h sub spl infin control of discrete time uncertain systems this paper considers h sub spl infin control problems involving discrete time uncertain linear systems the uncertainty is supposed to belong to convex bounded domains and no additional assumptions are made as for instance matching conditions two h sub spl infin guaranteed cost control problems are solved the first one concerns the determination of a state feedback gain if one exists in such way the h sub spl infin norm of a certain transfer function remains bounded by a prespecified h sub spl infin level for all possible models the second one includes this bound as an additional variable to be minimized to achieve the smallest feasible limiting bound the results follow from the simple geometry of those problems which are shown to be convex in the particular parametric space under consideration an example illustrates the theory

infinite horizon stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper studies the infinite horizon mixed h 2 h control for discrete time stochastic systems with state and disturbance dependent noise we shall first establish a version of stochastic bounded real lemma sbrl which by itself has theoretical importance based on the sbrl it is shown that under the condition of exact observability the existence of a static state feedback h 2 h controller is equivalent to the solvability of four coupled matrix valued equations a suboptimal h 2 h controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix valued equations

discrete time nonlinear h control with measurement feedback abstract this paper deals with the problem of h control via measurement feedback with internal stability for discrete time nonlinear systems using the theory of discrete time dissipative systems and differential game we first present a parameterization of a family of static state feedback h nonlinear controllers then we provide sufficient conditions for the existence of a dynamic output compensator which solves the problem of disturbance attenuation with internal stability for discrete time nonlinear systems the theory developed in this paper incorporates the well known results for discrete time linear systems and generalizes some recent advances in h control of continuous time nonlinear systems to their discrete time counterparts

h control for discrete time linear systems with frobenius norm bounded uncertainties in this paper we consider the problems of robust stability and control for the class of uncertain discrete time linear systems with frobenius norm bounded parameter uncertainties in all matrices of the system and output equations necessary and sufficient conditions for the above problems are proposed a linear static state feedback control law is designed which is in terms of a riccati inequality the results obtained here show that the robust control problem of the uncertain system is equivalent to the control problem for a corresponding uncertainty free system

robust h 2 and h control of discrete time systems with polytopic uncertainties via dynamic output feedback this paper addresses the problem of robust h 2 and h control of discrete linear time invariant lti systems with polytopic uncertainties via dynamic output feedback the problem has been known to be difficult when a parameter dependent lyapunov function is to be applied for a less conservative design due to non convexity our approach is based on a novel bounding technique that converts the non convex optimization into a convex one together with a line search which is simple but may be conservative to further reduce the design conservatism an algorithm based on the sequentially linear programming method slpmm is proposed a numerical example is given which demonstrates the feasibility of the proposed design methods

on the boundedness of the denominators in the zariski decomposition on surfaces zariski decompositions play an important role in the theory of algebraic surfaces for making geometric use of the decomposition of a given divisor one needs to pass to a multiple of the divisor in order to clear denominators it is therefore an intriguing question whether the surface has a universal denominator that can be used to simultaneously clear denominators in all zariski decompositions on the surface we prove in this paper that somewhat surprisingly this condition of bounded zariski denominators is equivalent to the bounded negativity of curves that is addressed in the bounded negativity conjecture furthermore we provide explicit bounds for zariski denominators and negativity of curves in terms of each other

optimal h filtering in networked control systems with multiple packet dropouts abstract this paper studies the problem of h filtering in networked control systems ncss with multiple packet dropouts a new formulation enables us to assign separate dropout rates from the sensors to the controller and from the controller to the actuators by employing the new formulation random dropout rates are transformed into stochastic parameters in the system s representation a generalized h norm for systems with stochastic parameters and both stochastic and deterministic inputs is derived the stochastic h norm of the filtering error is used as a criterion for filter design in the ncs framework a set of linear matrix inequalities lmis is given to solve the corresponding filter design problem a simulation example supports the theory

existence and comparison theorems for algebraic riccati equations for continuous and discrete time systems abstract we discuss two comparison theorems for algebraic riccati equations of the form xbr 1 b x x a br 1 c a br 1 c x q c r 1 c 0 simultaneously we give sufficient conditions to obtain the existence of the maximal hermitian solution of a riccati equation from the existence of a hermitian solution of a second riccati equation further similar results are given for discrete algebraic riccati equations

