brief paper a method for optimal control and filtering of multitime scale linear singularly perturbed stochastic systems in this paper we introduce a transformation for the exact closed loop decomposition of the optimal kalman filter and the linear quadratic optimal controller of multi time scale continuous time linear singularly perturbed stochastic systems the solution of the corresponding algebraic regulator and filter riccati equations are obtained in terms of solutions of reduced order subsystem algebraic riccati equations corresponding to the system time scales we have also obtained n completely independent reduced order subsystem kalman filters working in parallel in different time scales this allows parallel processing of information with lower order different rates kalman filters consistent with the system time scales

exponential convergence estimates for a single neuron system of neutral type the future behavior of a dynamical system is determined by its initial state or initial function nontrivial neuron system involving adaptive learning corresponds to the memorization of initial information in this paper exponential estimates and sufficient conditions for the exponential stability of a single neuron system of neutral type are studied of particular importance is the fact that exponential convergence guarantees that this system is capable of memorizing initial functions furthermore this system is also capable of conveying much more information with respect to the initial functions memorized by neuron system with time delay the proofs follow some new results on nonhomogeneous difference equations evolving in continuous time combined with the lyapunov krasovskii functional and the descriptor system approach the exponential stability conditions are expressed in terms of a linear matrix inequality which lead to less restrictive and less conservative exponential estimates

near optimum steady state regulators for stochastic linear weakly coupled systems abstract this paper presents an approach to the decomposition and approximation of the linear quadratic gaussian estimation and control problems for weakly coupled systems the global kalman filter is decomposed into separate reduced order local filters via the use of a decoupling transformation a near optimal control law is derived by approximating the coefficients of the truly optimal control law the order of approximation of the optimal performance is o en where n is the order of approximation of the coefficients a real world power system example demonstrates the failure of o e2 and o e4 approximations and the necessity for the existence of the o en theory the proposed method produces the reduction in both off line and on line computational requirements and leads to convergence under mild assumptions in addition only low order systems are involved in algebraic calculations and no analyticity requirement a standard assumption for the power series method is imposed on system coefficients

equilibrium problem for elastic body with delaminated t shape inclusion abstract we analyze an equilibrium problem for 2d elastic body with a t shape thin inclusion in presence of damage a part of the inclusion is elastic and the other part is a rigid one a delamination of the inclusion from the elastic body is assumed thus forming a crack between the elastic body and the inclusion nonlinear boundary conditions at the crack faces are considered to prevent a mutual penetration between the faces the damage is characterized by a positive parameter the paper provides an asymptotic analysis of the solutions as the damage parameter tends to infinity and to zero a passage to infinity of a rigidity parameter of the elastic part of the inclusion is also analyzed junction conditions are determined at the connection point between the elastic and rigid parts of the inclusion an existence theorem is proved for an inverse problem of finding displacement fields and the damage and rigidity parameters provided that a displacement of the tip point of the inclusion is known

elastoplastic damage modelling including the gradient of damage formulation and computational aspects a framework for continuum elastoplastic damage modelling which employs irreversible thermodynamics and internal state variables is investigated the damage part of the modelling involves the gradient of damage quantity which together with the equations of motion are issued from a new formulation of the principle of virtual power recently proposed it is shown how the plastic part of the modelling takes its standard format next we consider in detail the variational formulation and subsequent numerical implementation of the elastoplastic damage models the development of an algorithm consistent with the present formulation is given where for the plastic part it leaves the standard return mapping algorithms unchanged application is made to different classical rate independent and rate dependent plastic models with the presence of a damage mechanism the numerical implementation in the context of the finite element method is discussed in detail and a set of representative applications and numerical examples is given

solving the matrix differential riccati equation a lyapunov equation approach in this technical note we investigate a solution of the matrix differential riccati equation that plays an important role in the linear quadratic optimal control problem unlike many methods in the literature the approach that we propose employs the negative definite anti stabilizing solution of the matrix algebraic riccati equation and the solution of the matrix differential lyapunov equation an illustrative numerical example is provided to show the efficiency of our approach

