lasalle type theorems for stochastic differential delay equations the main aim of this paper is to establish the lasalle type asymptotic convergence theorems for the solutions of stochastic differential delay equations these stochastic versions are then applied to establish sufficient criteria for the stochastically asymptotic stability of the delay equations several examples are also given for illustration

a homogeneous domination approach to state feedback of stochastic high order feedforward nonlinear systems this paper investigates stochastic high order feedforward nonlinear systems for the first time by introducing the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

global stabilization of stochastic high order feedforward nonlinear systems with time varying delay in this paper we consider the problem of global stabilization for a class of stochastic high order feedforward nonlinear systems with time varying delay by introducing the homogeneous domination design method and constructing the appropriate lyapunov krasovskii functional a state feedback controller is constructed to drive the closed loop system to be globally asymptotically stable in probability

adaptive output feedback control for a class of uncertain stochastic non linear systems with time delays in this paper we investigate the adaptive output feedback stabilisation for a class of stochastic non linear systems with time varying time delays first we give some sufficient conditions to ensure the existence and uniqueness of the solution process for stochastic non linear systems with time delays and introduce a new stability notion and the related criterion then for a class of stochastic non linear systems with time varying time delays uncertain parameters in both drift and diffusion terms and general constant virtual control coefficients we present a systematic design procedure for a memoryless adaptive output feedback control law by using the backstepping method it is shown that under the control law based on a memoryless observer the closed loop equilibrium of interest is globally stable in probability and moreover the solution process can be regulated to the origin almost surely

robust h control for linear discrete time systems with norm bounded time varying uncertainty the problem of robust h analysis and synthesis for linear discrete time systems with norm bounded time varying uncertainty is studied in this paper it will be shown that this problem is equivalent to the problem of h analysis and synthesis of an auxiliary system the necessary and sufficient conditions for the equivalency are proved thus the original problem can be solved by existing h control methods

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

quadratic stability and stabilization of uncertain linear discrete time systems with state delay abstract this paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete time systems with state delay the system under consideration involves state time delay and time varying norm bounded parameter uncertainties appearing in all the matrices of the state space model necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities respectively a robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities two examples are presented to demonstrate the effectiveness of the proposed approach

robust backstepping control for a class of time delayed systems in this note the problem of robust output feedback control for a class of nonlinear time delayed systems is considered the systems considered are in strict feedback form state observer is first designed then based on the observed states the controller is designed via backstepping method both the designed observer and controller are independent of the time delays based on lyapunov stability theory we prove that the constructed controller can render the closed loop system asymptotically stable simulation results further verify the effectiveness of the proposed approach

a stackelberg game approach to distributed spectrum management we consider a cognitive radio system with one primary licensed user and multiple secondary unlicensed users given the interference temperature constraint the secondary users compete for the available spectrum to fulfill their own communication need borrowing the concept of price from market theory we develop a decentralized stackelberg game formulation for power allocation in this scheme the primary user leader announces prices for the available tones such that a system utility is maximized using the announced prices secondary users followers compete for the available bandwidth to maximize their own utilities we show that this stackelberg game is polynomial time solvable under certain channel conditions when the individual power constraints of secondary users are inactive due to strict interference temperature constraint the proposed distributed power control method is decomposable across the tones and unlike normal water filling it respects the interference temperature constraints of the primary user when individual power constraints are active we propose a distributed approach that solves the problem under an aggregate interference temperature constraint moreover we propose a dual decomposition based power control method and show that it solves the stackelberg game asymptotically when the number of tones becomes large

output feedback stabilization for a class of stochastic time delay nonlinear systems this note focuses on a class of stochastic time delay nonlinear systems the problem we address is to design a controller such that the closed loop system is exponentially stable it is shown that the stabilization via output feedback can be solved by a lyapunov based recursive design method

