system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

a simple solution of the bratu problem a brief survey of the properties and different treatments of the one dimensional 1d and 2d bratu problems is presented different iterative treatments of the resulting nonlinear system of equations are discussed the finite difference treatment of the problem is considered nonstandard finite difference methods with a simple sinusoidal starting function having an appropriate amplitude are recommended bounds on the amplitude for yielding both lower and upper solutions are given

variational approach to nonlinear problems and a review on mathematical model of electrospinning abstract variational approach to various nonlinear equations is briefly introduced mathematical models for electrospinning are also reviewed a simple scaling approach to predicting the diameter of the electrospun fiber is given and experimental verification is provided

an efficient iterative method for solving bratu type equations abstract in this paper an efficient analytical iterative method is introduced for solving the initial value and boundary value bratu problems a quasilinearization method with an optimal parameter is derived and utilized to reduce the highly nonlinear bratu equations to a sequence of linear problems an optimal picard iteration method is used to obtain approximate analytical solution of linearized versions of bratu s equations the numerical results presented the effectiveness and high performance of the proposed method and comparisons are made with many other existing numerical solution techniques the comparisons reveal the efficiency and applicability of the present work

averaging results and the study of uniform asymptotic stability of homogeneous differential equations that are not fast time varying within the liapunov framework a sufficient condition for uniform asymptotic stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the v function taken along solutions of the system may have positive and negative values it is shown that the proposed condition is useful for the study of uniform asymptotic stability of homogeneous systems with order tau 0 in particular it is established that asymptotic stability of the averaged homogeneous system implies local uniform asymptotic stability of the original time varying homogeneous system this shows that averaging techniques play a prominent role in the study of homogeneous not necessarily fast time varying systems

stability analysis of discrete time lur e systems a class of lyapunov functions is proposed for discrete time linear systems interconnected with a cone bounded nonlinearity using these functions we propose sufficient conditions for the global stability analysis in terms of linear matrix inequalities lmi only taking the bounded sector condition into account unlike frameworks based on the lur e type function the additional assumptions about the derivative or discrete variation of the nonlinearity are not necessary hence a wider range of cone bounded nonlinearities can be covered we also show that there is a link between global stability lmi conditions based on this new lyapunov function and a transfer function of an auxiliary system being strictly positive real in addition the novel function is considered in the local stability analysis problem of discrete time lur e systems subject to a saturating feedback a convex optimization problem based on sufficient lmi conditions is formulated to maximize an estimate of the basin of attraction another specificity of this new lyapunov function is the fact that the estimate is composed of disconnected sets numerical examples reveal the effectiveness of this new lyapunov function in providing a less conservative estimate with respect to the quadratic function

lpv system analysis via quadratic separator for uncertain implicit systems this paper considers a class of linear systems containing time varying parameters whose behavior is not known exactly we assume that the parameters vary within known intervals and there are known bounds on their rates of variation our objective is to give a computationally verifiable condition that guarantees stability of the system for all possible parameter variations we first point out that the information on the rate bounds can be exploited by considering an augmented system described by an implicit model we then develop a tool called the quadratic separator for stability analysis of uncertain implicit systems using this tool a sufficient stability condition is obtained for the original linear parameter varying system moreover we show that the stability condition obtained is equivalent to the existence of a lyapunov function that depends on the parameters in a linear fractional manner finally the computational aspects of the proposed stability conditions are addressed

on regulation under sampling the paper deals with linear and nonlinear regulation under sampling it is shown that digital solutions exist under assumptions which are closely related to the existence of robust solutions to the continuous problem approximated solutions are computed starting from the continuous ones

changing supply rates for input output to state stable discrete time nonlinear systems with applications we present results on changing supply rates for input output to state stable discrete time nonlinear systems our results can be used to combine two lyapunov functions none of which can be used to verify that the system has a certain property into a new composite lyapunov function from which the property of interest can be concluded the results are stated for parameterized families of discrete time systems that naturally arise when an approximate discrete time model is used to design a controller for a sampled data system we present several applications of our results i a lasalle criterion for input to state stability iss of discrete time systems ii constructing iss lyapunov functions for time varying discrete time cascaded systems iii testing iss of discrete time systems using positive semidefinite lyapunov functions iv observer based input to state stabilization of discrete time systems our results are exploited in a case study of a two link manipulator and some simulation results that illustrate advantages of our approach are presented