the recursive reduced order numerical solution of the singularly perturbed matrix differential riccati equation under stability observability conditions imposed on a singularly perturbed system an efficient numerical method for solving the corresponding matrix differential riccati equation is obtained in terms of the reduced order problems the order reduction is achieved via the use of the chang transformation applied to the hamiltonian matrix of a singularly perturbed linear quadratic control problem an efficient numerical recursive algorithm with a quadratic rate of convergence is developed for solving the algebraic equations comprising the chang transformation

a new filtering method for linear singularly perturbed systems in this paper we present a new method which allows complete decomposition of the optimal global kalman filter for linear singularly perturbed systems into pure slow and pure fast local optimal filters both driven by the system measurements the method is based on the exact decomposition of the global singularly perturbed algebraic riccati equation into pure slow and pure fast local algebraic riccati equations an f 8 aircraft example demonstrates the proposed method

two iterative algorithms for stochastic algebraic riccati matrix equations abstract in this paper two iterative algorithms are proposed to solve stochastic algebraic riccati matrix equations arising in the linear quadratic optimal control problem of linear stochastic systems with state dependent noise in the first algorithm a standard riccati matrix equation needs to be solved at each iteration step and in the second algorithm a standard lyapunov matrix equation needs to be solved at each iteration step in the proposed algorithms a weighted average of the estimates in the last and the previous steps is used to update the estimate of the unknown variable at each iteration step some properties of the sequences generated by these algorithms under appropriate initial conditions are presented and the convergence properties of the proposed algorithms are analyzed finally two numerical examples are employed to show the effectiveness of the proposed algorithms

convergence under dynamical thresholds with delays necessary and sufficient conditions are obtained for the existence of a globally asymptotically stable equilibrium of a class of delay differential equations modeling the action of a neuron with dynamical threshold effects

reduced order solution to the finite time optimal control problems of linear weakly coupled systems the optimal solution to the finite time optimal control problem of weakly coupled linear systems is found in terms of completely decoupled reduced order differential equations for both closed loop and open loop control this is achieved through the use of the decoupling transformation that block diagonalizes the hamiltonian matrix of the weakly coupled linear quadratic control problem the convergence to the optimal solution is pretty rapid the proposed technique is very well suited for parallel computations

new iterative algorithm for algebraic riccati equation related to h sub spl infin control problem of singularly perturbed systems we present the solution to the algebraic riccati equation are with indefinite sign quadratic term related to the h sub spl infin control problem for singularly perturbed systems by means of a kleinman type algorithm the resulting algorithm is very efficient from the numerical point of view because the are is solvable even if the quadratic term has an indefinite sign moreover the resulting iterative algorithm is quadratically convergent we also present an algorithm for solving the generalized algebraic lyapunov equation on the basis of the fixed point algorithm

an elastic viscoplastic quasistatic contact problem with damage abstract in this paper the contact between an elastic viscoplastic body and a deformable obstacle is studied the effect of the damage due to tension or compression is also considered the variational formulation leads to a coupled system of evolutionary equations for which an existence and uniqueness result is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are obtained and as a consequence the convergence of the algorithm is deduced finally some numerical simulations are presented to demonstrate the accuracy of the algorithm

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

decoupling and order reduction via the riccati transformation a program that dates back to riccati 1724 and that seeks to replace a given differential equation with an equivalent collection of effectively uncoupled equations of lower orders through the use

numerical analysis and simulations of a quasistatic frictional contact problem with damage in viscoelasticity we consider a quasistatic problem which models the bilateral contact between a viscoelastic body and a foundation taking into account the damage and the friction the damage which results from tension or compression is then involved in the constitutive law and it is modelled using a nonlinear parabolic inclusion the variational problem is formulated as a coupled system of evolutionary equations for which we state the existence of a unique solution then we introduce a fully discrete scheme using the finite element method to approximate the spatial variable and the euler scheme to discretize the time derivatives error estimates are derived and under suitable regularity hypotheses the convergence of the numerical scheme obtained finally a numerical algorithm and results are presented for some two dimensional examples

a new version of the chang transformation a new decoupling transformation is proposed for singularly perturbed linear systems this transformation has the advantage over the previous one in that in order to find such a transformation only one algorithm is required and the computation can be done in parallel because the transformation matrices are obtained from two independent equations that are identical in form

variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance friction and damage we consider a model for quasistatic frictional contact between a viscoelastic body and a foundation the material constitutive relation is assumed to be nonlinear the mechanical damage of the material caused by excessive stress or strain is described by the damage function the evolution of which is determined by a parabolic inclusion the contact is modeled with the normal compliance condition and the associated version of coulomb s law of dry friction we derive a variational formulation for the problem and prove the existence of its unique weak solution we then study a fully discrete scheme for the numerical solutions of the problem and obtain error estimates on the approximate solutions

asymptotic properties of input output operators norm associated with singularly perturbed systems with multiplicative white noise in this paper we study the problem of the asymptotic property of the norm of input output operators related to a class of singularly perturbed stochastic linear systems the system is under perturbation of multiplicative white noise by using reduction order and boundary layer techniques it is shown that the norm of the operator of the perturbed system is less than a given number gamma when the small perturbation varepsilon tends to zero if both the related norms of the reduced subsystem and the boundary layer subsystem are less than gamma furthermore a stabilizing robust controller is designed which is independent of perturbation varepsilon

brief paper h control for fast sampling discrete time singularly perturbed systems this paper is concerned with the h control problem via state feedback for fast sampling discrete time singularly perturbed systems a new h controller design method is given in terms of solutions to linear matrix inequalities lmis which eliminates the regularity restrictions attached to the riccati based solution a method for evaluating the upper bound of singular perturbation parameter e with meeting a prescribed h performance bound requirement is also given furthermore the results are extended to robust controller design for fast sampling discrete time singularly perturbed systems with polytopic uncertainties numerical examples are given to illustrate the validity of the proposed methods

robust stabilization of two time scale systems with respect to the normalized coprime factorization the present paper has two main purposes the first is to provide an explicit state space solution of the robust stabilization problem with respect to the nlcf for two time scale systems in this construction only the solutions of the control and of the filtering riccati equations associated with the slow and with the fast dynamics of the nominal plant are used these solutions do not depend upon the singular perturbation and therefore all computations are well conditioned the second purpose of the paper is to investigate the case when an k independent robust controller can be used for the robust stabilization of a two time scale nominal system two constructions of such controllers are developed under some additional assumptions numerical examples illustrate the theoretical developments

technical communique a revised kleinman algorithm to solve algebraic riccati equation of singularly perturbed systems in this paper we show that the kleinman algorithm can be used well to solve the algebraic riccati equation are of singularly perturbed systems where the quadratic term of the are may be indefinite the quadratic convergence property of the kleinman algorithm is proved by using the newton kantorovich theorem when the initial condition is chosen appropriately in addition the numerical method to solve the generalized algebraic lyapunov equation gale appearing in the kleinman algorithm is given

decoupling transformation for weakly coupled linear systems the non singular transformation that completely decouples a weakly coupled linear system under non restrictive conditions is defined the transformation matrices are obtained from two algebraic matrix equations algorithms that efficiently generate solutions to these equations are derived the proposed transformation also completely decouples the corresponding lyapunov matrix differential equation

general transformation for block diagonalization of multitime scale singularly perturbed linear systems in this technical note a general transformation for block diagonalization decoupling of multitime scale singularly perturbed linear systems composed of n subsystems is presented the resulting decoupling corresponds to subsystem time scales and produces n completely independent subsystems operating in different time scales

numerical fixed point solution for near optimum regulators of linear quadratic gaussian control problems for singularly perturbed systems the fixed point method is developed for obtaining an efficient numerical solution of the linear quadratic gaussian problem for singularly perturbed systems it is shown that each iteration step improves the accuracy by an order of magnitude that is the accuracy 0 ek can be obtained by performing only k 1 iterations in addition only low order systems are involved in algebraic manipulations and no analyticity requirements are imposed on the system coefficients

duality methods for solving variational inequalities abstract methods of maximal monotone operators are used in order to study from a general point of view duality numerical algorithms for solving variational inequalities with classical algorithms such as uzawa s method for the standard and augmented lagrangian this paper presents some new algorithms which appear to have very good numerical performances

