h sup spl infin control for linear time varying systems controller parameterization in this correspondence the h sup spl infin control problem is studied for finite dimensional linear time varying fdltv systems state space formulas are derived for all fdltv controllers solving the problem these controllers are parameterized by the interconnection of the central controller with an exponentially stable free system having h sup spl infin norm strictly less than spl gamma our approach is drawn from some changes of variables a time varying version of a strict bounded real lemma and youla parameterization thus the proofs given are simple and clear

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

linear discrete time h sub spl infin optimal tracking with preview the problem of finite time h sub spl infin tracking for linear discrete time varying systems is considered no a prior knowledge of the dynamics of the reference signal is assumed a distinction between three cases is made depending on whether the reference signal is perfectly known in advance measured online or previewed in a fixed interval of time ahead the tracking problem is formulated as a game where the controller plays against nature which may choose the initial condition or the system and any energy bounded driving disturbance and measurement noise inputs necessary and sufficient conditions are derived for the existence of saddle point equilibrium solutions to the three different information structures of the reference and the corresponding tracking controllers are derived

robust state estimation for uncertain systems with averaged integral quadratic constraints this paper considers a robust state estimation problem for a new class of uncertain systems the new uncertainty class introduced in the paper involves structured uncertainties which are required to satisfy a certain averaged integral quadratic constraint this uncertainty class combines aspects of norm bounded and stochastic uncertainty descriptions the solution to the robust state estimation problem is obtained by solving a parametrized riccati differential equation of the game type

multiobjective boldmath ht hf control design an important question in feedback control design is how to achieve desired performance for dynamical systems subject to both model uncertainties and white noise for this purpose it is desirable to develop a systematic design technique that combines the good aspects of both cal h 2 lqg and cal h infty methods which provides the motivation for the development of multiobjective design framework in this paper encouraged by a time domain game approach for cal h 2 cal h infty control design two multiobjective control design problems are formulated and solved in the time domain results for both the finite time horizon and the infinite time horizon are presented it is shown that all the results can be obtained by solving the corresponding set of coupled riccati equations

brief h performance of preview control systems performance of the preview control is investigated in terms of h criterion in the infinite horizon time setting the limitation of h performance in preview control action is characterized with the hamiltonian matrix by employing the property of hamiltonian matrix the solvability and analytic solution for the preview full information control problem are clarified based on an auxiliary introduced matrix riccati equation the property of resulting control law is illustrated with a numerical example

h output feedback control for linear discrete time varying systems via the bounded real lemma in this paper we develop a solution to the discrete time output feedback control problem for linear time varying ltv systems the solution is developed along the strategy set up by doyle et al in 1989 and the main ingredient in its derivation is the extension of the well known bounded real lemma to a discrete time varying context developed by van der veen and verhaegen in 1995 this approach contributes to the conceptual simplicity and hence to the accessibility of the solution apart from that we treat the infinite horizon case for ltv system of non uniform state dimension and varying input and output dimension both situations can easily occur in practice for example in multirate sampled data control systems the algorithm that can be derived from the solution presented in then applied to the output feedback of a dynamical system changing from one operation point in its operation envelope to another

recursive state estimation for uncertain systems with an integral quadratic constraint this paper considers a robust state estimation problem for a class of uncertain systems where the noise and uncertainty are modeled deterministically via an integral quadratic constraint the robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint

h sup spl infin control and estimation with preview part i matrix are solutions in continuous time preview control and fixed lag smoothing allow a noncausal component in the controller estimator time domain variational analysis is used in a reduction to an open loop differential game leading to a complete necessary and sufficient characterization of suboptimal values and an explicit state space design in terms of a parameterized nonstandard algebraic matrix riccati equation in a general continuous time linear system setting the solution offers insight into the appropriate structure of the associated hamiltonian where the state and co state are not the usual state of the original dynamic system and that of its adjoint rather the state and co state are selected to capture the respective lumped effects of initial data and future input selection in the allied game

global solutions to a game theoretic riccati equation of stochastic control abstract in this paper the existence of global solutions to game theoretic riccati equations associated to a controlled stochastic differential equation with state dependent white noise is investigated one proves that if a stabilizing and attenuating feed back exists then a matrix differential game theoretic riccati equation of stochastic control has a unique global bounded stabilizing positive semidefinite solution this solution is periodic if the coefficients are periodic functions and it solves an algebraic riccati equation if the coefficients are constant conversly if such a solution exists it allows an explicit construction of a stabilizing and disturbance attenuating state feedback