some qualitative properties of sampled data control systems the authors consider sampled data control systems which consist of an interconnection of a continuous time nonlinear plant and a digital controller which has quantizers but is otherwise linear along with the required interface elements a d and d a converters in the present paper the authors study the qualitative effects of the quantizers and the plant nonlinearities of these systems

dynamic anti windup design for a class of nonlinear systems abstractthis work addresses the dynamic anti windup design problem for a class of nonlinear systems subject to actuator saturation the considered class regards the systems that can be cast in a differential algebraic representation dar such as rational and polynomial systems considering that a nonlinear dynamic output feedback controller which can also be written as a dar has been designed to stabilise the nonlinear system disregarding the saturation effects lmi based conditions are proposed to compute a stabilising dynamic anti windup compensator two problems are considered the first one regards the regional internal stabilisation and the second one assuming that an energy bounded disturbance acts on the system concerns the l2 input to state stability the derived conditions can therefore be incorporated in convex optimisation problems that allow to compute the anti windup compensator in order to maximise the region of guaranteed asymptotic stability to maximise a bound on the admissible l2

multirate versions of sampled data stabilization of nonlinear systems the problem of state feedback sampled data stabilization of nonlinear systems is considered under the low measurement rate constraint and in the presence of not necessarily small time delay in the measurement channel a multirate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state from the delayed measurements for both the controller emulation approach and the approach based on approximate discrete time model of the system we show that under standard assumptions the closed loop multirate sampled data system is asymptotically stable in the semiglobal practical sense an illustrative example of sampled data control of vertical take off and landing aircraft is discussed

power characterizations of input to state stability and integral input to state stability new notions of external stability for nonlinear systems are introduced making use of average powers as signal norms and comparison functions as in the input to state stability iss framework several new characterizations of iss and integral iss are presented in terms of the new notions an example is discussed to illustrate differences and similarities of the newly introduced properties

brief paper continuous time controller redesign for digital implementation a trajectory based approach given a continuous time nonlinear closed loop system we investigate sampled data feedback laws for which the trajectories of the sampled data closed loop system converge to the continuous time trajectories with a prescribed rate of convergence as the length of the sampling interval tends to zero we derive necessary and sufficient conditions for the existence of such sampled data feedback laws and in case of existence provide explicit redesign formulas and algorithms for these controllers

an algorithm for solving boundary value problems in this paper a numerical algorithm based on the decomposition technique is presented for solving a class of nonlinear boundary value problems the method is implemented for well known examples including troesch s and bratu s problems which have been extensively studied the scheme is shown to be highly accurate and only a few terms are required to obtain accurate computable solutions

a decomposition method for solving the nonlinear klein gordon equation in this paper adomian s decomposition scheme is presented as an alternate method for solving the nonlinear klein gordon equation the method is demonstrated by several examples comparing the scheme with existing collocation finite difference and finite element techniques shows that the present approach is highly accurate and converges rapidly

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

technical communique robust backstepping for the euler approximate model of sampled data strict feedback systems stabilization of uncertain sampled data strict feedback systems is addressed the stability study is carried out on the euler approximation of the exact discretized model of the plant firstly a class of state feedback controllers is developed that guarantees an input to state stability property for the closed loop system additionally assuming some hypotheses on the uncertain terms hold a practical asymptotic stability property is ensured by designing an appropriate class of controllers

the decomposition method applied to chandrasekhar h equation in this paper adomian s decomposition method is applied to the nonlinear chandrasekhar h equation the solution is expressed as an infinite series it is shown that two or three iterations are sufficient to obtain good approximation of the exact solution adomian s method has been illustrated by considering some particular cases of this nonlinear integral equation that are of physical interest

brief paper fault tolerant control for a class of nonlinear sampled data systems via a euler approximate observer in this paper a fault tolerant control ftc scheme is developed for a class of nonlinear sampled data systems first a euler approximate discrete model is used to describe the plant under the sampling under this model an observer based fault estimation method is proposed to guarantee the accuracy of both the state and fault estimation values the conditions to make the approximate model consistent with the exact model are presented then an active fault tolerant controller which has a constraint condition for the sampling time is designed to make the faulty system stable finally an inverted pendulum is used to show the efficiency of the proposed method