finite horizon optimal control of singularly perturbed systems a differential lyapunov equation approach in this note we study the finite time horizon optimal control problem for singularly perturbed systems the solution is obtained in terms of the corresponding solution of the algebraic riccati equation and the decomposition of the singularly perturbed differential lyapunov equation into reduced order differential lyapunov sylvester equations an illustrative numerical example is provided to show the efficiency of the proposed approach

a frictionless contact problem for elastic viscoplastic materials with normal compliance and damage abstract we study a quasistatic frictionless contact problem with normal compliance and damage for elastic viscoplastic bodies the mechanical damage of the material caused by excessive stress or strain is described by a damage function whose evolution is modelled by an inclusion of parabolic type we provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution to the model we then introduce and study a fully discrete scheme for the numerical solutions of the problem an optimal order error estimate is derived for the approximate solutions under suitable solution regularity numerical examples are presented to show the performance of the method

new results for global stability of a class of neutral type neural systems with time delays this paper studies the global convergence properties of a class of neutral type neural networks with discrete time delays this class of neutral systems includes cohen grossberg neural networks hopfield neural networks and cellular neural networks based on the lyapunov stability theorems some delay independent sufficient conditions for the global asymptotic stability of the equilibrium point for this class of neutral type systems are derived it is shown that the results presented in this paper for neutral type delayed neural networks are the generalization of a recently reported stability result a numerical example is also given to demonstrate the applicability of our proposed stability criteria

an algorithm for solving the singularly perturbed h algebraic riccati equation abstract the algebraic riccati equation of singularly perturbed h linear quadratic optimal control problems is decoupled into two completely independent reduced order pure slow and pure fast h algebraic riccati equations even though the algebraic riccati equations obtained are nonsymmetric they are efficiently solved in terms of lyapunov iterations by using the newton method the presented algorithm can be used for h parallel filtering and regulation of systems displaying two time scale dynamics

technical communique improvement of system order reduction via balancing using the method of singular perturbations in this paper we first present several alternative techniques for system order reduction based on system balancing by employing the method of singular perturbations the techniques obtained have the same robustness accuracy evaluated with respect to the h norm of the reduced order system as the two techniques existing in the control literature known as the direct truncation and balancing residualization methods the newly proposed techniques preserve the exact dc gain as the original system and produce very good to excellent accuracy at low and medium frequencies we also present a simple formula that fixes the dc gain for the direct truncation method in the second part of the paper we propose how to perform order reduction of a balanced system using theory of singular perturbations that can produce very good accuracy at high frequencies particularly for systems that have lightly damped highly oscillatory modes the result obtained for such kind of systems requires that the modes with higher hankel singular values should be neglected and those with smaller hankel singular values should be retained this is a counter intuitive result in the spirit of h theory but an intuitive result in the spirit of theory of singular perturbations the second part of the paper raises an important question about validity of the system robustness estimate based on the h norm for linear systems with lightly damped highly oscillatory modes

bounds on the optimum quadratic cost of structure constrained controllers in this note lower and upper bounds are derived on the quadratic cost of optimal output feedback controllers subject to constraints on the controller structure the use of these bounds in forming a comparative assessment of alternative controller confugurations is described and an illustrative example is given the principal advantage of these bounds arises from the fact that they can save considerable computational effort

a shishkin mesh for a singularly perturbed riccati equation in this paper a singularly perturbed riccati initial value problem is examined parameter explicit bounds on the solution and its derivatives are given a numerical method composed of an implicit difference operator and a piecewise uniform shishkin mesh is constructed a theoretical parameter independently bound on the errors in the numerical approximations is established numerical results are presented which are in agreement with the theoretical error bound

new approach to block diagonalization of singularly perturbed systems by taylor expansion block diagonalization of a singularly perturbed system requires the solution of the riccati equation and the lyapunov equation a new approach is suggested for both equations using taylor expansions the convergence is studied in detail it is shown that it is ensured under restrictions which are less restrictive than the case of previously suggested methods