state feedback control of systems with multiplicative noise via linear matrix inequalities we consider lti systems perturbed by parametric uncertainties modeled as white noise disturbances we show how to maximize via state feedback control the smallest norm of the noise intensity vector producing instability in the mean square sense using convex optimization over linear matrix inequalities we also show how to maximize performance robustness where performance is measured by expected output energy with either bounded initial conditions and zero inputs classical lqg cost or zero initial conditions and deterministic inputs of bounded energy a generalization of the h norm

non smooth lyapunov function based global stabilization for quantum filters this paper addresses the global stabilization problem for a class of quantum filters via non smooth lyapunov functions due to the intrinsic symmetric topology of filter state space the smooth controls synthesized via the classical lyapunov stochastic stability theory fail to obtain the global stabilizability because of the existence of the so called antipodal eigenstates as such for the first time we introduce a non smooth lyapunov like theory for generic stochastic nonlinear systems which includes a continuous lyapunov like theorem and a discontinuous lyapunov like theorem for stability in probability applying the non smooth lyapunov like theory switching control and continuous control in saturation form are constructed for the quantum filters with consideration of the sliding motion of filter state the non smooth property enables these controls to deal with the symmetric topology of filter state space and to solve the problem of global stabilization for quantum filters the eigenstate transferring is obtained as a special result distinguishing these non smooth lyapunov based controls from classical control approaches for quantum filters the effectiveness of the non smooth lyapunov based controls is illustrated through the control design for the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the controls

adaptive fuzzy tracking control for stochastic nonlinear systems with unknown time varying delays an adaptive fuzzy controller is presented for a class of stochastic nonlinear systems an quadratic function is constructed to give the condition of the stability of systems the scheme guarantees the stability of closed loop system in the mean square sense the drawback of the quartic moment approach is overcome and the method is simplified this paper addresses the problem of adaptive tracking control for a class of stochastic strict feedback nonlinear time varying delays systems using fuzzy logic systems fls in this paper quadratic functions are used as lyapunov functions to analyze the stability of systems other than the fourth moment approach proposed by h deng and m krstic and the hyperbolic tangent functions are introduced to deal with the hessian terms this approach overcomes the drawback of the traditional quadratic moment approach and reduce the complexity of design procedure and controller based on the backstepping technique the appropriate lyapunov krasovskii functionals and the fls the adaptive fuzzy controller is well designed the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded in probability and the tracking error can converge to a small residual set around the origin in the mean square sense

completeness and spectral synthesis of nonselfadjoint one dimensional perturbations of selfadjoint operators abstract we study spectral properties of nonselfadjoint rank one perturbations of compact selfadjoint operators the problems under consideration include completeness of eigenvectors relations between completeness of the perturbed operator and its adjoint and the spectral synthesis problem we obtain new criteria for completeness and spectral synthesis in this class as well as a series of counterexamples which show that the spectral structure of rank one perturbations is in general unexpectedly rich and complicated a parallel spectral theory is developed for one dimensional singular perturbations of unbounded selfadjoint operators our approach is based on a functional model for this class which translates the properties of operators to completeness problems for systems of reproducing kernels and their biorthogonals in some spaces of analytic entire functions

quantum measurement based feedback control a nonsmooth time delay control approach this paper addresses the problem of measurement based feedback control for quantum systems in which the time to compute the filter based control input is taken into account by considering the input delay it starts with a new lyapunov lasalle like theorem for delay dependent stochastic stability of a class of time delay stochastic nonlinear systems nonsmooth time delay control is then constructed to compensate for the control computation time which is known but arbitrarily long while globally stabilizing the quantum filters almost surely the nonsmooth property enables the control to deal with the symmetric topology of filter state space the effectiveness of the proposed control is illustrated through the global stabilization of the spin 1 2 systems simulation results are presented and discussed to show the effectiveness of the proposed control

decentralised adaptive output feedback stabilisation for stochastic time delay systems via lasalle yoshizawa type theorem abstractthis paper deals with the decentralised output feedback stabilisation problem for a class of large scale stochastic time delay nonlinear systems a general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time delay systems in addition a stochastic version of the well known lasalle yoshizawa theorem with time varying delay is initially proposed for the controller design and stability analysis then for a class of large scale stochastic systems with time varying delays totally decentralised adaptive delay dependent controllers are designed by using k filter and backstepping approach via lasalle yoshizawa type theorem and constructing a general lyapunov function it is shown that all signals in the closed loop system are bounded almost surely and the solution is almost surely asymptotically stable finally a simulation example is given to illustrate the effectiveness of the results of this paper