one point pseudospectral collocation for the one dimensional bratu equation abstract the one dimensional planar bratu problem is u xx exp u 0 subject to u 1 0 because there is an analytical solution this problem has been widely used to test numerical and perturbative schemes we show that over the entire lower branch and most of the upper branch the solution is well approximated by a parabola u x u 0 1 x 2 where u 0 is determined by collocation at a single point x the collocation equation can be solved explicitly in terms of the lambert w function as u 0 w 1 2 2 1 2 where both real valued branches of the w function yield good approximations to the two branches of the bratu function we carefully analyze the consequences of the choice of we also analyze the rate of convergence of a series of even chebyshev polynomials which extends the one point approximation to arbitrary accuracy the bratu function is so smooth that it is actually poor for comparing methods because even a bad inefficient algorithm is successful it is however a solution so smooth that a numerical scheme the collocation or pseudospectral method yields an explicit analytical approximation we also fill some gaps in theory of the bratu equation we prove that the general solution can be written in terms of a single parameter free x without knowledge of the explicit solution the analytical solution can only be evaluated by solving a transcendental eigenrelation whose solution is not known explicitly we give three overlapping perturbative approximations to the eigenrelation allowing the analytical solution to be easily evaluated throughout the entire parameter space

on uniform boundedness of parameterized discrete time systems with decaying inputs applications to cascades a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been established recently within this framework naturally arises the need to investigate stability properties of parameterized discrete time systems further results that guarantee appropriate stability of the parameterized family of discrete time systems that is used within this framework have been also established for systems with cascaded structure a fundamental condition that is required in this framework is uniform boundedness of solutions of the cascade however this is difficult to check in general in this paper we provide a range of sufficient conditions for uniform boundedness that are easier to check these results further contribute to the toolbox for controller design of sampled data nonlinear systems via their approximate discrete time models

stabilization of sampled data nonlinear systems by receding horizon control via discrete time approximations abstract results on stabilizing receding horizon control of sampled data nonlinear systems via their approximate discrete time models are presented the proposed receding horizon control is based on the solution of bolza type optimal control problems for the parametrized family of approximate discrete time models this paper investigates both situations when the sampling period t is fixed and the integration parameter h used in obtaining approximate model can be chosen arbitrarily small and when these two parameters coincide but they can be adjusted arbitrary sufficient conditions are established which guarantee that the controller that renders the origin to be asymptotically stable for the approximate model also stabilizes the exact discrete time model for sufficiently small integration and or sampling parameters

improved stability analysis and gain scheduled controller synthesis for parameter dependent systems we present new algorithms for robust stability analysis and gain scheduled controller synthesis for linear systems affected by time varying parametric uncertainties these new techniques can also be applied to parameter dependent nonlinear systems with real rational nonlinearities sufficient conditions for robust stability as well as conditions for the existence of a robustly stabilizing gain scheduled controller are given in terms of a finite number of linear matrix inequalities lmis explicit formulas for constructing robustly stabilizing gain scheduled controllers are given in terms of the feasible set of these lmis the improvement offered by our approach over existing methods for stability analysis and gain scheduled controller synthesis for parameter dependent linear systems are analyzed in theory numerical examples demonstrate that our approach can offer significant improvement in practice

robust global stabilisability by means of sampled data control with positive sampling rate this work proposes a notion of robust reachability of one set from another set under constant control this notion is used to construct a control strategy involving sequential set to set reachability which guarantees robust global stabilisation of non linear sampled data systems with positive sampling rate sufficient conditions for robust reachability of one set from another under constant control are also provided the proposed method is illustrated through a number of examples including the study of the sampled data stabilisation problem of the chemostat

trajectory approximation based adaptive control for nonlinear systems under matching conditions uncertain nonlinear systems affine in the input are considered it is shown that under some matching conditions these systems can be made practically stable by state feedback we present an adaptive algorithm which renders the origin practically stable to any desired accuracy the presented algorithms are simple and computationally cheap

coprime factor based anti windup synthesis for parameter dependent systems abstract this paper presents a novel anti windup compensator synthesis for linear parameter varying lpv systems that have linear fractional transformation lft representations the lpv anti windup synthesis is based on a right coprime factor description of the lpv plant to be controlled it is shown that the anti windup compensator synthesis reduces to solving a robust l 2 gain state feedback control problem for the lpv lft system subject to input saturations the synthesis takes advantage of unstructured multipliers that is multipliers that do not commute with the parameter structure and exploits a detailed description of the parameter trajectory polytope the anti windup compensator is given in an explicit lpv lft form sharing with the plant the same order and same parameter structure