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

h sub spl infin state feedback control for discrete singular systems deals with the problem of state feedback h sub spl infin control for discrete singular systems it is not assumed that the singular system under consideration is necessarily regular the problem we address is the design of a state feedback controller such that the resulting closed loop system is not only regular causal and stable but also satisfies a prescribed h sub spl infin norm bound condition in terms of certain matrix inequalities a necessary and sufficient condition for the solution to this problem is obtained and a suitable state feedback control law is also given

bounding singular surfaces via chern numbers we prove the existence of a bound on the number of steps of the minimal model program for singular surfaces in terms of discrepancies and chern numbers as an application we prove that given r in mathbb r 0 and epsilon in 0 1 the class mathcal f r epsilon of 2 dimensional pairs x d of general type with epsilon klt singularities d with standard coefficients and 4c 2 x d c 1 2 x d le r forms a bounded family

robust h estimation of stationary discrete time linear processes with stochastic uncertainties the problem of h filtering of stationary discrete time linear systems with stochastic uncertainties in the state space matrices is addressed where the uncertainties are modeled as white noise the relevant cost function is the expected value with respect to the uncertain parameters of the standard h performance a previously developed stochastic bounded real lemma is applied that results in a modified riccati inequality this inequality is expressed in a linear matrix inequality form whose solution provides the filter parameters the method proposed is applied also to the case where in addition to the stochastic uncertainty other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope the problem of mixed h2 h filtering for the above system is also treated the theory developed is demonstrated by a simple tracking example

covariance bounds for discrete time linear systems with time varying parameter uncertainty this paper deals with the computation of upper bounds for the state covariance matrix of discrete time linear systems subject to stochastic excitation and additive time varying uncertainty in the system dynamic matrix such upper bounds are obtained as the stabilizing solutions of suitable h type riccati equations a necessary and sufficient condition for the existence of such solutions is given in terms of the h norm of a suitable transfer function as for the computation of the optimal bound it is demonstrated that the bounds are a convex function of a scalar parameter so that efficient numerical schemes can be worked out

technical communique new bounded real lemma for discrete time singular systems in this paper the problem of bounded real lemma for discrete time singular system with strict matrix inequalities is investigated it is proved that the bounded real lemma for discrete singular system can be described by a strict matrix inequality the results lead to more tractable and reliable computation when applying them to design control systems

discrete time h algebraic riccati equation and parametrization of all h filters this paper is concerned with the algebraic riccati equations ares related to the h filtering problem a necessary and sufficient condition for the h problem to be solvable is that the h are has a positive semidefinite stabilizing solution with an additional condition that a certain matrix is positive definite it is shown that such a stabilizing solution is a monotonically non increasing convex function of the prescribed h norm bound this property of the h are is very important for the analysis of the performance of the h filter in this paper the size of the set of all h filters is considered on the basis of the monotonicity of the above riccati solution it turns out that under a certain condition the degree of freedom of the h filter reduces a1 the optimal h norm bound these results provide a guideline for selecting the value of some numerical examples are included

inverse minimax optimality of model predictive control policies we present novel results linking model predictive control mpc and minimax optimal control theory specifically we show that for linear discrete time systems with constraints and disturbance inputs the closed loop optimal solutions of a particular class of minimax optimal control problems are a class of typical mpc policies we also present conditions which ensure that the inverse optimal mpc policies achieve a prescribed regional l2 gain from the disturbance input

robust h sub spl infin control for fuzzy systems with frobenius norm bounded uncertainties in this paper we investigate the problem of robust h sub spl infin performance and stabilization for a class of uncertain fuzzy systems with frobenius norm bounded parameter uncertainties in all system matrices both continuous and discrete time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems unlike the bounded real lemma in the linear theory of robust h sub spl infin control where necessary and sufficient conditions were obtained only sufficient condition based on lyapunov method is shown furthermore connection between robust h sub spl infin problems involving uncertainty and standard uncertainty free h sub spl infin problems is established via matrix algebra as for controller synthesis a state feedback fuzzy control law is designed via relaxed linear matrix inequality lmi formulations

algebraic riccati equation and j spectral factorization for h estimation abstract in this paper we investigate on the existence of the stabilizing solution of the algebraic riccati equation are related to the h filtering problem with a prescribed attenuation level it is well known that such a solution exists and is positive definite for larger than a certain f and it does not exist for smaller than a certain 0 we consider the intermediate case 0 f and show that in this interval the stabilizing solution does exist except for a finite number of values of we show how the solution of the are may be employed to obtain a minimum phase j spectral factor of the j spectrum associated with the h filtering problem

technical communique on the bounded real and positive real conditions for affine nonlinear state delayed systems and applications to stability in this paper bounded real conditions for affine nonlinear state delayed systems are derived using the concept of dissipativeness necessary and sufficient conditions for the system to be dissipative and to have finite l 2 gain also referred to as the bounded real condition are given the implications on the stability of the system and feedback interconnections of such systems are also considered finally an equivalent of the positive real lemma is derived and its implications on stability of the system and feedback interconnections of such systems are similarly discussed