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

finite time stabilization of stochastic nonlinear systems in strict feedback form in this paper we investigate the problem of almost surely finite time stabilization of a class of stochastic nonlinear systems based on the recently proposed almost surely finite time stability theorem in yin khoo man and yu 2011 we prove that almost surely global finite time stability of stochastic nonlinear systems in strict feedback form can be guaranteed by a continuous control law a systematic design algorithm is developed for the construction of the controller simulation results are given to illustrate the theoretical analysis

further results on output feedback stabilization for stochastic high order nonlinear systems with time varying delay this article further discusses the output feedback stabilization problem for stochastic high order nonlinear systems with time varying delay under the weaker conditions on nonlinearities in drift and diffusion vector fields by using the idea of homogeneous domination approach skillfully choosing an appropriate lyapunov krasoviskii functional and successfully solving several troublesome obstacles in the design and analysis procedure an output feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

technical communique stabilization of a class of uncertain large scale stochastic systems with time delays this paper focuses on a class of large scale interconnected bilinear stochastic systems with time delays and time varying parameter uncertainties the problem we address is to design a robust decentralized controller such that the closed loop interconnected stochastic system is globally asymptotically stable in probability for all admissible uncertainties and time delays first robust stability analysis is given in terms of a set of linear matrix inequalities lmis then it is shown that the robust decentralized stabilization can be solved by an lmi based design method

stability of stochastic systems with uncertain time delays abstract for linear delay systems with bilinear noise sufficient conditions are given for the global asymptotic stochastic stability independent of the length of the delay s for linear stochastic noise terms sufficient conditions for the existence of an invariant distribution for all values of the delay are given it is shown that the gaussian distribution is the unique invariant distribution the covariance and correlation matrix function of the resulting stationary process are completely characterized by a lyapunov type equation all these sufficient conditions are obtained in the form of the existence of some positive definite matrices satisfying certain riccati type equations

technical communique h state feedback control for generalized continuous discrete time delay system in this paper we consider the problem of designing h state feedback controller for the generalized time delay systems with delayed states and control inputs in continuous and discrete time cases respectively the generalized time delay system problems are solved on the basis of linear matrix inequality lmi technique considering time delays the sufficient condition for the existence of controller and h state feedback controller design methods are presented also using some changes of variables and schur complements the obtained sufficient condition can be rewritten as an lmi form in terms of transformed variables the proposed controller design method can be extended into the problem of robust h state feedback controller design method easily

on the spectral characterization of entire operators with deficiency indices 1 1 abstract for entire operators and entire operators in the generalized sense we provide characterizations based on the spectra of their selfadjoint extensions in order to obtain these spectral characterizations we discuss the representation of a simple regular closed symmetric operator with deficiency indices 1 1 as a multiplication operator in a certain de branges space

dual methods for nonconvex spectrum optimization of multicarrier systems the design and optimization of multicarrier communications systems often involve a maximization of the total throughput subject to system resource constraints the optimization problem is numerically difficult to solve when the problem does not have a convexity structure this paper makes progress toward solving optimization problems of this type by showing that under a certain condition called the time sharing condition the duality gap of the optimization problem is always zero regardless of the convexity of the objective function further we show that the time sharing condition is satisfied for practical multiuser spectrum optimization problems in multicarrier systems in the limit as the number of carriers goes to infinity this result leads to efficient numerical algorithms that solve the nonconvex problem in the dual domain we show that the recently proposed optimal spectrum balancing algorithm for digital subscriber lines can be interpreted as a dual algorithm this new interpretation gives rise to more efficient dual update methods it also suggests ways in which the dual objective may be evaluated approximately further improving the numerical efficiency of the algorithm we propose a low complexity iterative spectrum balancing algorithm based on these ideas and show that the new algorithm achieves near optimal performance in many practical situations

