voltage control for uncertain stochastic nonlinear system with application to energy internet non fragile robust h approach abstract in this paper a robust control method is used to intelligently regulate the dc bus voltage deviation for an islanded microgrid mg within the scenario of energy internet ei in order to cope with the uncertain and nonlinear nature of the power exchange in ei a new mathematical model is formulated to present the dynamics of the islanded mg where the state equation is expressed by a class of nonlinear stochastic differential equations sdes with parameter uncertainties appearing in system coefficients and the controllers specifically the nonlinearities appear in both drift and diffusion parts of such sdes our aim is to design a controller such that the effects of the modelling uncertainty and the external disturbance to the dc bus voltage of the off grid mg are minimized mathematically this can be regarded as problems of solving the non fragile robust stochastic stabilization and non fragile robust h control both of which can be solved via the linear matrix inequality lmi approach sufficiently we emphasize such new control system with its solution can also be applied into fields of industry economics etc based on real world data numerical results are illustrated and simulations show that our target is achieved

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

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

brief paper stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper is to study the discrete time stochastic h 2 h control with state and external disturbance dependent noise a necessary and sufficient condition for the existence of h 2 h control is presented which transforms the h 2 h controller design into solving four coupled matrix valued equations moreover a recursive algorithm for solving the four coupled matrix valued equations is also given

brief paper h filtering for nonlinear discrete time stochastic systems with randomly varying sensor delays this paper is concerned with the h filtering problem for a general class of nonlinear discrete time stochastic systems with randomly varying sensor delays where the delayed sensor measurement is governed by a stochastic variable satisfying the bernoulli random binary distribution law in terms of the hamilton jacobi isaacs inequalities preliminary results are first obtained that ensure the addressed system to possess an l 2 gain less than a given positive scalar c next a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the h performance constraint for all nonzero exogenous disturbances under the zero initial condition such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation furthermore it is shown that our main results can be readily specialized to the case of linear stochastic systems finally a numerical simulation example is used to demonstrate the effectiveness of the results derived

a characterization of rational singularities in terms of injectivity of frobenius maps the notions of f rational and f regular rings are defined via tight closure which is a closure operation for ideals in a commutative ring of positive characteristic the geometric significance of these notions has persisted and k e smith proved that f rational rings have rational singularities we now ask about the converse implication the answer to this question is yes and no for a fixed positive characteristic there is a rational singularity which is not f rational so the answer is no in this paper however we aim to show that the answer is yes in the following sense if a ring of characteristic zero has rational singularity then its modulo p reduction is f rational for almost all characteristic p this result leads us to the correspondence of f regular rings and log terminal singularities

the structure of f pure rings for a reduced f finite ring r of characteristic p 0 and q p e one can write open image in new window where m q has no free direct summands over r we investigate the structure of f finite f pure rings r by studying how the numbers a q grow with respect to q this growth is quantified by the splitting dimension and the splitting ratios of r which we study in detail we also prove the existence of a special prime ideal open image in new window r of r called the splitting prime that has the property that r open image in new window r is strongly f regular we show that this ideal captures significant information with regard to the f purity of r

h sup infinity control for nonlinear systems with output feedback the basic question of nonlinear h sup infinity control theory is to decide for a given two port system when feedback that makes the full system dissipative and internally stable exists this problem can also be viewed as a question about circuits and after translation also has a game theoretic statement several necessary conditions for solutions to exist are presented and sufficient conditions for a certain construction to lead to a solution are given

improved robust h2 and h filtering for uncertain discrete time systems this paper is concerned with the robust h 2 and h filtering problems for linear discrete time systems with polytopic parameter uncertainty we aim to derive a less conservative design than existing linear matrix inequality lmi based sufficient conditions it is shown that a more efficient evaluation of robust h 2 or h performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations when applying this new matrix inequality condition to the robust filter design these parameters provide extra degrees of freedom in optimizing the guaranteed h 2 or h performance and lead to a less conservative design