seshadri constants on the self product of an elliptic curve abstract the purpose of this paper is to study seshadri constants on the self product e e of an elliptic curve e we provide explicit formulas for computing the seshadri constants of all ample line bundles on the surfaces considered as an application we obtain a good picture of the behaviour of the seshadri function on the nef cone

on hankel singular values and reflected zeros of linear dynamical systems this note discusses a relationship between the hankel singular values and reflected zeros of linear systems our main result proves that the hankel singular values of a linear continuous time system increase decrease pointwise when one or more zeros of the transfer function are reflected with respect to the imaginary axis that is move from the left right half to the right left half of the complex plane we also derive a similar result for linear discrete time systems

model reduction of a class of discrete time nonlinear systems abstract this paper considers the problem of model reduction of a class of discrete time systems subject to lipschitzian nonlinearities it is shown that under some conditions the nonlinear system can be either approximated by a discrete time linear time invariant system or a nonlinear system of reduced order the computation of the matrices of the reduced order system is carried out through the solutions of a set of linear matrix inequalities the proposed design is approved by the simulation of reduced order dynamics of a mass spring system subject to a nonlinear friction and a linear electric circuit with uncertain parameters

diophantine classes of holomorphy rings of global fields abstract this paper introduces the notions of diophantine generation and diophantine equivalence and explores the resulting diophantine classes of holomorphy rings of number fields and of one variable function fields over finite fields of constants

robust kalman filtering for uncertain discrete time systems this paper is concerned with the problem of a kalman filter design for uncertain discrete time systems the system under consideration is subjected to time varying norm bounded parameter uncertainty in both the state and output matrices the problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties furthermore the guaranteed cost can be optimized by appropriately searching a scaling design parameter

robust discrete time minimum variance filtering the bounded variance filtered estimation of the state of an uncertain linear discrete time system with an unknown norm bounded parameter matrix is considered an upper bound on the variance of the estimation error is found for all admissible systems and estimators are derived that minimize the latter bound we treat the finite horizon time varying case and the infinite time case where the nominal system model is time invariant in the special stationary case where it is known that the uncertain system is time invariant we provide a robust filter for all uncertainties that still keep the system asymptotically stable

h sub spl infin filtering of 2 d discrete systems this paper deals with h sub spl infin filtering of two dimensional 2 d linear discrete systems described by a 2 d local state space lss fornasini marchesini 1978 second model several versions of the bounded real lemma of the 2 d discrete systems are established the 2 d bounded real lemma allows us to solve the finite horizon and infinite horizon h sub spl infin filtering problems using a riccati difference equation or a riccati inequality approach further a solution to the infinite horizon h sub spl infin filtering problem based on a linear matrix inequality lmi approach is developed our results extend existing work for one dimensional 1 d systems to the 2 d case and give a state space solution to the bounded realness of 2 d discrete systems as well as 2 d h sub spl infin filtering for the first time numerical examples are given to demonstrate the riccati difference equation approach to the 2 d finite horizon h sub spl infin filtering problem and the lmi approach to the 2 d infinite horizon h sub spl infin filtering problem

brief paper parameterization of all stabilizing h static state feedback gains application to output feedback design this paper presents a simplified parameterization of all h static state feedback controllers in terms of a single algebraic riccati equation and a free parameter matrix as a special case necessary and sufficient conditions for the existence of an static output feedback gain are given an efficient computational algorithm is given and its correctness proven no initial stabilizing output feedback gain is needed the technique is used to design an h lateral directional command augmentation system for the f 16 aircraft

brief h control and robust stabilization of two dimensional systems in roesser models feedback control of two dimensional 2 d systems is a problem of considerable importance in both theory and practical applications in this paper we present a state space solution to the problem of h control of 2 d systems for a linear discrete time 2 d system described by a 2 d state space roesser model a 2 d dynamic output feedback controller is designed to achieve the closed loop system asymptotic stability and a specified h performance using a linear matrix inequality lmi approach we further give a solution for robust stabilization of 2 d systems subject to a class of norm bounded uncertainties the results are demonstrated by an application example of stabilization of processes expressed in a darboux equation

negative curves on algebraic surfaces we study curves of negative self intersection on algebraic surfaces our main result shows there exist smooth complex projective surfaces x related to hilbert modular surfaces such that x contains reduced irreducible curves c of arbitrarily negative self intersection c 2 previously the only known examples of surfaces for which c 2 was not bounded below were in positive characteristic and the general expectation was that no examples could arise over the complex numbers indeed we show that the idea underlying the examples in positive characteristic cannot produce examples over the complex number field and thus our complex examples require a different approach