h sub spl infin differential riccati equations convergence properties and finite escape phenomena the paper studies the transient and asymptotic behavior of the solution of the sign indefinite differential riccati equation dre arising in finite horizon h sub spl infin filtering and control problems differently from the sign definite h sub spl infin dre the solution of the h sub spl infin dre can have finite escape times even for nonnegative initial conditions sufficient and necessary conditions for boundedness and convergence are derived in correspondence to a fixed value of the h sub spl infin norm attenuation level spl gamma finally a stepwise spl gamma switching strategy is devised to guarantee boundedness as well as asymptotic performance

robust spl hscr sub spl infin filtering for continuous time varying uncertain systems with deterministic input signals many dynamical systems involve not only process and measurement noise signals but also parameter uncertainty and known input signals when spl lscr sub 2 or spl hscr sub spl infin filters that were designed based on a nominal model of the system are applied the presence of parameter uncertainty will not only affect the noise attenuation property of the filter but also introduce a bias proportional to the known input signal and the latter may be very appreciable we introduce a finite horizon robust spl hscr sub spl infin filtering method that provides a guaranteed spl hscr sub spl infin bound for the estimation error in the presence of both parameter uncertainty and a known input signal this method is developed by using a game theoretic approach and the results generalize those obtained for cases without parameter uncertainty or without a known input signal it is also demonstrated via an example that the proposed method provides significantly improved signal estimates

fourth order iterative methods free from second derivative in this paper we present a family of new iterative methods with order of convergence four for solving non linear equations per iteration these methods require one evaluation of the function and two of its first derivative analysis of efficiency in term of function evaluations shows that this family of methods has great superiority which is also demonstrated by numerical examples

intervalwise receding horizon h sub spl infin tracking control for discrete linear periodic systems in this paper a fixed horizon h sub spl infin tracking control htc for discrete time varying systems is obtained in a state feedback form from the htc an intervalwise receding horizon htc ihtc is suggested for discrete periodic systems conditions are proposed under which ihtc can stabilize a closed loop system it is shown that under these conditions ihtc guarantees an h sub spl infin norm bound and that ihtc with integral action provides zero offset for a constant command signal the performance of ihtc is compared with those of existing controls via an example the results in this paper are also applicable to time invariant systems which belong to the class of periodic systems

the finite horizon singular h control problem with dynamic measurement feedback this paper is concerned with the finite horizon version of the h problem with measurement feedback given a finite dimensional linear time varying system together with a positive real number we obtain necessary and sufficient conditions for the existence of a possibly time varying dynamic compensator such that the l2 0 t1 induced norm of the closed loop operator is smaller than these conditions are expressed in terms of a pair of quadratic differential inequalities generalizing the well known riccati differential equations introduced recently in the context of finite horizon h control

equivariant gysin maps and pulling back fixed points we develop a new approach to the pulling back fixed points theorem of w browder and use it in order to prove various generalizations of this result

robust stochastic maximum principle for multi model worst case optimization this paper develops a version of the robust maximum principle applied to the minimax mayer problem formulated for stochastic differential equations with a control dependent diffusion term the parametric families of first and second order adjoint stochastic processes are introduced to construct the corresponding hamiltonian formalism the hamiltonian function used for the construction of the robust optimal control is shown to be equal to the sum of the standard stochastic hamiltonians corresponding to each possible value of the parameter the cost function is defined on a finite horizon and contains the mathematical expectation of a terminal term a terminal condition given by a vector function is also considered the optimal control strategies adapted for available information for the wide class of multi model systems given by a stochastic differential equation with parameters from a given finite set are constructed this problem belongs to the class of minimax stochastic optimization problems the p

on the h 2 two sided model matching problem with preview the h2 optimization problem with preview and asymptotic behavior constraints is considered in a general two sided model matching setting the solution is obtained in terms of two constrained sylvester equations associated with asymptotic behavior and stabilizing solutions of two algebraic riccati equations the riccati equations do not depend on the preview length yet are affected by asymptotic behavior constraints and are thus different from the standard h2 riccati equations arising in problems with no steady state requirements or in one sided problems

