criteria for quasi convexity and pseudo convexity relationships and comparisons a first order criterion for pseudo convexity and second order criteria for quasi convexity and pseudo convexity are given for twice differentiable functions on open convex sets the relationships between these second order criteria and other known criteria are also analysed finally the numbers of operations required to verify these criteria are calculated and compared

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

fractional hamiltonian monodromy from a gauss manin monodromy fractional hamiltonian monodromy is a generalization of the notion of hamiltonian monodromy recently introduced by nekhoroshev sadovskii and zhilinskii c r acad sci paris ser 1 335 985 2002 nekhoroshev sadovskii and zhilinskii ann henri poincare 7 1099 2006 for energy momentum maps whose image has a particular type of nonisolated singularities in this paper we analyze the notion of fractional hamiltonian monodromy in terms of the gauss manin monodromy of a riemann surface constructed from the energy momentum map and associated with a loop in complex space which bypasses the line of singularities we also prove some propositions on fractional hamiltonian monodromy for 1 n and m n resonant systems

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

robust h sub 2 h sub spl infin filtering for linear systems with error variance constraints in this correspondence we consider the robust h sub 2 h sub spl infin filtering problem for linear perturbed systems with steady state error variance constraints the purpose of this multiobjective problem is to design a linear filter that does not depend on the parameter perturbations such that the following three performance requirements are simultaneously satisfied 1 the filtering process is asymptotically stable 2 the steady state variance of the estimation error of each state is not more than the individual prespecified value 3 the transfer function from exogenous noise inputs to error state outputs meets the prespecified h sub spl infin norm upper bound constraint we show that in both continuous and discrete time cases the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like equations inequalities we present both the existence conditions and the explicit expression of desired robust filters an illustrative numerical example is provided to demonstrate the flexibility of the proposed design approach

on practical conditions for the existence and uniqueness of solutions to the general equality quadratic programming problem we present practical conditions under which the existence and uniqueness of a finite solution to a given equality quadratic program may be examined different sets of conditions allow this examination to take place when null space range space or lagrangian methods are used to find stationary points for the quadratic program

matrix theoretic criteria for the quasiconvexity of twice continuously differentiable functions abstract the author examines matrices and bordered matrices having exactly one or at most one negative eigenvalue these results are then used to state matrix theoretic criteria for the quasiconvexity of twice continuously differentiable functions for quadratic functions a new criterion for quasiconvexity is established and its equivalence to the already known criterion 11 23 is also shown

eigenvalue bounds versus semidefinite relaxations for the quadratic assignment problem it was recently demonstrated that a well known eigenvalue bound for the quadratic assignment problem qap actually corresponds to a semidefinite programming sdp relaxation however for this bound to be computationally useful the assignment constraints of the qap must first be eliminated and the bound then applied to a lower dimensional problem the resulting projected eigenvalue bound is one of the best available bounds for the qap especially when considering the quality of bounds relative to the complexity of obtaining them in this paper we show that the projected eigenvalue bound is also related to an sdp relaxation of the original qap this implicit sdp relaxation is similar to sdp relaxations of the qap proposed by lin and saigal on solving large scale semidefinite programming problems a case study of quadratic assignment problem department of industrial engineering and operations research university of michigan 1997 and zhao et al j combin optim 2 1998 pp 71 109

implementation of a variance reduction based lower bound in a branch and bound algorithm for the quadratic assignment problem the efficient implementation of a branch and bound algorithm for the quadratic assignment problem qap incorporating the lower bound based on variance reduction of li pardalos ramakrishnan and resende 1994 is presented a new data structure for efficient implementation of branch and bound algorithms for the qap is introduced computational experiments with the branch and bound algorithm on different classes of qap test problems are reported the branch and bound algorithm using the new lower bounds is compared with the same algorithm utilizing the commonly applied gilmore lawler lower bound both implementations use a greedy randomized adaptive search procedure for obtaining initial upper bounds the algorithms report all optimal permutations optimal solutions for previously unsolved instances from the literature of dimensions n 16 and n 20 have been found with the new algorithm in addition the new algorithm has been tested on a class of large data variance problems requiring the examination of much fewer nodes of the branch and bound tree than the same algorithm using the gilmore lawler lower bound

monodromy in the hydrogen atom in crossed fields abstract we show that the hydrogen atom in orthogonal electric and magnetic fields has a special property of certain integrable classical hamiltonian systems known as monodromy the strength of the fields is assumed to be small enough to validate the use of a truncated normal form h snf which is obtained from a two step normalization of the original system we consider the level sets of h snf on the second reduced phase space for an open set of field parameters we show that there is a special dynamically invariant set which is a doubly pinched 2 torus this implies that the integrable hamiltonian h snf has monodromy manifestation of monodromy in quantum mechanics is also discussed

dynamic approximate solutions of the hj inequality and of the hjb equation for input affine nonlinear systems the solution of most nonlinear control problems hinges upon the solvability of partial differential equations or inequalities in particular disturbance attenuation and optimal control problems for nonlinear systems are generally solved exploiting the solution of the so called hamilton jacobi hj inequality and the hamilton jacobi bellman hjb equation respectively an explicit closed form solution of this inequality or equation may however be hard or impossible to find in practical situations herein we introduce a methodology to circumvent this issue for input affine nonlinear systems proposing a dynamic i e time varying approximate solution of the hj inequality and of the hjb equation the construction of which does not require solving any partial differential equation or inequality this is achieved considering the immersion of the underlying nonlinear system into an augmented system defined on an extended state space in which a locally positive definite storage function or value function can be explicitly constructed the result is a methodology to design a dynamic controller to achieve l2 disturbance attenuation or approximate optimality with asymptotic stability

