robust l_ infty induced filtering and control of stochastic systems with state multiplicative noise linear continuous time systems with stochastic uncertainties in their state space model are considered the problems of induced l state feedback control and filtering are solved for the stationary case in both problems the cost function is defined to be the expected value of the standard induced l performance index with respect to the uncertain parameters an example that demonstrates the applicability of the theory is given

stochastic h2 h control with x u v dependent noise finite horizon case in this paper the finite horizon mixed h 2 h control problem is studied for the systems governed by ito type nonlinear stochastic differential equations with state control and external disturbance dependent noise it is shown that the mixed h 2 h control under consideration is associated with the four cross coupled hamilton jacobi equations a discrete approximation algorithm is presented for solving the coupled generalized differential riccati equations arising from linear stochastic h 2 h control a necessary condition and a sufficient condition for the existence of the finite horizon stochastic h 2 h control are derived in particular some previous results on deterministic and stochastic h 2 h control can be viewed as corollaries of our main theorems

closed loop model set validation under a stochastic framework this paper deals with probabilistic model set validation it is assumed that the dynamics of a multi input multi output mimo plant is described by a model set with unstructured uncertainties and identification experiments are performed in closed loop a necessary and sufficient condition has been derived for the consistency of the model set with both the stabilizing controller and closed loop frequency domain experimental data fded in this condition only the euclidean norm of a complex vector is involved and this complex vector depends linearly on both the disturbances and the measurement errors based on this condition an analytic formula has been derived for the sample unfalsified probability sup of the model set some of the asymptotic statistical properties of the sup have also been briefly discussed a numerical example is included to illustrate the efficiency of the suggested method in model set quality evaluation

generalized differential riccati equation and indefinite stochastic lq control with cross term a stochastic indefinite linear quadratic lq optimal control problem with cross term in a finite time horizon is studied a new generalized differential riccati equation gdre is introduced it is shown that the solvability of the gdre is equivalent to the solvability of the indefinite stochastic lq problem furthermore all of the optimal controls including feedback and open loop can be identified via the solution to the gdre an example is presented to illustrate the theory obtained

computing the positive stabilizing solution to algebraic riccati equations with an indefinite quadratic term via a recursive method an iterative algorithm to solve algebraic riccati equations with an indefinite quadratic term is proposed the global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of hamiltonian matrices a game theoretic interpretation of the algorithm is also provided

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

robust reduced order h output feedback control of retarded stochastic linear systems a method for designing reduced order output feedback controllers for linear time invariant retarded systems with state multiplicative wiener type noise is introduced which achieves a minimum bound on the h performance level a cost function is defined that is the expected value of the standard h performance cost with respect to the stochastic parameters a solution is thus obtained for the reduced order h output feedback control problem for the stationary case via the input output approach where the system is replaced by a non retarded one that contains deterministic norm bounded uncertainties the results achieved for the nominal case are extended to the uncertain case where the system matrices reside in a given polytope a numerical example taken from the field of aircraft control is given that demonstrates the applicability of the theory developed

l2 l filtering for stochastic systems driven by poisson processes and wiener processes this paper investigates the l2 l filtering problem for stochastic systems driven by poisson processes and wiener processes firstly this paper presents an approach to transform the expectation of stochastic integral with respect to poisson process into the expectation of lebesgue integral by the martingale theory then based on this a filter is designed to guarantee that the filtering error system is mean square asymptotically stable and its l2 l performance satisfies a prescribed level finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme

ζ function and heat kernel formulae abstract we present a systematic study of asymptotic behaviour of generalised functions and heat kernels used in noncommutative geometry and clarify their connections with dixmier traces we strengthen and complete a number of results from the recent literature and answer in the affirmative the question raised by m benameur and t fack 2006 1

monomials and temperley lieb algebras we classify the fully tight simply laced coxeter groups that is the ones whoseiji avoiding kazhdan lusztig basis elements are monomials in the generatorsbsi we then investigate the basis of the temperley lieb algebra arising from the kazhdan lusztig basis of the associated hecke algebra and prove that the basis coincides with the usual monomial basis

robust kalman filters for linear time varying systems with stochastic parametric uncertainties we present a robust recursive kalman filtering algorithm that addresses estimation problems that arise in linear time varying systems with stochastic parametric uncertainties the filter has a one step predictor corrector structure and minimizes an upper bound of the mean square estimation error at each step with the minimization reduced to a convex optimization problem based on linear matrix inequalities the algorithm is shown to converge when the system is mean square stable and the state space matrices are time invariant a numerical example consisting of equalizer design for a communication channel demonstrates that our algorithm offers considerable improvement in performance when compared with conventional kalman filtering techniques

some remarks on general nonlinear stochastic h_ infty control with state control and disturbance dependent noise this technical note studies the nonlinear stochastic h control of ito type differential systems with all the state control input and external disturbance dependent noise x u v dependent noise for short a sufficient condition is given for the finite infinite horizon h control of such a system by means of an hamilton jacobi inequality hji instead of three coupled hamilton jacobi equations hjes as in previous literature

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

robust fuzzy filter design for a class of nonlinear stochastic systems this paper describes the robust hinfin fuzzy filtering design for a class of nonlinear stochastic systems the system dynamic is modelled by itocirc type stochastic differential equations for general nonlinear stochastic systems the hinfin filter can be obtained by solving a second order nonlinear hamilton jacobi inequality in general it is difficult to solve the second order nonlinear hamilton jacobi inequality in this paper using fuzzy approach takagi sugeno t s fuzzy model the hinfin fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities lmis instead of a second order hamilton jacobi inequality when the worst case fuzzy disturbance is considered a near minimum variance fuzzy filtering problem is also solved by minimizing the upper bound on the variance of the estimation error the near minimum variance fuzzy filtering problem under the worst case fuzzy disturbance is also characterized in terms of linear matrix inequality problem lmip which can be efficiently solved by the convex optimization techniques simulation examples are provided to illustrate the design procedure and expected performance

model reduction of uncertain systems with multiplicative noise based on balancing this paper investigates the problem of model reduction based on balancing for uncertain discrete time systems with multiplicative noise such systems can be considered as linear systems with both deterministic and stochastic uncertainties two linear matrix inequalities lmis are proposed to find the balancing transformation through which the original uncertain model with multiplicative noise is balanced the reduced order model with the same structure as that of the original one is obtained by truncating the balanced model an upper bound of the model reduction error is guaranteed based on the derived model reduction error bound an optimization problem is suggested so that the solutions of the lmis can be uniquely found and the model reduction error is ensured to be small

dixmier measurability in marcinkiewicz spaces and applications abstract we present new results concerning the description of dixmier measurable elements in the sense of a connes in marcinkiewicz spaces and demonstrate some applications of our results in particular we complement famous connes trace theorem by describing the asymptotics of the singular function of order n classical pseudo differential operators on an n dimensional compact riemannian manifold

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

h 2 optimal filtering for continuous time periodic linear stochastic systems with state dependent noise abstract this note addresses the problem of optimal h 2 filtering for a class of continuous time time varying stochastic systems the time variation character is considered to be periodic the state space representation of the optimal filter is designed based on the unique periodic solution of a suitable lyapunov differential equation and the periodic and stabilizing solution of a suitable generalized periodic riccati differential equation some numerical experiments are also added to show the effectiveness of the proposed method

stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set we deal with nonlinear dynamical systems consisting of a linear nominal part perturbed by model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense to this aim we introduce a new notion of stabilization in probability which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability this notion requires that given a target set a trajectory starting from some compact region of the state space containing the target remains forever inside some larger compact set eventually enters any given neighborhood of the target in finite time and remains thereinafter all these events being guaranteed with some probability we give a lyapunov based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems which at least include feedback linearizable systems the generality of the result is promising for applications to other classes of stochastic nonlinear systems in the deterministic case our results recover classical stabilization results for nonlinear systems