h filtering for a class of uncertain nonlinear systems abstract this paper investigates the problem of h filtering for a class of uncertain continuous time nonlinear systems with real time varying parameter uncertainty and unknown initial state we develop an infinite horizon h filtering methodology which provides both robust stability and a guaranteed h performance for the filtering error irrespective of the parameter uncertainty

h norm computation for ltv systems using nonlinear optimal control algorithms we discuss the computation for 2 induced norms of finite horizon linear time varying systems it is well known that 2 induced norm calculating problems can be converted into optimal control problems so with the help of optimal control algorithms we propose a numerical technique for 2 induced norm computation our approach is as follows first we present a new computational method for nonlinear optimal control problems that is numerically reliable stable and robust analysing the convergence property under some assumptions next by modifying the presented method we propose an algorithm for the 2 induced norm calculation of finite horizon linear time varying systems which is essentially different from all other existing methods finally the effectiveness of our algorithm is demonstrated by simulation

some variants of cauchy s method with accelerated fourth order convergence in this paper we present some variants of cauchy s method for solving non linear equations analysis of convergence shows that the methods have fourth order convergence per iteration the new methods cost almost the same as cauchy s method numerical results show that the methods can compete with cauchy s method

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

h sup spl infin optimal control for singularly perturbed systems ii imperfect state measurements for pt i see ibid vol 29 no 2 p 401 423 1993 in this paper we study the h sup spl infin optimal control of singularly perturbed linear systems under general imperfect measurements for both finite and infinite horizon formulations using a differential game theoretic approach we first show that as the singular perturbation parameter say spl epsiv 0 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 and in some cases equal to the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions with the bound being computable independently of e and knowing only the slow and fast dynamics of the system we then construct a controller based on the slow subsystem only and obtain conditions under which it delivers a desired performance level even though the fast dynamics are completely neglected the ultimate performance level achieved by this slow controller can be uniformly improved upon however by a composite controller that uses some feedback from the output of the fast subsystem we construct one such controller via a two step sequential procedure which uses static feedback from the fast output and dynamic feedback from an appropriate slow output each one obtained by solving appropriate spl epsiv independent lower dimensional h sup spl infin optimal control problems under some informational constraints we provide a detailed analysis of the performance achieved by this lower dimensional spl epsiv independent composite controller when applied to the full order system and illustrate the theory with some numerical results on some prototype systems

linear estimation in krein spaces i theory the authors develop a self contained theory for linear estimation in krein spaces the derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between krein space projection and the recursive computation of the stationary points of certain second order or quadratic forms the authors use the innovations process to obtain a general recursive linear estimation algorithm when specialized to a state space structure the algorithm yields a krein space generalization of the celebrated kalman filter with applications in several areas such as h sup spl infin filtering and control game problems risk sensitive control and adaptive filtering

optimal and robust noncausal filter formulations the paper describes an optimal minimum variance noncausal filter or fixed interval smoother the optimal solution involves a cascade of a kalman predictor and an adjoint kalman predictor a robust smoother involving h sub spl infin predictors is also described filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error these bounds lead to a priori estimates for the scalar spl gamma in the h sub spl infin filter and smoother design the results of simulation studies are presented which demonstrate that optimal robust and extended kalman smoothers can provide performance benefits

sampled data h optimal control of time varying systems the sampled data h optimal control problem is studied for time varying systems the problem consists of finding all sampled data controllers with a piece wise constant control signal for which the l2 induced norm from the continuous time disturbance to the continuous time output is less than a specified bound a game theoretic approach is used to obtain a complete solution to the problem in the finite horizon time varying case the solution involves a mixed discrete continuous riccati equation and a variable transformation which takes the problem to a standard discrete finite dimensional h filtering problem

a game theoretic approach to a finite time disturbance attenuation problem a disturbance attenuation problem over a finite time interval is considered by a game theoretic approach where the control restricted to a function of the measurement history plays against adversaries composed of the process and measurement disturbances and the initial state a zero sum game formulated as a quadratic cost criterion subject to linear time varying dynamics and measurements is solved by a calculus of variation technique by first maximizing the quadratic cost criterion with respect to the process disturbance and initial state a full information game between the control and the measurement residual subject to the estimator dynamics results the resulting solution produces an n dimensional compensator which expresses the controller as a linear combination of the measurement history a disturbance attenuation problem is solved based on the results of the game problem for time invariant systems it is shown that under certain conditions the time varying controller becomes time invariant on the infinite time interval the resulting controller satisfies an h sub infinity norm bound