h control of discrete time linear systems with norm bounded uncertainties and time delay in state this paper deals with h control problem for discrete time linear systems with norm bounded uncertainties and time delay in state in terms of a modified riccati inequality for discrete time linear systems a sufficient condition is presented and a state feedback control law is also given the proposed control law is a memoryless state feedback control law

a stochastic successive minimization method for nonsmooth nonconvex optimization with applications to transceiver design in wireless communication networks consider the problem of minimizing the expected value of a cost function parameterized by a random variable the classical sample average approximation method for solving this problem requires minimization of an ensemble average of the objective at each step which can be expensive in this paper we propose a stochastic successive upper bound minimization method ssum which minimizes an approximate ensemble average at each iteration to ensure convergence and to facilitate computation we require the approximate ensemble average to be a locally tight upper bound of the expected cost function and be easily optimized the main contributions of this work include the development and analysis of the ssum method as well as its applications in linear transceiver design for wireless communication networks and online dictionary learning moreover using the ssum framework we extend the classical stochastic sub gradient method to the case of minimizing a nonsmooth nonconvex objective function and establish its convergence

brief canonical forms for stochastic nonlinear systems necessary and sufficient conditions for the existence of diffeomorphisms that transform stochastic nonlinear systems to three canonical forms are derived based on the so called invariance under transformation rule

robust stabilization of uncertain systems with time varying multistate delay the authors deal with the problem of stabilizing a class of uncertain linear systems with time varying multi state delay and subject to norm bounded parameter uncertainty via memoryless linear state feedback some sufficient conditions for the robust stabilizability are derived fur this class of uncertain systems if there exists a positive definite symmetric solution satisfying the algebraic riccati equation or inequality a suitable memoryless state feedback law can be derived also moreover all such parametric algebraic riccati inequalities have been transformed into some linear matrix inequality problems so there is no tuning of the parameters to gain a stabilizing solution

on input to state stability of stochastic retarded systems with markovian switching this note develops a razumikhin type theorem on pth moment input to state stability of hybrid stochastic retarded systems also known as stochastic retarded systems with markovian switching which is an improvement of an existing result an application to hybrid stochastic delay systems verifies the effectiveness of the improved result

robust stability of uncertain stochastic differential delay equations in this paper we first discuss the robust stability of uncertain linear stochastic differential delay equations we then extend the theory to cope with the robust stability of uncertain semi linear stochastic differential delay equations we shall also give several examples to illustrate our theory

stability analysis of random nonlinear systems with time varying delay and its application this paper studies a class of random nonlinear systems with time varying delay in which the r order moment of the random disturbance is finite firstly some general conditions are proposed to guarantee the existence and uniqueness of the global solution to random nonlinear time delay systems secondly some criteria on noise to state stability in the moment sense and in probability sense are given by lyapunov method respectively finally an adaptive output feedback regulation controller is constructed for a class of random nonlinear time delay systems and the effectiveness of the proposed recursive procedure is demonstrated by a simulation example

a note on the lasalle type theorems for stochastic differential delay equations the main aim of this note is to improve some results obtained in the author s earlier paper 1999 j math anal appl 236 350 369 from the improved result follow some useful criteria on the stochastic asymptotic stability and boundedness

operators with singular continuous spectrum ii rank one operators for an operator a with cyclic vector we studya p wherep is the rank one projection onto multiples of if spec a anda has no a c spectrum we prove thata p has purely singular continuous spectrum on for a denseg of s

the class of n entire operators we introduce a classification of simple regular closed symmetric operators with deficiency indices 1 1 according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized sense due to m g krein we show that these classes of operators have several distinctive properties some of them related to the spectra of their canonical self adjoint extensions in particular we provide necessary and sufficient conditions on the spectra of two canonical self adjoint extensions of an operator for it to belong to one of our classes our discussion is based on some recent results in the theory of de branges spaces