h optimal control for singularly perturbed systems part i perfect state measurements we study the h optimal control of singularly perturbed linear systems under perfect state measurements for both finite and infinite horizons using a differential game theoretic approach we show that as the singular perturbation parameter approaches zero the optimal disturbance attenuation level for the full order system under a quadratic performance index converges to a value that is bounded above by the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions furthermore we construct a composite controller based on the solution of the slow and fast games which guarantees a desired achievable performance level for the full order plant as approaches zero a slow controller however is not generally robust in this sense but still under some conditions which are delineated in the paper the fast dynamics can be totally ignored the paper also studies optimality when the controller includes a feedforward term in the disturbance and presents some numerical examples to illustrate the theoretical results

parallel reduced order controllers for stochastic linear singularly perturbed discrete systems an approach to the decomposition and approximation of linear quadratic gaussian control problems for singularly perturbed discrete systems at steady state is presented the global kalman filter is decomposed into separate reduced order local filters through the use of a decoupling transformation a near optimal control law is derived by approximating coefficients of the optimal control law the proposed method allows parallel processing of information and reduces offline and online computational requirements a real world example demonstrates the efficiency of the proposed method

asymptotic h sub spl infin control of singularly perturbed systems with parametric uncertainties this paper deals with the problem of control of singularly perturbed linear continuous time systems the authors attention is focused on the design of a composite linear controller based on the slow and fast problems such that both stability and a prescribed h sub spl infin performance for the full order system are achieved the asymptotic behavior of the composite controller is studied which is independent of the singular perturbation spl epsiv when spl epsiv is sufficiently small furthermore the problem of robust control for the above system with parameter uncertainty is also investigated

geometric properties and invariant manifolds of the riccati equation this short paper considers the general riccati matrix differential equation it reviews and extends results on the characterization and existence of equilibrium solutions establishes that the riccati equation has at most one stable equilibrium solution as t rightarrow infty or t rightarrow infty and confines the region of attraction to this unique stable equilibrium solution by identifying and utilizing linear and nonlinear invariant manifolds of the riccati equation

near optimal h sup spl infin control of linear singularly perturbed systems we consider the singularly perturbed h sup spl infin control problem under perfect state measurements for both finite and infinite horizons we suggest a construction of high order approximations to a controller that guarantees a desired performance level on the basis of the exact decomposition of the full order riccati equations to the reduced order slow and fast equations this leads to effective asymptotic and numerical algorithms we show that the high order accuracy controller improves the performance

optimal control of discrete time singularly perturbed systems in this paper we present a new algorithm for solving the optimal control of discrete time singularly perturbed systems the main idea of this algorithm is based on two steps first the hamiltonian difference equation is reduced to the backward recursive form rather than the forward recursive form second the bilinear transformation is applied to transform the derived non symmetric discrete time riccati equations into continuous time equations in order to improve the efficiency of this scheme two matrix permutations are introduced into this algorithm by taking into account the previous work of gajic and shen 1991 therefore substantial numerical advantages are gained namely computation and memory requirements the f 8 aircraft model is used to illustrate the efficiency of the proposed method

time scale decomposition of linear implicit singularly perturbed systems an implicit singularly perturbed system dot x a epsilon x where a 0 is singular is considered this note presents an algorithm for decomposing the system into a set of isolated subsystems at different time scales the decomposed form of the system is used to construct a uniform asymptotic approximation to exp a epsilon t

the exact slow fast decomposition of the algebraic ricatti equation of singularly perturbed systems the algebraic riccati equation for singularly perturbed control systems is completely and exactly decomposed into two reduced order algebraic riccati equations corresponding to the slow and fast time scales the pure slow and pure fast algebraic riccati equations are asymmetric ones but their o epsilon perturbations are symmetric it is shown that the newton method is very efficient for solving the obtained asymmetric algebraic riccati equations the method presented is very suitable for parallel computations due to the complete and exact decomposition of the riccati equation this procedure might produce new insight into the two time scale optimal filtering and control problems