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

robust spl hscr sub spl infin filtering for uncertain discrete time state delayed systems this paper addresses the problem of robust spl hscr sub spl infin filtering for linear discrete time systems subject to parameter uncertainties in the system state space model and with multiple time delays in the state variables the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain a methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed spl hscr sub spl infin performance for the filtering error irrespective of the uncertainty and the time delays the proposed design is given in terms of linear matrix inequalities which has the advantage in that it can be implemented numerically very efficiently

f purity and rational singularity we investigate singularities which are f pure respectively f pure type a ring r of characteristic p is f pure if for every r module m 0 m r m r is exact where 1r denotes the r algebra structure induced on r via the frobenius map if r e r and s e 1r then r s rps in 1r f pure type is defined in characteristic 0 by reducing to characteristicp it is proven that when r s i is the quotient of a regular local ring s r is f pure at the prime ideal q if and only if i pi i q p here j p denotes the ideal ap i a e j several theorems result from this criterion if f is a quasihomogeneous hypersurface having weights r1 r and an isolated singularity at the origin 1 17 1ri i implies k x1 x f has f pure type at m x1 x 2 1n i ri i implies k x1 xn f does not have f pure type at m 3 1 1ri i remains unsolved but does connect with a problem that number theorists have studied for many years this theorem parallels known results about rational singularities it is also proven that classifying f pure singularities for complete intersection ideals can be reduced to classifying such singularities for hypersurfaces and that the f pure locus in the maximal spectrum of k x1 xn i where k is a perfect field of characteristic p is zariski open an important conjecture is that r fr is f pure type should imply r is f pure type whenever r is a cohen macauley normal local ring it is proven that ext1 1r r 0 is a sufficient though not necessary condition a local ring r m of characteristic p is f injective if the frobenius map induces an injection on the local cohomology modules h r h 1r an example is constructed which is f injective but not f pure from this a counterexample to the conjecture that r fr is f pure implies r is f pure is constructed however it is not a domain much less normal moreover it does not lead to a counterexample to the characteristic 0 version of the conjecture 0 introduction let r be a ring of characteristic p and let r denote the ring r viewed as an r module via the frobenius map f r rp r is f pure if for every r module m 0 r m 4 r m is exact a notion of f pure type is then defined in characteristic 0 by reduction to characteristicp f pure rings are connected with invariant theory and appear in the proof that the ring of invariants of a linearly reductive affine linear group acting on a regular ring is cohen macaulay 3 it has also been demonstrated that f purity measures good singularities in the sense that it implies a great deal of simplification in the computation of local cohomology 1 received by the editors march 30 1982 and in revised form august 3 1982 1980 mathematics subject classification primary 13h99 1983 american mathematical society 0002 9947 82 0000 0829 05 25

a generalization of tight closure and multiplier ideals we introduce a new variant of tight closure associated to any fixed ideal a which we call tight closure and study various properties thereof in our theory the annihilator ideal r a of all tight closure relations which is a generalization of the test ideal in the usual tight closure theory plays a particularly important role we prove the correspondence of the ideal a and the multiplier ideal associated to a or the adjoint of a in lipman s sense in normal q gorenstein rings reduced from characteristic zero to characteristic p 0 also in fixed prime characteristic we establish some properties of r a similar to those of multiplier ideals e g a briancon skoda type theorem subadditivity etc with considerably simple proofs and study the relationship between the ideal and the f rationality of rees algebras

output feedback stabilization of networked control systems with random delays modeled by markov chains this note investigates the output feedback stabilization of networked control systems ncss the sensor to controller s c and controller to actuator c a random network induced delays are modeled as markov chains the focus is on the design of a two mode dependent controller that depends on not only the current s c delay but also the most recent available c a delay at the controller node the resulting closed loop system is transformed to a special discrete time jump linear system then the sufficient and necessary conditions for the stochastic stability are established further the output feedback controller is designed via the iterative linear matrix inequality lmi approach simulation examples illustrate the effectiveness of the proposed method

the frobenius complexity of a local ring of prime characteristic abstract we introduce a new invariant for local rings of prime characteristic called frobenius complexity that measures the abundance of frobenius actions on the injective hull of the residue field of a local ring we present an important case where the frobenius complexity is finite and prove that complete normal rings of dimension two or less have frobenius complexity less than or equal to zero moreover we compute the frobenius complexity for the determinantal ring obtained by modding out the 2 2 minors of a 2 3 matrix of indeterminates showing that this number can be positive irrational and depends upon the characteristic we also settle a conjecture of katzman schwede singh and zhang on the infinite generation of the ring of frobenius operators of a local normal complete q gorenstein ring

addendum to frobenius and cartier algebras of stanley reisner rings j algebra 358 2012 162 177 abstract we give a purely combinatorial characterization of complete stanley reisner rings having a principally generated equivalently finitely generated cartier algebra