feedforward control a full information approach the design of the feedforward part of a two degree of freedom controller is recast as a full information synthesis problem

convergence of the variants of the chebyshev halley iteration family under the holder condition of the first derivative the present paper is concerned with the convergence problem of the variants of the chebyshev halley iteration family with parameters for solving nonlinear operator equations in banach spaces under the assumption that the first derivative of the operator satisfies the holder condition of order p a convergence criterion of order 1 p for the iteration family is established an application to a nonlinear hammerstein integral equation of the second kind is provided

optimal tracking performance preview control and exponential signals we study tracking performance limitation problems two issues are addressed concerning how earlier results developed elsewhere may be extended to more general classes of reference signals and how tracking performance may be further improved beyond that offered by feedback control toward these issues we consider exponentially increasing reference inputs and examine the use of preview control for tracking using an optimal interpolation approach we develop analytical expressions and a conceptual insight which will aid in the understanding of these issues to this effect we derive explicit expressions for the optimal tracking error either as exact solutions or bounds it is found that for the exponential signals the earlier results can be directly extended and similar conclusive statements can be drawn it is also shown that in general preview can be used to advantage for improving tracking performance especially in dealing with the effect resulted from plant nonminimum phase zeros

product of nonnegative operators and infinite dimensional h riccati equations in this paper we collect some useful properties of the product of nonnegative operators in a hilbert space we then apply them to the standard h control problem for infinite dimensional time varying systems and give necessary and sufficient conditions for the existence of a suboptimal controller by three conditions involving two independent riccati equations with a coupling inequality

continuous time tracking problems in an h sub spl infin setting a game theory approach this paper investigates the problem of finite horizon h sub spl infin tracking for linear time varying systems three tracking problems are considered depending on whether the reference signal is perfectly known in advance measured on line or previewed in fixed interval of time ahead no a priori knowledge of a dynamic model for the reference signal is assumed a game theory approach to the latter tracking problems is presented where given a specific reference signal the controllers play against nature which can choose any initial state and any bounded energy disturbance input and measurement noise necessary and sufficient conditions for the existence of a saddle point equilibrium are determined and h sub spl infin tracking controllers for both the cases of state and output feedback are derived tracking problems for time invariant systems on infinite horizon are also analyzed and time invariant tracking controllers are obtained for zero initial conditions

h control of nonlinear time varying systems with finite time horizon the finite time horizon h control problems for nonlinear time varying systems are considered where the initial state is unknown they are solved by using both static state feedback and dynamic output feedback controllers a class of nonlinear h controllers is parameterized as nonlinear fractional transformation on contractive nonlinear parameters the solvability for nonlinear finite time horizon h control problem requires suitable solutions to some hamilton jacobi inequalities equations

a feedback theory of two degree of freedom optimal wiener hopf design the design of linear two degree of freedom stabilizing controllers is treated in a quadratic cost setting the class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance tracking cost sensitivity and stability margins is discussed

a modification of the super halley method under mild differentiability conditions a new two point iteration of order three is introduced to approximate a solution of a nonlinear operator equation in banach spaces under the same assumptions as for newton s method we provide a result on the existence of a unique solution for the nonlinear equation which is based on a technique consisting of a new system of recurrence relations

a dynamic games approach to controller design disturbance rejection in discrete time it is shown that the discrete time disturbance rejection problem formulated in finite and infinite horizons and under perfect state measurements can be solved by making direct use of some results on linear quadratic zero sum dynamic games for the finite horizon problem an optimal minimax controller exists and can be expressed in terms of a generalized time varying discrete time riccati equation the existence of an optimum also holds in the infinite horizon case under an appropriate observability condition with the optimal control given in terms of a generalized algebraic riccati equation also being stabilizing in both cases the corresponding worst case disturbances turn out to be correlated random sequences with discrete distributions which means that the problem viewed as a dynamic game between the controller and the disturbance does not admit a pure strategy saddle point results for the delayed state measurement and the nonzero initial state cases are presented