measures from dixmier traces and zeta functions for l functions on a closed compact riemannian manifold the noncommutative residue and the dixmier trace formulation of the noncommutative integral are shown to equate to a multiple of the lebesgue integral the identifications are shown to continue to and be sharp at l2 functions for functions strictly in lp 1 p 2 symmetrised noncommutative residue and dixmier trace formulas must be introduced for which the identification is shown to continue for the noncommutative residue however a failure is shown for the dixmier trace formulation at l1 functions it is shown the noncommutative residue remains finite and recovers the lebesgue integral for any integrable function while the dixmier trace expression can diverge the results show that a claim in the monograph j m gracia bondia j c varilly h figueroa elements of noncommutative geometry birkhauser adv texts birkhauser boston 2001 that the equality on c functions between the lebesgue integral and an operator theoretic expression involving a dixmier trace obtained from connes trace theorem can be extended to any integrable function is false the results of this paper include a general presentation for finitely generated von neumann algebras of commuting bounded operators including a bounded borel or l functional calculus version of c results in iv 2 of a connes noncommutative geometry academic press new york 1994

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

a numerical procedure to compute the stabilising solution of game theoretic riccati equations of stochastic control in this article the problem of the numerical computation of the stabilising solution of the game theoretic algebraic riccati equation is investigated the riccati equation under consideration occurs in connection with the solution of the h control problem for a class of stochastic systems affected by state dependent and control dependent white noise and subjected to markovian jumping the stabilising solution of the considered game theoretic riccati equation is obtained as a limit of a sequence of approximations constructed based on stabilising solutions of a sequence of algebraic riccati equations of stochastic control with definite sign of the quadratic part the proposed algorithm extends to this general framework the method proposed in lanzon feng anderson and rotkowitz lanzon a feng y anderson b d o and rotkowitz m 2008 computing the positive stabilizing solution to algebraic riccati equations with an indefinite quadratic term viaa recursive method ieee transactions on automat

stochastic optimal lqr control with integral quadratic constraints and indefinite control weights a standard assumption in traditional deterministic and stochastic optimal minimizing linear quadratic regulator lqr theory is that the control weighting matrix in the cost functional is strictly positive definite in the deterministic case this assumption is in fact necessary for the problem to be well posed because positive definiteness is required to make it a convex optimization problem however it has recently been shown that in the stochastic case when the diffusion term is dependent on the control the control weighting matrix may have negative eigenvalues but the problem remains well posed in this paper the completely observed stochastic lqr problem with integral quadratic constraints is studied sufficient conditions for the well posedness of this problem are given indeed we show that in certain cases these conditions may be satisfied even when the control weighting matrices in the cost and all of the constraint functionals have negative eigenvalues it is revealed that the seemingly nonconvex problem with indefinite control weights can actually be a convex one by virtue of the uncertainty in the system finally when these conditions are satisfied the optimal control is explicitly derived using results from duality theory

multiobjective investment policy for a nonlinear stochastic financial system a fuzzy approach the financial market always suffers from continuous and discontinuous jump changes and can be regarded as a nonlinear stochastic jump diffusion system most investors expect their investment policies to be not only higher benefits but also lower risk as a multiobjective optimization problem mop in this study a multiobjective h 2 h infty fuzzy investment is proposed for nonlinear stochastic jump diffusion financial systems to achieve the desired target with minimum investment cost and risk in pareto optimal sense simultaneously the takagi sugeno t s fuzzy model is used to approximate the nonlinear stochastic jump diffusion financial system to simplify the multiobjective h 2 h infty investment policy design procedure by the help of the t s fuzzy model the multiobjective h 2 h infty fuzzy investment policy problem of nonlinear stochastic financial system can be transformed to a linear matrix inequality constrained lmi constrained mop to avoid solving the annoying hamilton jacobi inequalities because the lmi constrained mop is not easy to directly calculate its pareto optimal solutions an indirect method is proposed to solve this mop for the multiobjective h 2 h infty fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems an lmi constrained multiobjective evolution algorithm lmi constrained moea is also developed to efficiently solve the pareto optimal solutions of the lmi constrained mop for the multiobjective h 2 h infty fuzzy investment policy design of nonlinear stochastic jump diffusion financial systems when the pareto optimal regulation solutions are solved by the proposed lmi constrained moea investors can select one investment policy to achieve their desired target with minimum investment cost and risk according to his her own preference