test ideals in local rings it is shown that certain aspects of the theory of tight closure are well behaved under localization let j be the parameter test ideal for r a complete local cohen macaulay ring of positive prime characteristic for any multiplicative system u c r it is shown that ju 1r is the parameter test ideal for u 1 r this is proved by proving more general localization results for the here introduced classes of f ideals of r and f submodules of the canonical module of r which are annihilators of r modules with an action of frobenius it also follows that the parameter test ideal cannot be contained in any parameter ideal of r tight closure has produced surprising new results for instance that the absolute integral closure of a complete local domain r of prime characteristic is a cohen macaulay algebra for r as well as tremendously simple proofs for otherwise difficult theorems such as the fact that the ring of invariants of a linearly reductive group acting on a regular ring is cohen macaulay the definition of tight closure is recalled in section 1 but we refer the reader to the papers of hochster and huneke listed in the bibliography for more about its applications while primarily a prime characteristic notion tight closure offers insight into arbitrary commutative rings containing q by fairly standard reduction to characteristic p techniques despite its successes the tight closure operation which in its principal setting is a closure operation performed on ideals in a commutative noetherian ring of prime characteristic remains poorly understood for example tight closure is not known to behave well under localization given an ideal i of a ring r letting i denote the tight closure of i it is not known whether or not

robust spl hscr sub spl infin filtering for discrete time linear systems with uncertain time varying parameters this paper deals with the problem of robust spl hscr sub spl infin filtering for linear discrete time state space models with uncertain time varying parameters the parameters enter affinely into the state space model matrices and their admissible values and variations are assumed to belong to given intervals a method is derived for designing a linear stationary asymptotically stable filter with a prescribed spl hscr sub spl infin performance in spite of large parameter uncertainty the proposed method incorporates information on available bounds on both the admissible values and variation of the uncertain parameters and is based on a lyapunov function with quadratic dependence on the parameters the filter design is given in terms of linear matrix inequalities

estimates of essential norms of weighted composition operators between bloch type spaces abstract we estimate the essential norm of weighted composition operators u c acting on bloch type spaces b in terms of the analytic function u d c and the n th power of the analytic selfmap of the open unit disc d we obtain new characterizations for boundedness and compactness of u c b b for all 0 thus answering an open problem of manhas and zhao concerning the case 1

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

output regulation of nonlinear systems with delay abstract output regulation of retarded type nonlinear systems is considered regulator equations are derived which generalize francis byrnes isidori equations to the case of systems with delay it is shown that under standard assumptions the regulator problem is solvable if and only if these equations are solvable in the linear case the solution of these equations is reduced to linear matrix equations an example of a delayed van der pol equation illustrates the efficiency of the results

state feedback ℋ control for stochastic time delay nonlinear systems with state and disturbance dependent noise this article focuses on the state feedback control problem for the stochastic nonlinear systems with state and disturbance dependent noise and time varying state delays based on the maxmin optimisation approach both the delay independent and the delay dependent hamilton jacobi inequalities hjis are developed for synthesising the state feedback controller for a general type of stochastic nonlinear systems it is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level for a class of stochastic affine nonlinear systems the delay independent as well as delay dependent matrix valued inequalities are proposed the resulting control system satisfies global asymptotic stability in the mean square sense and the required disturbance attenuation level by modelling the nonlinearities as uncertainties in corresponding stochastic time delay systems the sufficient conditions in terms of a linear matrix inequality lmi and a bili

graded annihilators and tight closure test ideals abstract let r be a commutative noetherian local ring of prime characteristic p with maximal ideal m the main purposes of this paper are to show that if the injective envelope e of r m has a structure as an x torsion free left module over the frobenius skew polynomial ring over r in the indeterminate x then r has a tight closure test element for modules and is f pure and to relate the test ideal of r to the smallest e special ideal of r of positive height a byproduct is an analogue of a result of janet cowden vassilev she showed in the case where r is an f pure homomorphic image of an f finite regular local ring that there exists a strictly ascending chain 0 0 1 t r of radical ideals of r such that for each i 0 t 1 the reduced local ring r i is f pure and its test ideal has positive height and is exactly i 1 i this paper presents an analogous result in the case where r is complete but not necessarily f finite and e has a structure as an x torsion free left module over the frobenius skew polynomial ring whereas cowden vassilev s results were based on r fedder s criterion for f purity the arguments in this paper are based on the author s work on graded annihilators of left modules over the frobenius skew polynomial ring

discreteness and rationality of f jumping numbers on singular varieties we prove that the f jumping numbers of the test ideal tau x delta mathfrak a t are discrete and rational under the assumptions that x is a normal and f finite scheme over a field of positive characteristic p kx is mathbb q cartier of index not divisible p and either x is essentially of finite type over a field or the sheaf of ideals mathfrak a is locally principal this is the largest generality for which discreteness and rationality are known for the jumping numbers of multiplier ideals in characteristic zero