state feedback h_ infty control for a class of nonlinear stochastic systems this paper discusses the h infty control problem for a class of nonlinear stochastic systems with both state and disturbance dependent noise by means of hamilton jacobi equations both infinite and finite horizon nonlinear stochastic h infty control designs are developed some results on nonlinear h infty control of deterministic systems are generalized to a stochastic setting we introduce some useful concepts such as zero state observability and zero state detectability which together with the stochastic lasalle invariance principle yield some valuable consequences in infinite horizon nonlinear stochastic h infty control

permutation complexes and modular representation theory hc g o iti has two basic functors a rg 2 di rh and a rh 2 rg given by restriction and induction which play an essential role in representation theory an important and elementary class of rg representations is permutation modules which are direct sums of modules indz r obtained by induction from the trivial rh module r for various hs g in another extreme one has rg modules which arise by induction from rh projective modules leading to the concept of relative projectivity and green s theory of vertices and sources cr gr the value of these subcategories of modules in representation theory and related areas is well known in a different direction influenced by algebraic geometry and topology one considers not only module categories but various categories of chain complexes of modules and their cohomologies this culminates in the more recent approaches to representation theory through the theory of derived categories see sc cps and their many references

robust maximum principle for multi model lq problem this paper presents the version of the robust maximum principle in the context of multi model control formulated as the minimax bolza problem the cost function contains a terminal term as well as an integral one a fixed horizon and terminal set are considered the necessary conditions of the optimality are derived for the class of uncertain systems given by an ordinary differential equation with parameters from a given finite set this problem consists in the control design providing a good behaviour for a given class of multi model system it is shown that the design of the minimax optimal controller is reduced to a finite dimensional optimization problem given at the corresponding simplex set containing the weight parameters to be found the robust optimal control may be interpreted as a mixture with the optimal weights of the controls which are optimal for each fixed parameter value the proof is based on the recent results obtained for minimax mayer problem boltyanski and poznyak 1999a the mini

convergence of the family of the deformed euler halley iterations under the holder condition of the second derivative the convergence problem of the family of the deformed euler halley iterations with parameters for solving nonlinear operator equations in banach spaces is studied under the assumption that the second derivative of the operator satisfies the holder condition a convergence criterion of the order 2 p of the iteration family is established an application to a nonlinear hammerstein integral equation of the second kind is provided

stochastic h sub spl infin tracking with preview for state multiplicative systems the problem of finite horizon h sub spl infin tracking for linear time varying systems with stochastic parameter uncertainties is investigated we consider three tracking patterns depending on the nature of the reference signal i e whether it is perfectly known in advance measured on line or previewed in a fixed time interval ahead the stochastic uncertainties appear in both the dynamic and measurement matrices of the system for each of the above three cases a game theory approach is applied for the state feedback case where given a specific reference signal the controller plays against nature which chooses the initial condition and the energy bounded disturbance the problems are solved using an expected value of the standard performance index over the stochastic parameters where necessary and sufficient conditions are found for the existence of a saddle point equilibrium the infinite horizon time invariant tracking problem is also solved the theory developed is demonstrated by a simple tracking example

the jarratt method in banach space setting abstract in this note we extend the jarratt method of order four into banach spaces we also establish a kantorovich type convergence theorem see the references and give an explicit expression for the error bound of the method jarratt 1966 1969

game theory approach to optimal linear state estimation and its relation to the minimum h sub infinity norm estimation a possible game theory approach to optimal state estimation is presented it is found that in a certain differential game the minimizer s policy is identical to the one obtained by optimal estimation in the minimum h sub infinity norm sense this interpretation of h sub infinity optimal state estimation provides better insight into the mechanism of h sub infinity optimal filtering especially in the case where the exogenous signals are not energy bounded