an algorithm for solving a nonlinear integro differential equation in this paper an algorithm based on adomian s decomposition method is developed to approximate the solution of the nonlinear integro differential equationu t x t email protected t 0a email protected email protected email protected u x x t email protected f x t 0

numerical solution of a biological population model using he s variational iteration method this paper presents numerical solution of a degenerate parabolic equation arising in the spatial diffusion of biological populations the variational iteration method and adomian decomposition method are used for solving this equation and then numerical results are compared with each other showing that the variational iteration method leads to more accurate results furthermore variational iteration method overcomes the difficulty arising in calculating the adomian s polynomials which is an important advantage over the adomian decomposition method

robust performance of linear parametrically varying systems using parametrically dependent linear feedback abstract in this paper a parameter dependent control problem for linear parametrically varying lpv systems is presented sufficient conditions are given that guarantee an lpv system is exponentially stable and achieves an induced l 2 norm performance objective from the disturbance to error signals the usefulness of parameter dependent controllers is motivated from a gain scheduling viewpoint the resulting synthesis problem is reformulated into a convex optimization problem which can be solved using efficient new algorithms

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

on stability of sets for sampled data nonlinear inclusions via their approximate discrete time models and summability criteria this paper consists of two main parts in the first part we provide a framework for stabilization of arbitrary not necessarily compact closed sets for sampled data nonlinear differential inclusions via their approximate discrete time models we generalize d nesic a r teel and p v kokotovic systems control lett 38 1999 pp 259 270 theorem 1 in several different directions we consider stabilization of arbitrary closed sets plants described as sampled data differential inclusions and arbitrary dynamic controllers in the form of difference inclusions our result does not require the knowledge of a lyapunov function for the approximate model which is a standing assumption in d nesic and a r teel ieee trans automat control 49 2004 pp 1103 1122 and d nesic a r teel and p v kokotovic systems control lett 38 1999 pp 259 270 theorem 2 we present checkable conditions that one can use to conclude semiglobal asymptotic stability or global exponential stability ges of the sampled data system via appropriate properties of its approximate discrete time model in the second part we present sufficient conditions for stability of parameterized difference inclusions that involve various summability criteria on trajectories of the system to conclude global asymptotic stability gas or ges and they represent discrete time counterparts of results given in a r teel e panteley and a loria math control signals systems 15 2002 pp 177 201 these summability criteria are not lyapunov based and they are tailored to be used within our above mentioned framework for stabilization of sampled data differential inclusions via their approximate discrete time models we believe that these tools will be a useful addition to the toolbox for controller design for sampled data nonlinear systems via their approximate discrete time models

sufficient conditions for stabilization of sampled data nonlinear systems via discrete time approximations given a parameterized by sampling period t family of approximate discrete time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all t sufficiently small we present conditions which guarantee that the same family of controllers semi globally practically stabilizes the exact discrete time model of the plant for sufficiently small sampling periods when the family of controllers is locally bounded uniformly in the sampling period the inter sample behavior can also be uniformly bounded so that the time varying sampled data model of the plant is uniformly semi globally practically stabilized the result justifies controller design for sampled data nonlinear systems based on the approximate discrete time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied our analysis is applicable to a wide range of time discretization schemes and general plant models

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

stability analysis of hybrid composite dynamical systems descriptions involving operators and differential equations we address the stability analysis of composite hybrid dynamical feedback systems of the type depicted in fig 1 consisting of a block usually the plant which is described by an operator l and of a finite dimensional block described by a system of ordinary differential equations usually the controller we establish results for the well posedness attractivity asymptotic stability uniform boundedness asymptotic stability in the large and exponential stability in the large for such systems the hypotheses of these results are phrased in terms of the i o properties of l and in terms of the lyapunov stability properties of the subsystem described by the indicated ordinary differential equations the applicability of our results is demonstrated by means of general specific examples involving c 0 semigroups partial differential equations or integral equations which determine l

controllability of nonlinear discrete time systems a lie algebraic approach this paper presents a geometric study of controllability for discrete time nonlinear systems various accessibility properties are characterized in terms of lie algebras of vector fields some of the results obtained are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