h control for non linear stochastic systems the output feedback case the h output feedback control problem for non linear stochastic systems is considered a solution for a large class of non linear stochastic systems is introduced including non linear diffusion systems as a subclass this solution is based on a bounded real lemma for non linear stochastic systems that was previously established via a stochastic dissipativity concept the theory yields sufficient conditions for the closed loop system to possess a prescribed l 2 gain bound in terms of two hamilton jacobi inequalities one that is associated with the state feedback part of the problem is n dimensional where n is the underlying system s state dimension and the other inequality that stems from the estimation part is 2n dimensional both stationary and non stationary systems are considered stability of the closed loop system is established both in the mean square and the in probability senses as the solution to the hamilton jacobi inequalities may in general lead to a non realisable state estimator

centers of f purity in this paper we study a positive characteristic analogue of the centers of log canonicity of a pair r we call these analogues centers of f purity we prove positive characteristic analogues of subadjunction like results prove new stronger subadjunction like results and in some cases lift these new results to characteristic zero using a generalization of centers of f purity which we call uniformly f compatible ideals we give a characterization of the test ideal which unifies several previous characterizations finally in the case that 0 we show that uniformly f compatible ideals coincide with the annihilators of the mathcal f e r k submodules of e r k as defined by lyubeznik and smith

f signature of pairs and the asymptotic behavior of frobenius splittings abstract we generalize f signature to pairs r d where d is a cartier subalgebra on r as defined by the first two authors in particular we show the existence and positivity of the f signature for any strongly f regular pair in one application we answer an open question of aberbach and enescu by showing that the f splitting ratio of an arbitrary f pure local ring is strictly positive furthermore we derive effective methods for computing the f signature and the f splitting ratio in the spirit of the work of r fedder

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

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

brief paper robust h filtering for nonlinear stochastic systems with uncertainties and markov delays this paper investigates the h filtering problem for a class of general nonlinear stochastic systems considering model uncertainties and random time delays governed by markov chains simultaneously the general algebraic hamilton jacobi inequality hji is established first for general nonlinear stochastic systems with uncertainties and random markovian delays then a set of sufficient conditions are derived for the filtering system to achieve stochastic stability in the sense of mean square and the prescribed disturbance attenuation level moreover the developed results are specialized for a special class of nonlinear stochastic systems by presenting the sufficient conditions in terms of matrix inequalities simulation results demonstrate the effectiveness of the proposed approach

new estimates of essential norms of weighted composition operators between bloch type spaces abstract we give estimates of the essential norms of the weighted composition operators u c between different bloch type spaces in terms of the n th power of we also give similar characterizations for boundedness and compactness of u c between different bloch type spaces

essential norm estimates for composition operators on bmoa abstract we provide two function theoretic estimates for the essential norm of a composition operator c acting on the space bmoa one in terms of the n th power n of the symbol and one which involves the nevanlinna counting function we also show that if the symbol is univalent then the essential norm of c is comparable to its essential norm on the bloch space

integrated nonlinear optimal control of spacecraft in proximity operations this article proposes an integrated optimal control strategy for a servicing spacecraft in proximity operations on a target in space the relative position vector between the servicing spacecraft and the target is required to direct towards the docking port of the target while the attitude of the two bodies must be synchronised without exciting large flexible vibrations the control of translational rotational and flexible motions is formulated in one unified optimal control framework in which the tracking errors in relative position and attitude and flexible structure vibrations can be minimised simultaneously using one cost function this formulation results in a highly nonlinear system that poses a challenging control problem the nonlinear optimal control technique is employed to design a closed form feedback control law for this nonlinear control problem by finding an approximate solution to the hamilton jacobi bellman hjb equation through a perturbation process the closed form controller offere

test ideals in quotients of f finite regular local rings let s be an f finite regular local ring and i an ideal contained in s let r s i fedder proved that r is f pure if and only if i p i m p we have noted a new proof for his criterion along with showing that i q i q where is the pullback of the test ideal for r combining the the f purity criterion and the above result we see that if r s i is f pure then r is also f pure in fact we can form a filtration of r i 0 1 i that stabilizes such that each r i is f pure and its test ideal is i 1 to find examples of these filtrations we have made explicit calculations of test ideals in the following setting let r t i where t is either a polynomial or a power series ring and i p1 pn is generated by monomials and the r pi are regular set j p1 pi pn then j par this paper concerns the study of the test ideal in f finite quotients of regular local rings test elements play a key role in tight closure theory once known they make computing tight closures of ideals and modules easier in fact in an excellent gorenstein local ring with an isolated singularity r hom i i e where i is generated by a system of parameters that are test elements and e is the injective hull of r see hu1 and s1 we also know for parameter ideals i that i i thus knowing is basically equivalent to knowing the tight closure of a system of parameters which is contained in the test ideal a recent paper of huneke and smith hs links tight closure to kodaira vanishing for graded rings r with characteristic either 0 or p where p 0 recall that the a invariant for a graded ring r denoted a is equal to min i r i 6 0 where r is the canonical module for r if r is gorenstein then r r a huneke and smith prove that the test ideal is exactly the ideal generated by elements of degree greater than the a invariant of r if and only if a strong kodaira vanishing holds on r a recent paper of hara ha confirms that this strong kodaira vanishing holds in finitely generated algebras over a field of characteristic zero in this paper we study test ideals of f finite rings which are reduced quotients of a regular local ring reduced quotients of f finite regular local rings have been studied by both fedder fe and glassbrenner gl fedder s work concerns f purity aspects of these rings and glassbrenner s results use fedder s techniques to examine strong f regularity the object that plays a key role in their work is received by the editors november 4 1996 1991 mathematics subject classification primary 13a35