robust control design for nonlinear stochastic partial differential systems with poisson noise fuzzy implementation abstract this study addresses the robust h control design problem for nonlinear stochastic partial differential systems nspdss with poisson noise under the environment of random external disturbance in the spatio temporal domain for nspdss with poisson noise the robust h control design needs to solve a complex hamilton jacobi integral inequality hjii for robust control despite random external disturbance in general it is very difficult to solve the nonlinear partial differential hjii in order to simplify the design procedure a fuzzy stochastic partial differential system is proposed to approximate the nspds based on fuzzy interpolation approach then a fuzzy stochastic spatial state space model is developed to represent the fuzzy stochastic partial differential system via the semi discretization finite difference scheme and the kronecker product based on this model the robust h control design is proposed to achieve the robust control of nspdss via solving linear matrix inequalities lmis instead of an hjii the proposed robust fuzzy h controller has an efficient ability to attenuate the effect of spatio temporal external disturbance on the controlled output of nspdss from the area energy point of view finally a robust h control of the nervous system is given to confirm the control performance of the proposed robust control design method for nspdss with poisson noise

infinite markov jump bounded real lemma abstract a bounded real lemma is established providing an equivalent condition to stochastic stability ss of a continuous time infinite markovian jump linear system mjls with a prescribed l 2 stochastic disturbance attenuation level in terms of existence of solutions to an infinite set of coupled linear matrix inequalities lmis besides the interest in its own right the main result provides a fundamental tool for the development of an h like theory devoted to this class of systems

stabilization control for ito stochastic system with indefinite state and control weight costs in standard linear quadratic lq control the first step in investigating infinite horizon optimal control is to derive the stabilisation condition with the optimal lq controller this paper focus

cal h representation and applications to generalized lyapunov equations and linear stochastic systems this paper introduces an h representation method to express an n2 1 vector x as x h x tilde based on the introduced h representation approach several topics are extensively discussed including the generalized lyapunov equations gles arising from stochastic control stochastic observability generalized d stability and d stabilization weak stability and stabilization a necessary and sufficient condition for the existence and uniqueness of the symmetric and skew symmetric solutions of gles is presented respectively moreover the solution structure of gles is also clarified through the h representation method several necessary and sufficient conditions are also obtained for stochastic observability generalized d stability and d stabilization weak stability and stabilization

fubini theorem in noncommutative geometry abstract we discuss the fubini formula in alain connes noncommutative geometry we present a sufficient condition on spectral triples for which a fubini formula holds true the condition is natural and related to heat semigroup asymptotics we provide examples of spectral triples for which the fubini formula fails

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

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

traces of compact operators and the noncommutative residue abstract we extend the noncommutative residue of m wodzicki on compactly supported classical pseudo differential operators of order d and generalise a connes trace theorem which states that the residue can be calculated using a singular trace on compact operators contrary to the role of the noncommutative residue for the classical pseudo differential operators a corollary is that the pseudo differential operators of order d do not have a unique trace pseudo differential operators can be non measurable in connes sense other corollaries are given clarifying the role of dixmier traces in noncommutative geometry including the definitive statement of connes original theorem

systems of matrix rational differential equations arising in connection with linear stochastic systems with markovian jumping abstract in this paper a class of systems of matrix nonlinear differential equations containing as particular cases the systems of coupled riccati differential equations arising in connection with control of some linear stochastic systems is considered the system of differential equations considered in this paper are converted in a suitable nonlinear differential equation on a finite dimensional hilbert space adequately choosen this allows us to use the positivity properties of the linear evolution operator defined by the linear differential equations of lyapunov type our aim is to investigate properties of stabilizing and bounded solutions of the considered differential equations and to obtain some conditions ensuring the existence of such solutions conditions providing the existence of a maximal solution minimal solution respectively with respect to some classes of global solutions are presented it is shown that if the coefficients of the equations are periodic functions all these special solutions stabilizing maximal minimal are periodic functions too whenever possible the probabilistic arguments were avoided and so the results proved in the paper appear as results in the field of differential equations with interest in themselves