a framework for stabilization of nonlinear sampled data systems based on their approximate discrete time models a unified framework for design of stabilizing controllers for sampled data differential inclusions via their approximate discrete time models is presented both fixed and fast sampling are considered in each case sufficient conditions are presented which guarantee that the controller that stabilizes a family of approximate discrete time plant models also stabilizes the exact discrete time plant model for sufficiently small integration and or sampling periods previous results in the literature are extended to cover 1 continuous time plants modeled as differential inclusions 2 general approximate discrete time plant models 3 dynamical discontinuous controllers modeled as difference inclusions and 4 stability with respect to closed arbitrary not necessarily compact sets

an iterative finite difference method for solving bratu s problem in this paper we propose a new iterative finite difference ifd scheme based on the newton raphson kantorovich approximation method in function space to solve the classical one dimensional bratu s problem this new numerical method produces accurate solutions with low computational cost the effectiveness and accuracy of the ifd method are confirmed through several numerical examples and compared to some existing numerical solvers

uniform semiglobal practical asymptotic stability for non autonomous cascaded systems and applications it is due to the modularity they provide that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on adding integrators nevertheless the standing assumptions in most of the present literature on cascaded systems is that when decoupled the subsystems constituting the cascade are uniformly globally asymptotically stable ugas hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable uspas this situation is often encountered in control practice e g in control of physical systems with external perturbations measurement noise unmodelled dynamics etc after giving a rigorous framework for the analysis of such stability properties this paper generalizes previous results for cascades by establishing that under a uniform boundedness condition on its solutions the cascade of two uspas systems remains uspas an analogous result is derived for uniformly semiglobally asymptotically stable usas systems in cascade furthermore we show the utility of our results in the pid control of mechanical systems affected by unknown non dissipative forces and considering the dynamics of the dc motors

backstepping designs for the stabilisation of nonlinear sampled data systems via approximate discrete time model the problems of backstepping adaptive backstepping and reduced order observer based output feedback control of sampled data nonlinear systems in strict feedback form are considered controller design methods based on the euler approximate model are presented for these problems the controllers are designed to compensate the effects of the discrepancy between the euler approximate model and exact discrete time model parameter estimation error in adaptive control and observer error in output feedback control which behave as disturbance it is shown that the obtained controllers semi globally practically asymptotically stabilise the plant model under standard assumptions then numerical examples are given to illustrate the design methods

new smoother to enhance multigrid based methods for bratu problem abstract in this paper we present more investigations of the numerical solution of the 2d bratu equation to obtain the second solution on the upper branch by multigrid classical smoothers such as gauss seidel and weighted jacobi have proven ineffective for obtaining the second solution due to the loss of diagonal dominance and the presence of indefinite jacobian system at some parameter values in this paper we modify the multigrid algorithms by adding and combining some krylov methods as smoothers to enhance the multigrid efficiency though the idea is not new but we could get new enhanced results compared to that presented by hackbusch w hackbusch comparison of different multi grid variants for nonlinear equations zamm z angew math mech 72 1992 148 151 and washio and oosterlee t washio c w oosterlee krylov subspace acceleration for nonlinear multigrid schemes electron trans numer anal 6 1997 271 290

stabilization of sampled data nonlinear systems via backstepping on their euler approximate model two integrator backstepping designs are presented for digitally controlled continuous time plants in special form the controller designs are based on the euler approximate discrete time model of the plant and the obtained control algorithms are novel the two control laws yield respectively semiglobal practical stabilization and global asymptotic stabilization of the euler model both designs achieve semiglobal practical stabilization in the sampling period that is regarded as a design parameter of the closed loop sampled data system a simulation example illustrates that the obtained controllers may sometimes be superior to backstepping controllers based on the continuous time plant model that are implemented digitally

stability of homogeneous nonlinear systems with sampled data inputs abstract the main goal of this article is to use properties of homogeneous systems for addressing the problem of stability for a class of nonlinear systems with sampled data inputs this nonlinear strategy leads to several kinds of stability i e local asymptotic stability global asymptotic stability or global asymptotic set stability depending on the sign of the degree of homogeneity the results are illustrated with the case of the double integrator

backstepping control under multi rate sampling the paper deals with the design of sampled data controllers which preserve the stabilizing performance of a continuous time backstepping control strategy this is achieved through matching of the control lyapunov functions evolutions at the sampling instants the method is developed for systems in strict feedback form the results are discussed and compared with similar strategies through simulated examples