cartier modules finiteness results on a locally noetherian scheme x over a field of positive characteristic p we study the category of coherent ox modules m equipped with a pe linear map i e an additive map c ox ox satisfying rc m c r p e m for all m a m r a ox the notion of nilpotence meaning that some power of the map c is zero is used to rigidify this cate gory the resulting quotient category called cartier crystals satisfies some strong finiteness conditions the main result in this paper states that if the frobenius morphism on x is a finite map i e if x is f finite then all cartier crystals have finite length we further show how this and related results can be used to recover and generalize other finiteness results of hartshorne speiser 19 lyubeznik 27 sharp 30 enescu hochster 14 and hochster 20 about the structure of modules with a left action of the frobenius for example we show that over any regular f finite scheme x lyubeznik s f finite modules 27 have finite length

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

static h2 and h output feedback of discrete time lti systems with state multiplicative noise abstract a parameter dependent approach for designing static output feedback controller for linear time invariant systems with state multiplicative noise is introduced which achieves a minimum bound on either the stochastic h 2 or the h performance levels a solution is obtained also for the case where in addition to the stochastic parameters the system matrices reside in a given polytope in this case a parameter dependent lyapunov function is described which enables the derivation of the required constant feedback gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope the stochastic parameters appear in both the dynamics and the input matrices of the state space model of the system the problems are solved using the expected value of the standard performance indices over the stochastic parameters the theory developed is demonstrated by a simple example

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

generating functions associated to frobenius algebras abstract we introduce a generating function associated to the homogeneous generators of a graded algebra that measures how far is this algebra from being finitely generated for the case of some algebras of frobenius endomorphisms we describe this generating function explicitly as a rational function

h sub spl infin control via measurement feedback for general nonlinear systems this paper shows how the problem of local disturbance attenuation via measurement feedback with internal stability can be solved for a nonlinear system of rather general structure the solution of the problem is shown to be related to the existence of solutions of a pair of hamilton jacobi inequalities in n independent variables which are associated with state feedback and respectively output injection design

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

robust h sub spl infin filtering for nonlinear stochastic systems this paper describes the robust h sub spl infin filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance dependent noise we assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by ito spl circ type stochastic differential equations for general nonlinear stochastic systems the h sub spl infin filter can be obtained by solving second order nonlinear hamilton jacobi inequalities when the worst case disturbance is considered in the design procedure a mixed h sub 2 h sub spl infin filtering problem is also solved by minimizing the total estimation error energy it is found that for a class of special nonlinear stochastic systems the h sub spl infin filtering design can be given via solving several linear matrix inequalities instead of hamilton jacobi inequalities a few examples show that the proposed methods are effective

the essential norm of a weighted composition operator on bmoa we consider weighted composition operators w psi varphi f mapsto psi f circ varphi on the space bmoa which consists of the analytic functions on the unit disc whose boundary values have bounded mean oscillation on the unit circle we provide an estimate for the essential norm of w psi varphi in terms of the weight function psi and the n th power varphi n of the analytic self map varphi of the open unit disc we also provide a new estimate for the norm of w psi varphi

frobenius and cartier algebras of stanley reisner rings we study the generation of the frobenius algebra of the injective hull of a complete stanley reisner ring over a field with positive characteristic in particular by extending the ideas used by m katzman to give a counterexample to a question raised by g lyubeznik and k e smith about the finite generation of frobenius algebras we prove that the frobenius algebra of the injective hull of a complete stanley reisner ring can be only principally generated or infinitely generated also by using our explicit description of the generators of such algebra and applying the recent work by m blickle about cartier algebras and generalized test ideals we are able to show that the set of f jumping numbers of generalized test ideals associated to complete stanley reisner rings form a discrete subset inside the non negative real numbers