minimum h sub infinity norm regulation of linear discrete time systems and its relation to linear quadratic discrete games a solution is derived to the h sub infinity optimization problem that arises in multivariable discrete time regulation when the controller has full access to the state vector the solution method is based on the close relations that exist between linear quadratic differential game theory and h sub infinity optimization the existing theory of discrete time quadratic games is readily applied in order to derive the solution to a finite time horizon version of the h sub infinity optimization problem the solution of the infinite time horizon h sub infinity optimization problem is obtained by formally taking the limit of the number of stages to infinity

comments on bounded real criteria for linear time delay systems xiefu jiang et al point out some some misleading statements in the above mentioned paper shaked et al 1998 and relation results are given also wen shyong yu points out serious mistakes in the same paper and also untenable main results

h sub spl infin control of discrete time nonlinear systems this paper presents an explicit solution to the problem of disturbance attenuation with internal stability via full information feedback state feedback and dynamic output feedback respectively for discrete time nonlinear systems the h sub spl infin control theory is first developed for affine systems and then extended to general nonlinear systems based on the concepts of dissipation inequality differential game and lasalle s invariance principle in discrete time a substantial difficulty that v a x b x u e x w respectively v f x u w is no longer quadratic in sub w sup u arising in the case of discrete time nonlinear systems has been surmounted in the paper in the case of a linear system we show how the results reduce to the well known ones recently proposed in the literature

robust h control for discrete time fuzzy systems via basis dependent lyapunov functions this paper deals with the robust h control problem for a class of discrete time fuzzy systems with uncertainty the uncertainty is assumed to be of structured linear fractional form by using basis dependent lyapunov function an h control design approach is developed the control design approach is facilitated by introducing some additional instrumental matrix variables these additional matrix variables decouple the lyapunov and the system matrices which makes the control design feasible the proposed approach leads to some sufficient results in the form of strict linear matrix inequalities lmis it is expected that the basis dependent results are less conservative than the basis independent ones due to the introduction of basis dependent lyapunov function finally numerical examples including the discrete chaotic lorenz system are also given to demonstrate the applicability of the proposed approach

brief dissipative control for linear discrete time systems this paper focuses on the problem of quadratic dissipative control for linear discrete time systems we consider the design of feedback controllers to achieve asymptotic stability and strict quadratic dissipativeness both the linear static state feedback and the dynamic output feedback controllers are considered necessary and sufficient conditions for the solutions of the quadratic dissipative control problems are obtained using the linear matrix inequality lmi approach the main result of this paper unifies existing results on h and positive real control and it provides a more flexible and less conservative control design as it allows for a better trade off between phase and gain performances

examples of mori dream surfaces of general type with pg 0 abstract in this paper we study effective nef and semiample cones of minimal surfaces of general type with p g 0 we provide examples of minimal surfaces of general type with p g 0 and 2 k 2 9 which are mori dream spaces on these examples we also give explicit description of their effective cones with all negative curves we also present non minimal surfaces of general type with p g 0 that are not mori dream surfaces

existence of unmixed solutions of the discrete time algebraic riccati equation and a nonstrictly bounded real lemma abstract the existence of a solution of the discrete time algebraic riccati equation is established assuming modulus controllability and positive semidefiniteness on the unit circle of the popov function as an application a nonstrictly bounded real lemma is obtained

on stabilizing properties of solutions of the riccati difference equation monotonicity and stabilizing properties of solutions of the riccati difference equation rde are discussed the author considers the problem of selecting an initial condition for the rde in such a way that the update of the kalman filter gain can be stopped at any time and the resulting frozen filter is asymptotically stable the author also considers the case in which the initial condition of the rde may be less than the asymptotic solution the results are relevant to control and observer design including the stability of finite time horizon discrete time predictive control

the positive real lemma and construction of all realizations of generalized positive rational functions we here extend the well known positive real lemma also known as the kalman yakubovich popov lemma to complex matrix valued general ized positive rational function when non minimal realizations are considered we then exploit this result to provide an easy construction procedure of all not necessarily minimal state space realizations of generalized positive func tions as a by product we partition all state space realizations into subsets each is identified with a set of matrices satisfying the same lyapunov inclusion and thus form a convex invertible cone cic in short moreover this approach enables us to characterize systems which may be brought to be generalized positive through static output feedback the formulation through lyapunov inclusions suggests the introduction of an equivalence class of rational functions of various dimensions associated with the same system matrix