convex design of a robust antiwindup controller for an lft model in the context of a closed loop lft model an lmi technique is proposed for the synthesis of a static or dynamic antiwindup controller which can be seen as a nontrivial extension of existing lmi methods for designing a robust filter or feedforward controller a missile example is given to illustrate the feasibility of the technique

letter to the editor on the integral solution of the one dimensional bratu problem a brief survey of the properties and different treatments of the one dimensional 1d planar bratu problem is presented the treatment using green s function is considered different iterative treatments of the resulting nonlinear system of equations are discussed starting the solution with simple sinusoidal function having appropriate amplitude is recommended then the resulting system is solved using a nonlinear conjugate gradient nl cg method the importance of the proper choice of the starting function as well as the stopping criterion of the iterative solution are stressed

sampled data adaptive nn tracking control of uncertain nonlinear systems in this paper for a class of single input single output siso uncertain nonlinear systems adaptive neural tracking controllers designed for digital computer implementation are proposed the overall scheme can be considered as a sampled data adaptive neural control system as an intermediate result it is proven that for a sufficiently small sampling period the emulated adaptive neural controller i e the discrete implementation of the continuous time adaptive neural network controller ensures semiglobal uniformly ultimate boundedness of the closed loop system then based on the exact discrete time model a controller redesign is proposed that performs efficiently for sampling periods for which the emulation controller fails the redesigned controller consists of two terms the emulated control law and an extra robustness term designed to increase the order of the perturbation with respect to the sampling period in the lyapunov difference in all cases high order neural networks are employed to approximate the unknown nonlinearities using lyapunov techniques it is proven that for a sufficiently small sampling period the proposed redesigned controller ensures the semiglobal boundedness of all the signals in the closed loop while the output of the system converges to a small neighborhood of the desired trajectory simulation results illustrate the superiority of the proposed scheme with respect to the emulation controller and verify the theoretical analysis

brief on exponential stability of nonlinear time varying differential equations within the liapunov framework a sufficient condition for exponential stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the liapunov function taken along solutions of the system may have positive and negative values verification of the conditions of the main theorem may be harder than in the classical case it is shown that the proposed conditions are useful for the investigation of the exponential stability of fast time varying systems this sets the stability study by means of averaging in a liapunov context in particular it is established that exponential stability of the averaged system implies exponential stability of the original fast time varying system a comparison of our work with results taken from the literature is included

control of rational systems using linear fractional representations and linear matrix inequalities abstract every system of the form x f x u y g x u where f and g are rational functions of the state x and linear functions of the input u possesses a linear fractional representation lfr in this lfr the system is viewed as an lti system connected with a diagonal feedback element linear in the state we devise an algorithm for computing lfrs based on this construction we give sufficient conditions for various properties to hold for the open loop system these include checking whether a given polytope is stable finding a lower bound on the decay rate of trajectories initiating in this polytope computing an upper bound on the l2 gain etc all these conditions are obtained by analyzing the properties of a differential inclusion related to the lfr and given as convex optimization problems over linear matrix inequalities lmis we show how to use this approach for static state feedback synthesis we then generalize the results to dynamic output feedback synthesis in the case when f and g are linear in every state coordinate that is not measured extensions towards a class of nonrational and uncertain nonliner systems are discussed

an eigenvalue condition for sampled weak controllability of bilinear systems abstract weak controllability of bilinear systems is preserved under sampling provided that the sampling period satisfies a condition related to the eigenvalues of the autonomous dynamics matrix this condition generalizes the classical kalman ho narendra criterion which is well known in the linear case

brief paper a discrete time observer design for spacecraft attitude determination using an orthogonality preserving algorithm this paper studies a nonlinear discrete time partial state observer design problem for rigid spacecraft systems particularly for spacecraft attitude estimation the construction is inspired by an orthogonality preserving numerical algorithm and it yields a semiglobal practical asymptotic observer we show that the separation principle holds and hence stabilization using output feedback is possible an example is provided to illustrate the usefulness of our results in a sampled data implementation of an attitude control for a rigid spacecraft using output feedback and to illustrate the advantages of the proposed observer design especially compared to a sample and hold version of a similar type observer designed in continuous time

