstract for the circular arc of angle 0 we present the explicit form of the best gc 3 quartic approximation and the best gc 2 quartic approximations of various types and give the explicit form of the hausdorff distance between the circular arc and the approximate bezier curves for each case we also show the existence of the gc 4 quintic approximations to the arc and find the explicit form of the best gc 3 quintic approximation in certain constraints and their distances from the arc all approximations we construct in this paper have the optimal order of approximation twice of the degree of approximate bezier curves

exponential stabilization of linear systems with time varying delayed state feedback via partial spectrum assignment abstract we consider the problem of controlling a linear system when the state is available with a known time varying delay delayed state feedback control or the actuator is affected by a delay the solution proposed in this paper consists in partially assigning the spectrum of the closed loop system to guarantee the exponential zero state stability with a prescribed decay rate by means of a finite dimensional control law a non conservative bound on the maximum allowed delay for the prescribed decay rate is presented which holds for both cases of constant and time varying delays an advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required we compare the performance of our approach in terms of delay bound and input signal with another recent approach

on asymptotic stabilizability of linear systems with delayed input this paper examines the asymptotic stabilizability of linear systems with delayed input by explicit construction of stabilizing feedback laws it is shown that a stabilizable and detectable linear system with an arbitrarily large delay in the input can be asymptotically stabilized by either linear state or output feedback as long as the open loop system is not exponentially unstable i e all the open loop poles are on the closed left half plane a simple example shows that such results would not be true if the open loop system is exponentially unstable it is further shown that such systems when subject to actuator saturation are semiglobally asymptotically stabilizable by linear state or output feedback

functional differential equations of delay type and nonlinear evolution in lp spaces abstract nonlinear nonautonomous functional differential equations of delay type with lp initial functions is studied by means of the theory of evolution operators in lp spaces using the evolution operator in c it is shown that the evolution operator constructed in lp rn determines the solutions of the initial value problem in the exact sense a variation of parameters formula is developed for the nonlinear perturbed equation

stabilization by means of approximate predictors for systems with delayed input sufficient conditions for global stabilization of nonlinear systems with delayed input by means of approximate predictors are presented an approximate predictor is a mapping which approximates the exact values of the stabilizing input for the corresponding system with no delay a systematic procedure for the construction of approximate predictors is provided for globally lipschitz systems the resulting stabilizing feedback can be implemented by means of a dynamic distributed delay feedback law illustrative examples show the efficiency of the proposed control strategy