numerical integration of the differential matrix riccati equation two new bernoulli substitution methods for solving the riccati differential equation are tested numerically against direct integration of the riccati equation the chandrasekhar algorithm and the davison maki method on a large set of problems taken from the literature the first of these new methods was developed for the time invariant case and uses the matrix analog of completing the square to transform the problem to a bisymmetric riecati equation whose solution can be given explicitly in terms of a matrix exponential of order n this method is fast and accurate when the extremal solutions of the associated algebraic riccati equation are well separated the second new method was developed as a means of eliminating the instabilities associated with the davison maki algorithm by using reinitialization at each time step the davison maki algorithm can be recast as a recursion which is over three times faster than the original method and is easily shown to be stable for both time invariant and time dependent problems from the results of our study we conclude that the modified davison maki method gives superior performance except for those problems where the number of observers and controllers is small relative to the number of states in which ease the chandrasekhar algorithm is better

theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage this paper presents the theory and the numerics of an isotropic gradient damage formulation within a thermodynamical background the main motivation is provided by localization computations whereby classical local continuum formulations fail to produce physically meaningful and numerically converging results we propose a formulation in terms of the helmholtz free energy incorporating the gradient of the damage field a dissipation potential and the postulate of maximum dissipation as a result the driving force conjugated to damage evolution is identified as the quasi nonlocal energy release rate which essentially incorporates the divergence of a vectorial damage flux besides the strictly local energy release rate on the numerical side besides balance of linear momentum the algorithmic consistency condition must be solved in weak form thereby the crucial issue is the selection of active constraints which is solved by an active set search algorithm borrowed from convex nonlinear programming in the examples we compare the behavior in local damage with the performance of the gradient formulation

damage gradient of damage and principle of virtual power a theory of continuum damage mechanics is developed within the framework of the principle of virtual power because the damage in a solid results from microscopic movements we decided to include the power of these microscopic movements in the power of the internal forces the microscopic velocities are related to the damage rate the power of the internal forces we choose depends on the damage velocity and its gradient to take into account the interactions models issued from this theory are presented they are coherent from the mechanical and mathematical points of view the numerical computations show no mesh sensitivity they describe with good agreement the main experimental properties concrete is chosen as an example to illustrate the theory a model using two damage quantities is also presented it yields the correct description of the unilateral phenomenon observed in concrete finally an extension of the existing models is proposed to describe the fatigue damage behaviour

exact slow fast decomposition of the singularly perturbed matrix differential riccati equation in this paper the hamiltonian matrix formulation of the riccati equation is used to derive the reduced order pure slow and pure fast matrix differential riccati equations of singularly perturbed systems these pure slow and pure fast matrix differential riccati equations are obtained by decoupling the singularly perturbed matrix differential riccati equation of dimension n 1 n 2 into the pure slow regular matrix differential riccati equation of dimension n 1 and the pure fast stiff matrix differential riccati equation of dimension n 2 a formula is derived that produces the solution of the original singularly perturbed matrix differential riccati equation in terms of solutions of the pure slow and pure fast reduced order matrix differential riccati equations and solutions of two reduced order initial value problems in addition to its theoretical importance the main result of this paper can also be used to implement optimal filtering and control schemes for singularly perturbed linear time invariant systems independently in pure slow and pure fast time scales

exact slow fast decomposition of the nonlinear singularly perturbed optimal control problem abstract we study the infinite horizon nonlinear quadratic optimal control problem for a singularly perturbed system which is nonlinear in both the slow and the fast variables it is known that the optimal controller for such problem can be designed by finding a special invariant manifold of the corresponding hamiltonian system we obtain exact slow fast decomposition of the hamiltonian system and of the special invariant manifold into the slow and the fast ones on the basis of this decomposition we construct high order asymptotic approximations of the optimal state feedback and optimal trajectory

asymptotic stability of a class of neutral delay neuron system in a critical case in this brief the asymptotic stability properties of a neutral delay neuron system are studied mainly in a critical case when the exponential stability is not possible if a critical value of the coefficient in the neutral delay neuron system is considered then the difficulty for our investigation is caused by the fact that the spectrum of the linear operator is asymptotically approximated to the imaginary axis it is obvious that in such a case the equation is not exponentially stable and one needs more subtle methods in order to characterize this type of asymptotic stability hence first the local asymptotic stability for the neutral delay neuron system is studied and the main tools involved are the asymptotic expansions of characteristic roots laplace transforms and function series and a complete analysis of the stability diagram is also presented then based on the energy method the globally asymptotic stability results for the neutral delay neuron system are derived