sufficient lmi stability conditions for lur e type systems governed by a control law designed on their euler approximate model in this paper the stability issue of lur e systems governed by a control law stabilising their forward euler approximate model is investigated more specifically the considered control law is obtained by exploiting the advantages of a new lur e type lyapunov function with disconnected level sets this lyapunov function is adapted to discrete time lur e systems and to the structure of the forward euler approximate model the main result consists of linear matrix inequality conditions allowing to guarantee that the continuous time lur e system associated with the proposed digital control law is globally asymptotically stable the relevance of this approach is illustrated using a numerical example

antiwindup for stable linear systems with input saturation an lmi based synthesis this paper considers closed loop quadratic stability and l sub 2 performance properties of linear control systems subject to input saturation more specifically these properties are examined within the context of the popular linear antiwindup augmentation paradigm linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification called the unconstrained closed loop behavior building on known results on h sub spl infin and lpv synthesis the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem which has an attractive system theoretic interpretation the lower bound on the achievable l sub 2 performance is the maximum of the open and unconstrained closed loop l sub 2 gains in the special cases of zero order static and plant order antiwindup compensation the feasibility conditions become convex linear matrix inequalities it is shown that if and only if the plant is asymptotically stable plant order linear antiwindup compensation is always feasible for large enough l sub 2 gain and that static antiwindup compensation is feasible provided a quasi common lyapunov function between the open loop and unconstrained closed loop exists using the solutions to the matrix feasibility problems the synthesis of the antiwindup augmentation achieving the desired level of l sub 2 performance is then accomplished by solving an additional lmi

new perturbation iteration solutions for bratu type equations perturbation iteration theory is systematically generated for both linear and nonlinear second order differential equations and applied to bratu type equations different perturbation iteration algorithms depending upon the number of taylor expansion terms are proposed using the iteration formulas derived using different perturbation iteration algorithms new solutions of bratu type equations are obtained solutions constructed using different perturbation iteration algorithms are contrasted with each other as well as with numerical solutions it is found that algorithms with more taylor series expansion terms yield more accurate results

formulas relating kl stability estimates of discrete time and sampled data nonlinear systems abstract we provide an explicit kl stability or input to state stability iss estimate for a sampled data nonlinear system in terms of the kl estimate for the corresponding discrete time system and a k function describing inter sample growth it is quite obvious that a uniform inter sample growth condition plus an iss property for the exact discrete time model of a closed loop system implies uniform iss of the sampled data nonlinear system our results serve to quantify these facts by means of comparison functions our results can be used as an alternative to prove and extend results in 1 or extend some results in 4 to a class of nonlinear systems finally the formulas we establish can be used as a tool for some other problems which we indicate

on uniform global asymptotic stability of nonlinear discrete time systems with applications this paper presents new characterizations of uniform global asymptotic stability for nonlinear and time varying discrete time systems under mild assumptions it is shown that weak zero state detectability is equivalent to uniform global asymptotic stability for globally uniformly stable systems by employing the notion of reduced limiting systems another characterization of uniform global asymptotic stability is proposed on the basis of the detectability for the reduced limiting systems associated with the original system as a by product we derive a generalized discrete time version of the well known krasovskii lasalle theorem for general time varying not necessarily periodic systems furthermore we apply the obtained stability results to analyze uniform asymptotic stability of cascaded time varying systems and show that some technical assumptions in recent papers can be relaxed through a practical application it is shown that our results play a similar role to the classic lasalle invariance principle in guaranteeing attractivity noting that reduced limiting systems are used instead of the original system to validate the conceptual characterizations we study the problem of sampled data stabilization for the benchmark example of nonholonomic mobile robots via the exact discrete time model rather than approximate models this case study also reveals that in general sampled data systems may become non periodic even though their original continuous time system is periodic a novel sampled data stabilizer design is proposed using the new stability results and is supported via simulation results

preservation of input to state stability under sampling and emulation multi rate case the stabilization problem of sampled data non linear systems is considered under the low measurement rate constraint a multi rate control scheme is proposed that utilizes a numerical integration scheme to approximately predict the current state we show that if we design a continuous time controller for a continuous time plant so that the closed loop continuous time system is input to state stable and then discretize the controller and implement it using sample and zero order hold devices then input to state stability property will be preserved for the sampled data multi rate closed loop system in a practical sense