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

quadratic stabilization with an h performance bound of uncertain linear time varying systems in this paper we deal with linear time varying systems subject to uncertain parameters in the so called one block norm bounded form we consider the problem of designing a controller which guarantees the quadratic stabilization of the closed loop system while keeping the norm of the operator mapping the exogenus input to the controlled output under a prespecified level necessary and sufficient conditions for the existence of such a controller are given

two degree of freedom h sub infinity optimization of multivariable feedback systems a solution to the two degree of freedom h sub infinity minimization problem that arises in the design of multivariable optimal continuous time stochastic control systems is derived a decoupling approach that enables a partially independent design of the prefilter and the feedback controller and yields a simple solution to the optimization problem is applied this solution is obtained by transforming the optimization problem into two standard form four block problems

pulling back fixed points if x y are g spaces spaces on which a compact lie group g acts and f x y is a g map then the image of a fixed point in x is fixed in i1 when does the inverse image of a fixed point contain a fixed point in particular if x y are g manifolds and f has degree prime to gi order of g in unpublished work of the author1 this is shown for elementary abelian p groups with x y more general spaces n near manifolds in this paper we show that this is true for abelian p groups g acting smoothly on x with p odd or with p 2 with an additional complex hypothesis we give a counterexample for nonabelian g the method is to prove a generalization of a theorem of bredon 1973 for 7lip actions which says that maps of degree prime to p induce injections on the mod p cohomology of the fixed set we generalize this theorem to abelian p groups where the action on x is smooth and p 4 2 or other hypothesis this seems to be new even in the case of elementary abelian p groups of rank 1 we actually prove a stronger theorem for a generalization of the notion of degree which may be non zero for maps between manifolds of different dimension the proof involves complex linear equivariant k theory in an essential way which requires smoothness and p 2 or a complexity hypothesis on x in order to produce the appropriate complex linear bundles among the corollaries we show that an abelian p group p odd cannot act smoothly on a closed manifold with exactly one isolated fixed point generalizing an old result of atiyah and bott 1964 for g z p this was found independently by ewing and stong 1986 by a different argument i am indebted to ib madsen for his comments in particular for discussions on equivariant k theory thanks are due also to michael davis for carefully reading the manuscript and pointing out several difficulties i also wish to thank the referee for his comments

a new parametrization of h suboptimal controllers elementary state space concepts are used to derive a transparent solution to the h control problem on an infinite horizon the main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric riccati equations with a coupling constraint unlike the classical parametrization in terms of linear fractional transformation this state space representation has a homogeneous riccati formulation which should help to make the most of the suboptimal controller diversity potential applications include the design of reduced order controllers and more generally the selection of suboptimal controllers to meet or optimize additional constraints

h optimal terminal state control for linear systems with lumped and distributed time delays in this paper we consider a linear time varying system whose state equation is affected by time delays and subject to unknown square integrable disturbances using a differential games approach we provide a necessary and sufficient condition for the existence of an optimal control law minimizing the h norm of the operator mapping the disturbance to the weighted control and terminal state an example which illustrates the proposed technique is also provided at the end of the paper

finite subgroups of ham and symp let x omega be a compact symplectic manifold of dimension 2n and let text ham x omega be its group of hamiltonian diffeomorphisms we prove the existence of a constant c depending on x but not on omega such that any finite subgroup g subset text ham x omega has an abelian subgroup a subseteq g satisfying g a le c and a can be generated by n elements or fewer if b 1 x 0 we prove an analogous statement for the entire group of symplectomorphisms of x omega if b 1 x ne 0 we prove the existence of a constant c depending only on x such that any finite subgroup g subset text symp x omega has a subgroup n subseteq g which is either abelian or 2 step nilpotent and which satisfies g n le c these results are deduced from the classification of the finite simple groups the topological rigidity of hamiltonian loops and the following theorem which we prove in this paper let e be a complex vector bundle over a compact connected smooth and oriented manifold m suppose that the real rank of e is equal to the dimension of m and that langle e e m rangle ne 0 where e e is the euler class of e then there exists a constant c such that for any prime p and any finite p group g acting on e by vector bundle automorphisms preserving an almost complex structure on m there is a subgroup g 0 subseteq g satisfying m g 0 ne emptyset and g g 0 le c

risk sensitive estimation and a differential game a large deviation result is employed to solve the state estimation problem of a continuous time gauss markov system with an exponential cost the exponential cost is the expected value of an exponential function of the state estimation error a scalar spl theta appearing in the cost termed as the risk factor determines the penalty on the higher order moments of the error in contrast to the minimum variance estimate penalty on large deviations of the estimation error is possible

h sub infinity control and filtering for sampled data systems h sub infinity control and filtering problems for sampled data systems are studied necessary and sufficient conditions are obtained for the existence of controllers and filters that satisfy a specified h sub infinity performance bound when these conditions hold explicit formulas for a controller and a filter satisfying the h sub infinity performance bound are also given