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

on stabilizability and exact observability of stochastic systems with their applications this paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications with the aid of the operator spectrum a necessary and sufficient condition is given for the stabilizability of stochastic systems some new concepts such as unremovable spectrum and strong solution are introduced an unremovable spectral theorem and a stochastic popov belevith hautus criterion for exact observability are presented as applications a comparison theorem for stochastic algebraic riccati equations and a result on lyapunov type equations are obtained

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

brief h control and filtering of discrete time stochastic systems with multiplicative noise linear discrete time systems with stochastic uncertainties in their state space matrices are considered the problems of finite horizon filtering and output feedback control are solved taking into account possible cross correlations between the uncertain parameters in both problems a cost function is defined which is the expected value of the relevant standard h performance index with respect to the uncertain parameters a solution to the filtering problem is obtained first by applying the adjoint system and deriving a bounded real lemma for this system this solution guarantees a prescribed estimation level of accuracy while minimizing an upper bound on the covariance of the estimation error the solution of the filtering problem is also extended to the infinite horizon case the results of the filtering problem are used to solve the corresponding output feedback problem a filtering example is given where a comparison is made with the results obtained using bounded uncertainty design techniques

static output feedback of state multiplicative systems with application to altitude control a linear parameter dependent approach for designing a constant output feedback controller for a linear time invariant system with stochastic multiplicative wiener type noise that achieves a minimum bound on either the stochastic h 2 or the h performance level is introduced a solution is achieved 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 introduced which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that corresponds to the vertices of the uncertainty polytope the stochastic uncertainties appear in both the dynamic and the measurement matrices of the system the problems are solved using the expected value of the standard performance index over the stochastic parameters the theory developed is applied to an altitude control example

generalized lyapunov equation approach to state dependent stochastic stabilization detectability criterion in this paper the generalized lyapunov equation approach is used to study stochastic stabilization detectability with state multiplicative noise some practical test criteria for stochastic stabilization and detectability such as stochastic popov belevitch hautus criterion for exact detectability are obtained moreover useful properties of the generalized lyapunov equation are derived based on critical stability and exact detectability introduced in this paper as applications first the stochastic linear quadratic regulator as well as the related generalized algebraic riccati equation are discussed extensively second the infinite horizon stochastic h 2 h infin control with state and control dependent noise is also investigated which extends and improves the recently published results

obituary to a j pritchard on the 12th of august 2007 tony pritchard professor of mathematics at the university of warwick died suddenly at the age of 70 from a heart attack while on holiday with his family on the island of lanzarote both of the authors have had the privilege of working with him for many years we have lost both a colleague and a friend the following notes are dedicated to his memory

brief paper a unified design for state and output feedback h control of nonlinear stochastic markovian jump systems with state and disturbance dependent noise for a class of continuous time nonlinear stochastic markovian jump systems with state and disturbance dependent noise both the state and output feedback h control problems are studied based on the solvability of a set of coupled hamilton jacobi inequalities hjis we give a unified design for both state and dynamic output feedback h control via a common function u r t i e u x r t is a state feedback h control while u email protected r t is the desired output feedback h control