getting robustness against unstructured uncertainty a tube based mpc approach this note extends tube based model predictive control to the control of nonlinear systems with unmodeled dynamics the problem of obtaining robustness against unstructured uncertainty is converted into the easier problem of achieving robustness against an additional bounded disturbance while satisfying an additional output constraint the output constraint depends on the maximum l gain of the unstructured dynamics

self triggering under state independent disturbances this note extends the prior work in l2 stability of self triggered feedback systems where the next task release time and finishing time are predicted based on the sampled states a self triggering scheme is proposed which relaxes the assumption in the prior work that the magnitude of the process noise is bounded by a linear function of the norm of the system state we show that the sample periods generated by this scheme are always greater than a positive constant we also provide state based deadlines for delays and propose a way that may enlarge those deadlines without breaking l2 stability

a new approach to bratu s problem in this paper a laplace transform decomposition numerical algorithm is introduced for solving bratu s problem the numerical scheme is based on the application of laplace transform integral operator to the differential equation the nonlinear term is then decomposed and an iterative algorithm is constructed for the determination of the infinite series solution the technique is illustrated with two numerical examples and the results show that the method converges rapidly and approximates the exact solution very accurately using only few iterates of the recursive scheme

anti windup design for saturating quadratic systems abstract this paper proposes an anti windup design method for systems which contain two sources of nonlinearities namely actuator saturation and a quadratic nonlinearity two classes of systems are considered 1 the saturation nonlinearity is additive to the quadratic nonlinearity 2 the saturation nonlinearity is multiplicative of a state dependent matrix a nonlinear dynamic inversion controller is augmented with an anti windup compensator the design of the anti windup compensator is carried out in order to enlarge the region of attraction in the subspace of the plant variables from theoretical conditions some convex optimization problems are proposed to compute the gains of the anti windup compensator numerical examples illustrate the effectiveness of the proposed technique

matrosov theorem for parameterized families of discrete time systems a version of matrosov s theorem for parameterized discrete time time varying systems is presented the theorem is a discrete time version of the continuous time result in loria et al 2002 d persistency of excitation a necessary and sufficient condition for uniform attractivity 2002 submitted for publication our result facilitates controller design for sampled data nonlinear systems via their approximate discrete time models an application of the theorem to establishing uniform asymptotic stability of systems controlled by model reference adaptive controllers designed via approximate discrete time plant models is presented

lpv control and full block multipliers a novel construction of linear parameter varying controllers is presented for arbitrarily fast parameter variations it is shown how full block multipliers allow to considerably reduce conservatism various auxiliary results of independent interest are included

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

a new asymptotic stability criterion for nonlinear time variant differential equations a new sufficient condition for asymptotic stability of ordinary differential equations is proposed unlike classical lyapunov theory the time derivative along solutions of the lyapunov function may have positive and negative values the classical lyapunov approach may be regarded as an infinitesimal version of the present theorem verification in practical problems is harder than in the classical case an example is included in order to indicate how the present theorem may be applied

input output stability of sampled data systems the authors study the l sub p input output stability of a continuous time controller using the usual arrangement of periodic sampling and zero order hold it is noted that even if the hybrid system is exponentially stable this arrangement does not yield l sub p 1

stability analysis of discrete time infinite horizon optimal control with discounted cost we analyze the stability of general nonlinear discrete time systems controlled by an optimal sequence of inputs that minimizes an infinite horizon discounted cost first assumptions related to the controllability of the system and its detectability with respect to the stage cost are made uniform semiglobal and practical stability of the closed loop system is then established where the adjustable parameter is the discount factor stronger stability properties are thereupon guaranteed by gradually strengthening the assumptions next we show that the lyapunov function used to prove stability is continuous under additional conditions implying that stability has a certain amount of nominal robustness the presented approach is flexible and we show that robust stability can still be guaranteed when the sequence of inputs applied to the system is no longer optimal but near optimal we also analyze stability for cost functions in which the importance of the stage cost increases with time opposite to discounting finally we exploit stability to derive new relationships between the optimal value functions of the discounted and undiscounted problems when the latter is well defined

controlling nonlinear time varying systems via euler approximations abstract a discrete time model reference control algorithm for continuous time systems represented by essentially unknown nonlinear time varying ordinary differential equations is presented and analysed provided the reference model and the inverse dynamics of the plant are bounded input bounded output stable it is shown that a discrete control using state measurements based on euler approximations for the systems response can achieve arbitrary tracking accuracy the effect of unmodelled dynamics and disturbances is analysed