a novel alleviating fuzzy control algorithm for a class of nonlinear stochastic systems in pure feedback form abstract in this paper a novel alleviating computation adaptive fuzzy control scheme is presented for a class of uncertain stochastic nonlinear pure feedback systems different from the existing results that are based on traditional back stepping schemes as well as approximation technique of fuzzy logic systems flss for stochastic nonlinear systems this new approach assumes that the norm of optimal approximation parameter vector of flss is bounded by unknown parameter at each design step of this new approach fewer bounded adaptive parameters need to be adjusted thus this new approach can alleviate the online computation burden and improve the robust control performance meanwhile combining lyapunov theorem analysis it is proven that all the signals in the closed loop system are uniformly ultimately bounded uub and the tracking error can converge to a small neighborhood of zero the good performance of this approach is well demonstrated in a simulation example

one dimensional perturbations of unbounded selfadjoint operators with empty spectrum abstract we study spectral properties of one dimensional singular nonselfadjoint perturbations of an unbounded selfadjoint operator and give criteria for the possibility to remove the whole spectrum by a perturbation of this type a counterpart of our results for the case of bounded operators provides a complete description of compact selfadjoint operators whose rank one perturbation is a volterra operator

global finite time stabilisation for a class of stochastic nonlinear systems by output feedback in this paper the problem of global finite time stabilisation by output feedback is considered for a class of stochastic nonlinear systems first based on homogeneous systems theory and the adding a power integrator technique a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system then the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms it is shown that the proposed output feedback control law can guarantee that the closed loop system is global finite time stable in probability finally simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme

state feedback stabilization for stochastic feedforward nonlinear systems with time varying delay this paper investigates a class of stochastic feedforward nonlinear systems with time varying delay by introducing the homogeneous domination approach to stochastic systems a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

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

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

robust h control for uncertain discrete time systems with circular pole constraints this paper investigates the problem of robust h control for uncertain discrete time systems with circular pole constraints the system under consideration is subject to norm bounded time invariant uncertainties in both the state and input matrices the problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region and the h norm of the closed loop transfer function is strictly less than a given positive scalar for all admissible uncertainties by introducing the notion of quadratic d stabilizability with an h norm bound the problem is solved necessary and sufficient conditions for quadratic d stabilizability with an h norm bound are derived our results can be regarded as extensions of existing results on robust h control and robust pole assignment of uncertain systems

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

a multiple model mrac scheme for multivariable systems with matching uncertainties this paper develops a multivariable multiple model adaptive control scheme for adaptive state feedback state tracking control of systems whose plant model matching conditions are uncertain and parameters are unknown to deal with the uncertainty of plant model matching conditions needed for adaptive control multiple reference model systems are employed to generate multiple parameter estimation and feedback control signals from which a most suitable control input is selected by a control switching mechanism designed using multiple estimation errors such a new multiple model control design is based on an expanded control system parametrization which has the capacity to cover system structural uncertainties stability analysis and simulation results ensure and verify the desired adaptive control system stability and tracking performance

real and complex monotone communication games noncooperative game theoretic tools have been increasingly used to study many important resource allocation problems in communications networking smart grids and portfolio optimization in this paper we consider a general class of convex nash equilibrium problems neps where each player aims at solving an arbitrary smooth convex optimization problem differently from most of current works we do not assume any specific structure for the players problems and we allow the optimization variables of the players to be matrices in the complex domain our main contribution is the design of a novel class of distributed asynchronous best response algorithms suitable for solving the proposed neps even in the presence of multiple solutions the new methods whose convergence analysis is based on variational inequality vi techniques can select among all the equilibria of a game those that optimize a given performance criterion at the cost of limited signaling among the players this is a major departure from existing best response algorithms whose convergence conditions imply the uniqueness of the ne some of our results hinge on the use of vi problems directly in the complex domain the study of these new kind of vis also represents a noteworthy innovative contribution we then apply the developed methods to solve some new generalizations of single input single output siso and multiple input multiple output mimo games in cognitive radio systems showing a considerable performance improvement over classical pure noncooperative schemes