robust h sub spl infin output feedback control for nonlinear systems in this paper we present a new approach to the solution of the output feedback robust h sub spl infin control problem we employ the recently developed concept of information state for output feedback dynamic games and obtain necessary and sufficient conditions for the solution to the robust control problem expressed in terms of the information state the resulting controller is an information state feedback controller and is intrinsically infinite dimensional stability results are obtained using the theory of dissipative systems and our results are expressed in terms of dissipation inequalities

a variational approach to spl hscr sup spl infin control with transients this paper presents a variational approach to spl hscr sup spl infin control with transients in the state feedback case the approach here provides a precise description with equality instead of inequality in the necessary and sufficient conditions for the existence of a linear controller furthermore the solution existence and uniqueness are proved in terms of certain properties of the indefinite riccati equations derived in this paper the linear time variant ltv plant on finite horizon is considered first and then the results are extended to the linear time invariant lti plant on the infinite horizon by this approach it can be directly concluded that only suboptimal spl hscr sup spl infin state feedback control can be achieved in an input output point of view and that the performance measure spl gamma spl mu sup 1 2 used in this paper is a strict upper bound

characterization of ℋ index for linear time varying systems the increasing interest in index in fault detection has led to some recent development in time domain investigation this paper at first presents a necessary and sufficient condition of the index in finite time horizon for linear time varying systems it is shown that the feasibility of the index which is given when the index is greater than a predefined value is equivalent to the existence of a certain backward differential riccati equation under a constraint the square system as a special case is discussed the corresponding results are extended to systems with unknown initial condition with a modified definition of the index the condition for weighted index to emphasize the signal effect at different time instant is also derived by transformation the result is also compared with the famous bounded real lemma the connection with the linear time invariant lti case is also discussed finally examples are given to illustrate the main results

model validation for iqc uncertain systems with fixed initial conditions abstract the paper considers a model validation problem for a class of uncertain systems in which the uncertainty is described by an integral quadratic constraint and the uncertain system has zero initial condition the problem is solved by applying methods from linear quadratic optimal control with a fixed endpoint this leads to a method for model validation which is based around a robust kalman filter structure the paper also yields a result on robust set valued state estimation for uncertain systems in which the initial condition is known to be zero

h sub infinity state estimation for linear periodic systems this note deals with the h sub infinity state estimation problem for linear periodic systems the question addressed is the design of an unbiased linear periodic and asymptotically stable estimator that achieves a prescribed h sub infinity performance on an infinite horizon necessary and sufficient conditions for the existence of a periodic estimator have been derived asymptotic properties of the finite horizon estimation problem when the time horizon tends to infinity are also investigated

newton kantorovich theorem for a family of modified halley s method under holder continuity conditions in banach space abstract in this study under p holder continuity conditions a family of new modified halley s method with 2 p order is proposed in banach space which is used to solve the nonlinear operator equations the newton kantorovich convergence theorem for the family of new modified halley s method is established under holder continuity conditions the error estimate also is gotten finally two examples are provided to show the application of our theorem

a characterization of all solutions to the four block general distance problem all solutions to the four block general distance problem which arises in h infty optimal control are characterized the procedure is to embed the original problem in an all pass matrix which is constructed it is then shown that part of this all pass matrix acts as a generator of all solutions special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all pass transfer functions as an application necessary and sufficient conditions are found for the existence of an h infty optimal controller following that a descriptor representation of all solutions is derived

h optimal sampled data control in continuous time systems we consider the design of h optimal discrete time digital controllers in continuous time systems an apparent difficulty especially in utilizing modern transform domain analysis in this context stems from the absence of an appropriate transfer function model for the hybrid time discrete and continuous closed loop system this difficulty is overcome through the introduction of an equivalent difference equation model for the continuous time system with distributed inputs and outputs equivalence being in the sense that the continuous and discrete time inputs and outputs are essentially identical using the interplay between the discrete and the continuous time models solutions of the well known purely continuous time and purely discrete time standard problems extend to solutions of the problem at hand they comprise riccati equation characterizations of feasible combinations of sampling rates and bounds on the closed loop induced input output norm and parameterization of compensators we consid