characterizing integers among rational numbers with a universal existential formula we prove that bbb z in definable in bbb q by a formula with two universal quantifiers followed by seven existential quantifiers it follows that there is no algorithm for deciding given an algebraic family of bbb q morphisms whether there exists one that is surjective on rational points we also give a formula again with universal quantifiers followed by existential quantifiers that in any number field defines the ring of integers

a transfer function approach to the problems of discrete time systems h sub infinity optimal linear control and filtering a solution is derived to the problems of h sub infinity optimal linear state regulation and filtering the solution method for both problems is based on a transfer function approach which applies standard spectral factorization return difference relations are given which are extensions of the relations associated with the linear quadratic problem

on finite horizon l 2 induced norms of discrete time switched linear systems the finite horizon 2 induced norm evaluation problem of discrete time switched linear systems is considered in this paper the set of worst case switching laws is characterized which is a subset of the whole set of switching laws under consideration based on the properties of the worst case switching law set a low complexity complete solution to the 2 induced norm evaluation problem is provided for general switched linear systems it is shown that under the assumption of exponential stability the finite horizon 2 induced norm monotonically converges to the infinite horizon norm and the volume of the worst case switching law set gradually becomes constant as the time horizon approaches infinity some numerical properties of the worst case switching law set are also exploited a numerical example is presented to illustrate the proposed results

on the discrete time bounded real lemma with application in the characterization of static state feedback h controllers abstract this paper deals with the discrete time bounded real lemma and its application in the characterization of all static state feedback h controllers for discrete time systems we first present two versions of the discrete time bounded real lemma the results apply to non minimal stable state space realizations and are given in terms of either the positive semi definite strong solution or the positive semi definite stabilizing solution of a discrete algebraic riccati equation based on the discrete time bounded real lemma we obtain a characterization of all static state feedback h controllers for discrete time systems as an application of the parameterization of all static state feedback h controllers we develop a solution to the discrete time h control problem via static output feedback also a numerical procedure is proposed to determine an output feedback gain

robust stabilization subject to structured uncertainties and mean power constraint abstract this paper deals with a robust stabilization problem for discrete time systems subject to multiple disturbances occurring in controller and actuating channel where both linear structured uncertainties and white gaussian noises are included the desired control law is aimed to robustly stabilize the system and to satisfy some pre specified mean power constraint simultaneously by the philosophy of the mixed h 2 h control a solvability condition is first derived for single input systems that reveals the intrinsic relation between the unstable poles of the plant and the disturbance parameters together with two cross coupled algebraic riccati equations the result is further generalized to multiple input systems with a sufficient condition given again by the unstable poles of the plant an example is included to illustrate the current results

a short note on constrained linear control systems with multiplicative ellipsoidal uncertainty this technical note revisits the classical robust control question of how to design linear control laws for uncertain linear dynamic systems we formulate this robust control design problem from a modern optimal control perspective which allows us to take into account control and state constraints that have to be satisfied by the closed loop system for all possible uncertainty scenarios the contribution of this technical note is the derivation of a conservative but computationally tractable robust control design problem formulation for the case that multiplicative uncertainties are present in the linear dynamic systems which render the robust control problem non convex in general here our approximation technique relies on propagating ellipsoidal bounds on the reachable states of the closed loop system the methods developed in this technical note can also be used as a building block for tube based model predictive control schemes where robustly designed linear control laws can help to reduce the conservatism of open loop predictions we illustrate the proposed techniques with a numerical case study

robust h sub spl infin filtering of stationary continuous time linear systems with stochastic uncertainties the problem of applying h sub spl infin filters on stationary continuous time linear systems with stochastic uncertainties in the state space signal model is addressed these uncertainties are modeled via white noise processes the relevant cost function is the expected value of the standard h sub spl infin performance index with respect to the uncertain parameters the solution is obtained via a stochastic bounded real lemma that results in a modified riccati inequality this inequality is expressed in the form of a linear matrix inequality whose solution provides the filter parameters the method proposed is also applied to the case where in addition to the stochastic uncertainty other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope the problem of mixed h sub 2 h sub spl infin filtering for the above system is also treated the theory developed is demonstrated by a practical example

technical communique robust h control of discrete systems with uncertain parameters and unknown delays in this paper we address the problems of robust h performance analysis and control synthesis for a class of discrete time systems with norm bounded parameter uncertainty and unknown constant state delay through finite dimensional algebraic riccati equations we provide a necessary and sufficient condition for designing a memoryless state feedback controller which stabilizes the discrete time delay system under consideration and guarantees an h norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown delays an example is worked out to illustrate the developed theory