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

exponential stability of stochastic delay interval systems abstract although deterministic interval systems have received a great deal of attention so far there is no work on stochastic interval systems the main aim of this paper is to initiate the study of stochastic interval systems of course there are many properties of such systems to be investigated but this paper will concentrate on the study of exponential stability of stochastic interval systems with time varying delays the main technique used in this paper is the razumikhin type theorem established recently by mao stochastic process appl 65 1996 233 250

robust h control for linear time invariant systems with norm bounded uncertainty in the input matrix abstract this paper focuses on the problem of robust h control design for a class of linear time invariant systems with uncertainty in the state space model we consider uncertain systems with norm bounded parameter uncertainty in the input matrix the paper presents a state feedback control design which stabilizes the plant for all admissible uncertainties and also guarantees an h norm bound constraint on disturbance attenuation paralleling to the theory of robust control the robust h control problem is solved via the notion of quadratic stabilization with an h norm bound constraint necessary and sufficient conditions for quadratic stabilization with an h norm bound are derived it is shown that the solution to this problem involves solving a parameter dependent algebraic riccati equation the results can be regarded as extensions of existing results on robust stabilization of linear uncertain systems and h optimal control

robust h sub spl infin compensator design for time delay systems with norm bounded time varying uncertainties considers robust h sub spl infin compensator design for linear systems that involve unknown time delays both in states and controls and time varying norm bounded parameter uncertainties sufficient conditions for designing robust compensators are obtained in terms of two riccati inequalities which are not mutually coupled through which a full order robust h sub spl infin compensator can be obtained finally a small example is given to show the applicability of the proposed approach

rank one perturbations and singular integral operators abstract we consider rank one perturbations a a of a self adjoint operator a with cyclic vector h 1 a on a hilbert space h the spectral representation of the perturbed operator a is given by a singular integral operator of special form such operators exhibit what we call rigidity and are connected with two weight estimates for the hilbert transform also some results about two weight estimates of cauchy hilbert transforms are proved in particular it is proved that the regularized cauchy transforms t e are uniformly in e bounded operators from l 2 to l 2 where and are the spectral measures of a and a respectively as an application a sufficient condition for a to have a pure absolutely continuous spectrum on a closed interval is given in terms of the density of the spectral measure of a with respect to some examples like jacobi matrices and schrodinger operators with l 2 potentials are considered

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control

design of cognitive radio systems under temperature interference constraints a variational inequality approach the concept of cognitive radio cr has recently received great attention from the research community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed primary and unlicensed secondary users in the same bandwidth in this paper we propose a novel nash equilibrium ne problem to model concurrent communications of cognitive secondary users who compete against each other to maximize their information rate the formulation contains constraints on the transmit power and possibly spectral masks as well as aggregate interference tolerable at the primary users receivers the coupling among the strategies of the players due to the interference constraints presents a new challenge for the analysis of this class of nash games that cannot be addressed using the game theoretical models proposed in the literature for this purpose we need the framework given by the more advanced theory of finite dimensional variational inequalities vi this provides us with all the mathematical tools necessary to analyze the proposed ne problem e g existence and uniqueness of the solution and to devise alternative distributed algorithms along with their convergence properties

robust h state feedback control for linear systems with state delay and parameter uncertainty this paper addresses the problem of robust h state feedback control design for linear systems with state delay and parameter uncertainty based on a positive definite solution of a modified algebraic riccati equation the proposed robust h static state feedback controller stabilizes uncertain time delay systems independently of delays and guarantees an h norm bound constraint on disturbance attenuation for all admissible uncertainties furthermore it is shown that no advantage can be obtained from the use of a proper linear dynamic state feedback compared with the use of static state feedback illustrative examples are given to demonstrate the applicability of the proposed approach