brief paper a delay decomposition approach to l2 l filter design for stochastic systems with time varying delay this paper investigates the problem of l 2 l filter design for a class of stochastic systems with time varying delay the addressed problem is the design of a full order linear filter such that the error system is asymptotically mean square stable and a prescribed l 2 l performance is satisfied in order to develop a less conservative filter design a new lyapunov krasovskii functional lkf is constructed by decomposing the delay interval into multiple equidistant subintervals and a new integral inequality is established in the stochastic setting then based on the lkf and integral inequality the delay dependent conditions for the existence of l 2 l filters are obtained in terms of linear matrix inequalities lmis the resulting filters can ensure that the error system is asymptotically mean square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances finally two examples are given to illustrate the effectiveness of the proposed method

type ii non commutative geometry i dixmier trace in von neumann algebras abstract we define the notion of connes von neumann spectral triple and consider the associated index problem we compute the analytic chern connes character of such a generalized spectral triple and prove the corresponding local formula for its hochschild class this formula involves the dixmier trace for ii von neumann algebras in the case of foliations we identify this dixmier trace with the corresponding measured wodzicki residue

stochastic linear quadratic control via semidefinite programming we study stochastic linear quadratic lq optimal control problems over an infinite time horizon allowing the cost matrices to be indefinite we develop a systematic approach based on semidefinite programming sdp a central issue is the stability of the feedback control and we show this can be effectively examined through the complementary duality of the sdp furthermore we establish several implication relations among the sdp complementary duality the generalized riccati equation and the optimality of the lq control problem based on these relations we propose a numerical procedure that provides a thorough treatment of the lq control problem via primal dual sdp it identifies a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution for the latter case we develop an epsilon approximation scheme that is asymptotically optimal

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

stochastic stability analysis for 2 d roesser systems with multiplicative noise this paper is concerned with the robust stochastic stability analysis for two dimensional 2 d discrete state multiplicative noisy systems smnss in the roesser form we first derive a new sufficient condition under which linear discrete 2 d smnss are 2 d robustly stochastically stable the underlying problem can then be recast as a convex problem expressed by linear matrix inequalities which can be facilitated using existing numerical algorithms we then apply the obtained result to examine the 2 d robust stochastic stability for 2 d digital filters in the roesser form with random coefficient variation and saturation overflow arithmetic based on free weighting matrices and diagonally dominant matrices an illustrative example is presented to verify the usefulness and potential of the proposed results

predictor based control of stochastic systems with nonlinear diffusions and input delay abstract we consider the problem of state feedback control of linear continuous time stochastic systems with nonlinear diffusion terms affected by time varying input delays or equivalently by time varying state measurement delays we propose a finite dimensional control law based on closed loop predictors and derive sufficient delay bounds for the exponential stability in mean and exponential mean square stability with prescribed rate

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

optimal mean variance control for discrete time linear systems with markovian jumps and multiplicative noises in this paper we consider the stochastic optimal control problem of discrete time linear systems subject to markov jumps and multiplicative noises under two criteria the first one is an unconstrained mean variance trade off performance criterion along the time and the second one is a minimum variance criterion along the time with constraints on the expected output we present explicit conditions for the existence of an optimal control strategy for the problems generalizing previous results in the literature we conclude the paper by presenting a numerical example of a multi period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor

indefinite stochastic linear quadratic control and generalized differential riccati equation a stochastic linear quadratic lq control problem is indefinite when the cost weighting matrices for the state and the control are allowed to be indefinite indefinite stochastic lq theory has been extensively developed and has found interesting applications in finance however there remains an outstanding open problem which is to identify an appropriate riccati type equation whose solvability is it equivalent to the solvability of the indefinite stochastic lq problem this paper solves this open problem for lq control in a finite time horizon a new type of differential riccati equation called the generalized differential riccati equation is introduced which involves algebraic equality inequality constraints and a matrix pseudoinverse it is then shown that the solvability of the generalized riccati equation is not only sufficient but also necessary for the well posedness of the indefinite lq problem and the existence of optimal feedback open loop controls moreover all of the optimal controls can be identified via the solution to the riccati equation an example is presented to illustrate the theory developed

brief paper on detectability of stochastic systems we discuss notions of detectability for stochastic linear control systems of ito type a natural concept of detectability requires a non zero output if the state process is unstable we show that this property can equivalently be characterized by a generalized version of the hautus test the proof is based on spectral theory for positive operators

