non uniqueness of quantized yang mills theories we consider quantized yang mills theories in the framework of causal perturbation theory which goes back to epstein and glaser in this approach gauge invariance is expressed by a simple commutator relation for the s matrix the most general coupling which is gauge invariant to first order contains a two parametric ambiguity in the ghost sector a divergence and a coboundary coupling may be added we prove not completely that the higher orders with these two additional couplings are also gauge invariant moreover we show that the ambiguities of the n point distributions restricted to the physical subspace are only a sum of the divergences in the sense of vector analysis it turns out that the theory without divergence and coboundary coupling is the simplest one in a quite technical sense the proofs for the n point distributions containing coboundary couplings are given up to third or fourth order only whereas the statements about the divergence coupling are proved for all orders

state feedback h type control of linear systems with time varying parameter uncertainty this paper is concerned with stabilisation and disturbance attenuation problems for linear systems with uncertain parameters we consider the case where the uncertainties are possibly unbounded but have a certain normal distribution and the case where the uncertainties are arbitrary but bounded criteria for the solvability of the disturbance attenuation problem are presented in terms of generalized riccati type matrix inequalities and equations the main part of the paper is devoted to the analysis and solution of these equations a numerical example is given to illustrate our results

robust controller design for stochastic nonlinear systems via convex optimization this paper presents a new nonlinear control design framework called convex optimization based stochastic steady state tracking error minimization cvstem for a class of ito stochastic nonlinear systems including stochastic lagrangian systems this state feedback controller design involves the use of multiple state dependent coefficient sdc models of a nonlinear system equation and computes its controller parameters by solving a convex optimization problem in order to minimize an upper bound of the steady state tracking error this problem is shown to be equivalent to the original nonlinear optimization problem of minimizing the upper bound the exponential stability and robustness properties due to the state dependent riccati inequality are proven using stochastic contraction analysis discrete time stochastic incremental contraction analysis with respect to a state and time dependent metric is also presented along with its explicit connection to continuous time contraction analysis a result of simulation is used to validate the superiority of the proposed controller compared to a known nonlinear controller a pid controller and an h infinity controller

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

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

robust h infinity control in the presence of stochastic uncertainty this paper considers a robust h infinity state feedback control problem for linear uncertain systems with stochastic uncertainty the uncertainty class considered in the paper involves uncertain multiplicative white noise perturbations which satisfy a certain variance constraint a state feedback controller is presented which guarantees a prescribed level of disturbance attenuation for all admissible stochastic uncertainties

h control of linear time varying systems a state space approach in this paper the standard problem of h infty control theory for finite dimensional linear time varying continuous time plants is considered the problem is given a real number gamma 0 f

dissipativity theory for nonlinear stochastic dynamical systems in this paper we develop stochastic dissipativity theory for nonlinear dynamical systems using basic input output and state properties specifically a stochastic version of dissipativity using both an input output as well as a state dissipation inequality in expectation for controlled markov diffusion processes is presented the results are then used to derive extended kalman yakubovich popov conditions for characterizing necessary and sufficient conditions for stochastic dissipativity of stochastic dynamical systems using two times continuously differentiable storage functions in addition feedback interconnection stability in probability results for stochastic dynamical systems are developed thereby providing a generalization of the small gain and positivity theorems to stochastic systems

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

the standard model and its generalizations in the epstein glaser approach to renormalization theory we continue our study of non abelian gauge theories in the framework of the epstein glaser approach to renormalization theory we consider the case when massive spin 1 bosons are present in the theory and we modify appropriately the analysis of the origin of the gauge invariance performed in a preceding paper in the case of null mass spin 1 bosons then we are able to extend a result of dutsch and scharf concerning the uniqueness of the standard model consistent with renormalization theory in fact we consider the most general case i e the consistent interaction of r spin 1 bosons and we do not impose any restrictions on the gauge group and the mass spectrum of the theory we show that besides the natural emergence of a group structure as in the massless case we obtain new conditions of a group theoretical nature namely the existence of a certain representation of the gauge group associated to the higgs fields some other mass relations connecting the structure constants of the gauge group and the masses of the bosons emerge naturally the proof is carried out using the epstein glaser approach to renormalization theory

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

robust stabilization design of nonlinear stochastic partial differential systems fuzzy approach abstract in this paper we address the robust stabilization design problem for nonlinear stochastic partial differential systems nspdss in the presence of random external disturbances and measurement noise in the spatio temporal domain we propose a fuzzy stochastic partial differential system to approximate the nspdss based on fuzzy interpolation approach next we develop a fuzzy stochastic spatial state space model to represent the fuzzy stochastic partial differential system by employing a semi discretization finite difference scheme based on this model we propose a robust fuzzy estimator based stabilization controller to stabilize the nspdss furthermore robust stochastic h stabilization design is suggested to attenuate the effects of random external disturbances and measurement noise in the spatio temporal domain from the area energy point of view the lmi technique is applied to solve the issue of control gains and estimator gains of the controller by using a systematic control design procedure finally a simulation is presented as an example to illustrate the design procedure and to confirm the performance of the proposed robust fuzzy estimator based stabilization design for the nspdss

some coincidence theorems and stability of iterative procedures the purpose of this paper is to obtain coincidence theorems and study the problem of stability of iterations for solving coincidence equations on a general setting several special cases are discussed

coincidences and fixed points of nonself hybrid contractions ahmad and imdad and ahmed and khan have studied coincidences and fixed points of nonself hybrid contractions on metrically convex spaces however most of their main theorems contain errors and admit counterexamples in this paper we rectify these results and obtain coincidence and fixed point theorems on a more general setting

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

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

some coincidence point results in ordered b metric spaces and applications in a system of integral equations the aim of this paper is to present some coincidence point results for four mappings satisfying generalized j f weakly contractive condition in the framework of ordered b metric spaces an example and an application are also provided to support our results

a passive system approach to feedback stabilization of nonlinear control stochastic systems the purpose of this paper is to provide sufficient conditions for asymptotic stabilization in probability of nonlinear control stochastic differential systems by means of smooth state feedback laws in particular we prove that as in the case of stochastic differential systems affine in the control one can compute stabilizing feedback laws provided the unforced stochastic differential system is lyapunov stable in probability and some rank conditions are fulfilled some well known stabilization results for stochastic differential systems affine in the control proved in the literature are extended to nonaffine nonlinear control stochastic differential systems

absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty this paper is concerned with existence and optimality properties of so called guaranteed cost controllers for an uncertain system subject to structured uncertainty the uncertainty in the system is assumed to have a stochastic character and to satisfy certain stochastic integral constraints it is shown that a minimax optimal guaranteed cost state feedback controller for a stochastic system can be synthesized as a state feedback controller absolutely stabilizing this system for each initial state of the system this controller can be found by parametric optimization of solutions of a parameter dependent generalized matrix riccati equation arising in stochastic h infty theory

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

h control with transients in h infty or uniformly optimal control problems it is usually assumed that the system initial conditions are zero in this paper an h infty like control problem that incorporates uncertainty in initial conditions is formulated this is done by defining a worst case performance measure both finite and infinite horizon problems are considered necessary and sufficient conditions are derived for the existence of controllers that yield a closed loop system for which the above mentioned performance measure is less than a prespecified value state space formulae for the controllers are also presented

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

gauge independence of the s matrix in the causal approach the gauge dependence of the time ordered products for yang mills theories is analysed in perturbation theory by means of the causal method of epstein and glaser together with perturbative gauge invariance this approach allows a simple inductive proof of the gauge independence of the physical s matrix

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

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

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