brief paper new results on h control of discrete singularly perturbed systems this paper studies the problem of h control of discrete time singularly perturbed systems a new sufficient condition which ensures the existence of state feedback controllers such that the resulting closed loop system is asymptotically stable while satisfying a prescribed h norm bound is obtained this condition is in terms of a linear matrix inequality which is independent of the singular perturbation parameter furthermore a new condition on searching for the allowable upper bound of the singular perturbation parameter is proposed under which the discrete time singularly perturbed system is asymptotically stable with an h norm bound when the singular perturbation parameter is lower than this upper bound in these derived conditions the upper bound of the singular perturbation parameter is not required to be smaller than one the reduced conservatism of our results is demonstrated via a numerical example

on the approximation of the boundary layers for the controllability problem of nonlinear singularly perturbed systems abstract a new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the boundary layers is proposed for example problems with feedback control such as the steady states of the thermostats where the controllers add or remove heat depending upon the temperature registered in another place of the heated bar can be interpreted with a second order ordinary differential equation subject to a nonlocal three point boundary condition the o accurate approximation of behavior of these nonlinear systems in terms of the exponentially small boundary layer functions is given at the end of this paper we formulate the unsolved controllability problem for nonlinear systems

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

variable structure control for singularly perturbed linear continuous systems with matched disturbances a variable structure system can be studied using the singular perturbation theory the discontinuous control that leads to a finite time reaching of the sliding surface creates fast time transients analogous to the stable boundary layer dynamics of a singularly perturbed system as the sliding mode is attained the slow time dynamics prevails just as that of a singularly perturbed system after the boundary layer dynamics fades away in this technical note the problem of sliding mode control for singularly perturbed systems in the presence of matched bounded external disturbances is investigated a composite sliding surface is constructed from solutions of algebraic lyapunov equations which are derived from both the fast and the slow subsystems the resultant sliding motion ensures lyapunov stability with disturbance rejection two proposed schemes that ensure the asymptotic stability of the system are presented the effectiveness of the proposed methods is demonstrated in a numerical example of a magnetic tape control system

existence and uniqueness of solutions for a dynamic one dimensional damage model we consider a one dimensional dynamic model that describes the evolution of damage caused by tension in a viscoelastic material the process is modeled by a coupled set of two differential inclusions for the elastic displacement and damage fields we establish the existence of local weak solutions the existence result is derived from the a priori estimates obtained for a sequence of regularized truncated and time retarded approximations we also establish the existence of the unique weak solution of a simplified version of the model

brief paper eigenvector approach for order reduction of singularly perturbed linear quadratic optimal control problems in this paper we show how to decompose the singularly perturbed algebraic riccati equation and the corresponding linear quadratic optimal control problem at steady state in terms of reduced order pure slow and pure fast problems by using the eigenvector approach the eigenvector approach should be used for decomposition of singularly perturbed control systems in the cases when the singular perturbation parameter is not very small in such cases the decomposition methods based on series expansions fixed point iterations subspace iterations and newton iterations either fail to produce solutions of the corresponding algebraic equations or display very slow convergence

damageable contact between an elastic body and a rigid foundation in this work the contact problem between an elastic body and a rigid obstacle is studied including the development of material damage which results from internal compression or tension the variational problem is formulated as a first kind variational inequality for the displacements coupled with a parabolic partial differential equation for the damage field the existence of a unique local weak solution is stated then a fully discrete scheme is introduced using the finite element method to approximate the spatial variable and an euler scheme to discretize the time derivatives error estimates are derived on the approximate solutions from which the linear convergence of the algorithm is deduced under suitable regularity conditions finally three two dimensional numerical simulations are performed to demonstrate the accuracy and the behaviour of the scheme

the recursive reduced order solution of an open loop control problem of linear singularly perturbed systems a reduced order method with an arbitrary degree of accuracy is obtained for solving the linear quadratic optimal open loop control problem the original two point boundary value problem is transformed into the pure slow and pure fast reduced order completely decoupled initial value problems by doing this the stiffness of the singularly perturbed two point boundary value problem is converted into the problem of an ill defined linear system of algebraic equations