filtering for discrete fuzzy stochastic systems with sensor nonlinearities this paper deals with the filtering problem for discrete time fuzzy stochastic systems with sensor nonlinearities there exist time varying parameter uncertainties and random noise depending on state and external disturbance the characteristic of nonlinear sensor is handled by a decomposition method by means of the parallel distributed compensation technique the design method of the robust h filter is presented sufficient conditions for the stochastic stability of the filtering error systems are derived such that the filter parameters can be explicitly obtained simulation results are given to illustrate the proposed method

generalized limits with additional invariance properties and their applications to noncommutative geometry abstract let n be the set of all natural numbers and l l n resp l l 0 be the banach space of all bounded sequences x x 1 x 2 resp classes of lebesgue measurable bounded functions on 0 with the uniform norm we work with subsets of the set of all normalized positive functionals on l and l which are used in noncommutative geometry to define various classes of dixmier traces singular positive traces on the ideal m 1 of compact operators on an infinite dimensional hilbert space h with logarithmic divergence of the partial sums of their singular values these classes of traces are of importance in noncommutative geometry and with each such a class say b of traces a subset m 1 b m 1 on which all traces from b coincide is linked the main objective of the present article is to give new characterizations of m 1 b for commonly occurring classes of dixmier traces we also answer a question from benameur and fack 2006 4 concerning conditions on a dixmier trace under which lidskii type formulae from that article hold

technical communique infinite horizon h2 h control for stochastic systems with markovian jumps this paper studies robust h 2 h control problem for systems subjected to multiplicative noise and markovian parameter jumps a necessary sufficient condition for the existence of h 2 h control is presented by means of two coupled algebraic riccati equations respectively finally a suboptimal h 2 h controller design algorithm is also obtained by solving a convex optimization problem

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

commutator structure of operator ideals commutator structure of operator ideals ken dykema 1 tadeusz figiel gary weiss and mariusz wodzicki department of mathematics texas a m university college station tx 77843 3368 usa b instytut matematyczny polskiej akademii nauk 81 825 sopot poland department of mathematical sciences university of cincinnati cincinnati oh 45221 0025 usa department of mathematics university of california berkeley ca 94720 3840 usa

robust h filter design for neutral stochastic uncertain systems with time varying delay abstract in this paper the robust h filtering problem for a class of neutral stochastic systems is discussed the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delay the parameter uncertainties are assumed to be time varying norm bounded using the stochastic lyapunov stability theory and ito s differential rule a full order filter is designed for all admissible uncertainties and time varying delay which is expressed in the form of linear matrix inequality lmi the dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable while achieving a prescribed stochastic robust h performance level at the end of this paper a numerical example is given to demonstrate the usefulness of the proposed method

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

ad nilpotent ideals and equivalence relations abstract in this paper we study ad nilpotent ideals of a complex simple lie algebra g and their connections with affine weyl groups and nilpotent orbits we define a left equivalence relation for ad nilpotent ideals based on their normalizer and generators and prove that the equivalence relation corresponds to lusztig s star operation for simply laced algebraic group g

brief paper almost sure exponential stabilisation of stochastic systems by state feedback control so far a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean square stability this paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean square sense the results are expressed in terms of linear matrix inequalities lmis which are easy to be checked in practice by using matlab toolbox moreover the control structure in this paper appears not only in the drift part but also in the diffusion part of the underlying stochastic system

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

connes integration formula for the noncommutative plane our aim is to prove the integration formula on the noncommutative moyal plane in terms of singular traces a la connes

stochastic linear quadratic regulators with indefinite control weight costs this paper considers optimal minimizing control of stochastic linear quadratic regulators lqrs the assumption that the control weight costs must be positive definite inherited from the determ

numerical solution of stochastic nash games with state dependent noise for weakly coupled large scale systems abstract this paper discusses the infinite horizon stochastic nash games with state dependent noise after establishing the asymptotic structure along with the positive semidefiniteness for the solutions of the cross coupled stochastic algebraic riccati equations csares a new algorithm that combines newton s method with two fixed point algorithms for solving the csares is derived as a result it is shown that the proposed algorithm attains quadratic convergence and the reduced order computations for sufficiently small parameter e as another important feature the high order approximate strategy that is based on the iterative solutions is proposed using such strategy the degradation of the cost functional is investigated finally in order to demonstrate the efficiency of the proposed algorithms computational examples are provided

infinite horizon h control for nonlinear stochastic markov jump systems with x u v dependent noise via fuzzy approach in this paper the h control problem is studied for nonlinear stochastic markov jump systems with state control and external disturbance dependent noise x u v dependent noise for short a sufficient condition is derived for the infinite horizon h control of such systems in terms of a set of coupled second order hamilton jacobi inequalities hjis in general it is difficult to solve these coupled hjis by using fuzzy approach the infinite horizon h control design for nonlinear stochastic markov jump systems is developed via solving a set of linear matrix inequalities lmis instead of hjis two numerical examples are presented to illustrate the effectiveness of the proposed design methods

some examples of square integrable representations of semisimple p adic groups we construct irreducible representations of the hecke algebra of an affine weyl group analogous to kilmoyer s reflection representation corresponding to finite weyl groups and we show that in many cases they correspond to a square integrable representation of a simple p adic group

robust output feedback control of nonlinear stochastic systems using neural networks we present an adaptive output feedback controller for a class of uncertain stochastic nonlinear systems the plant dynamics is represented as a nominal linear system plus nonlinearities in turn these nonlinearities are decomposed into a part obtained as the best approximation given by neural networks plus a remaining part which is treated as uncertainties modeling approximation errors and neglected dynamics the weights of the neural network are tuned adaptively by a lyapunov design the proposed controller is obtained through robust optimal design and combines together parameter projection control saturation and high gain observers high performances are obtained in terms of large errors tolerance as shown through simulations

on a class of rational matrix differential equations arising in stochastic control we prove a monotonicity and a comparison theorem for the solutions of a rational matrix differential equation appearing in stochastic control and derive existence and convergence results for the solutions of this differential equation moreover in the time invariant case we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing solution

robust h control with maximal decay rate for linear discrete time stochastic systems abstract the problems of robust stabilization and robust h control with maximal decay rate are investigated for discrete time stochastic systems with time varying norm bounded parameter uncertainties for the robust stabilization problem an optimal state feedback controller is designed which ensures that the closed loop system is robustly stochastically stable with maximal decay rate while for the robust h control problem the designed state feedback controller guarantees that the resulting closed loop system is with a specified h performance level besides robust stochastic stability with maximal decay rate the method based on the convex optimization and linear matrix inequality is developed to solve these problems two examples are provided to show the effectiveness of the proposed approach

indefinite quadratic with linear costs optimal control of markov jump with multiplicative noise systems in this paper we consider the stochastic optimal control problem of discrete time markov jump with multiplicative noise linear systems the performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables the weighting matrices of the state and control for the quadratic part are allowed to be indefinite we present a necessary and sufficient condition under which the problem is well posed and a state feedback solution can be derived from a set of coupled generalized riccati difference equations interconnected with a set of coupled linear recursive equations for the case in which the quadratic term matrices are non negative this necessary and sufficient condition can be written in a more explicit way the results are applied to a problem of portfolio optimization

linear moving horizon estimation with pre estimating observer in this note a moving horizon estimation mhe strategy for detectable linear systems is proposed like the idea of pre stabilizing model predictive control the states are estimated by a forward simulation with a pre estimating observer in the mhe formulation compared with standard linear mhe approaches it has more degrees of freedom to optimize the noise filtering tuning parameters are chosen to minimize the effects of measurement noise and model errors which is implemented by finding tightest estimation error bounds the performance of the proposed observer is demonstrated on one linear discrete time example