dynamic lyapunov functions lyapunov functions are a fundamental tool to investigate stability properties of equilibrium points of linear and nonlinear systems the existence of lyapunov functions for asymptotically stable equilibrium points is guaranteed by converse lyapunov theorems nevertheless the actual computation of the analytic expression of the function may be difficult herein we propose an approach to avoid the computation of an explicit solution of the lyapunov partial differential inequality introducing the concept of dynamic lyapunov function these functions allow to study stability properties of equilibrium points similarly to standard lyapunov functions in the former however a positive definite function is combined with a dynamical system that render dynamic lyapunov functions easier to construct than lyapunov functions moreover families of standard lyapunov functions can be obtained from the knowledge of a dynamic lyapunov function by rendering invariant a desired submanifold of the extended state space the invariance condition is given in terms of a system of partial differential equations similar to the lyapunov pde differently from the latter however in the former no constraint is imposed on the sign of the solution or on the sign of the term on the right hand side of the equation several applications and examples conclude the paper

non hamiltonian monodromy abstract it is well known that the energy momentum map of a two degree of freedom integrable hamiltonian system with a focus focus singularity has monodromy in this paper we generalize this result to systems which are not necessarily hamiltonian

rotation forms and local hamiltonian monodromy the monodromy of torus bundles associated with completely integrable systems can be computed using geometric techniques constructing homology cycles or analytic arguments computing discontinuities of abelian integrals in this article we give a general approach to the computation of monodromy that resembles the analytical one reducing the problem to the computation of residues of polar 1 forms we apply our technique to three celebrated examples of systems with monodromy the champagne bottle the spherical pendulum the hydrogen atom and to the case of non degenerate focus focus singularities re obtaining the classical results an advantage of this approach is that the residue like formula can be shown to be local in a neighborhood of a singularity hence allowing the definition of monodromy also in the case of non compact fibers this idea has been introduced in the literature under the name of scattering monodromy we prove the coincidence of the two definitions with the monodromy of an appropr

new approach to mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems this paper revisits the problem of mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems differing from previous results in the quadratic framework the filter design makes full use of the parameter dependent stability idea not only is the filter dependent of the parameters which are assumed to reside in a polytope and be measurable online but in addition the lyapunov matrices are different for the entire polytope domain as well as for different channels with respect to the mixed performances these ideas are realized by introducing additional slack variables to the well established performance conditions and by employing new bounding techniques which results in a much less conservative filter design method a numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method

lower bounds for the quadratic assignment problem based upon a dual formulation a new bounding procedure for the quadratic assignment problem qap is described which extends the hungarian method for the linear assignment problem lap to qaps operating on the four dimensional cost array of the qap objective function the qap is iteratively transformed in a series of equivalent qaps leading to an increasing sequence of lower bounds for the original problem to this end two classes of operations which transform the four dimensional cost array are defined these have the property that the values of the transformed objective function z are the corresponding values of the old objective function z shifted by some amount c in the case that all entries of the transformed cost array are nonnegative then c is a lower bound for the initial qap if moreover there exists a feasible solution u to the qap such that its value in the transformed problem is zero then c is the optimal value of z and u is an optimal solution for the original qap the transformations are iteratively applied until no significant increase in constant c as above is found resulting in the so called dual procedure dp several strategies are listed for appropriately determining c or equivalently transforming the cost array the goal is the modification of the elements in the cost array to obtain new equivalent problems that bring the qap closer to solution in some cases the qap is actually solved though solution is not guaranteed the close relationship between the dp and the linear programming formulation of adams and johnson is presented the dp attempts to solve adams and johnson s clp a continuous relaxation of a linearization of the qap this explains why the dp produces bounds close to the optimum values for clp calculated by johnson in her dissertation and by resende et al in their interior point algorithm for linear programming the benefit of using dp within a branch and bound algorithm is described then two versions of dp are tested on the nugent test instances from size 5 to size 30 as well as several other test instances from qaplib these compare favorably with earlier bounding methods

definiteness and semidefiniteness of quadratic forms revisited abstract it is shown how the schur complement theory can be used for the derivation of criteria for the definiteness or semidefiniteness of the restriction of a quadratic form to the null space of a matrix

s lemma with equality and its applications let f x x tax 2a tx c f x xtax 2atx c and h x x tbx 2b tx d h x xtbx 2btx d be two quadratic functions having symmetric matrices a a and b b the s lemma with equality asks when the unsolvability of the system f x 0 h x 0 f x 0 h x 0 implies the existence of a real number mu such that f x mu h x ge 0 forall x in mathbb r n f x h x 0 x rn the problem is much harder than the inequality version which asserts that under slater condition f x 0 h x le 0 f x 0 h x 0 is unsolvable if and only if f x mu h x ge 0 forall x in mathbb r n f x h x 0 x rn for some mu ge 0 0 in this paper we show that the s lemma with equality does not hold only when the matrix a a has exactly one negative eigenvalue and h x h x is a non constant linear function b 0 b not 0 b 0 b 0 as an application we can globally solve inf f x h x 0 inf f x h x 0 as well as the two sided generalized trust region subproblem inf f x l le h x le u inf f x l h x u without any condition moreover the convexity of the joint numerical range f x h 1 x ldots h p x x in mathbb r n f x h1 x hp x x rn where f f is a possibly non convex quadratic function and h 1 x ldots h p x h1 x hp x are affine functions can be characterized using the newly developed s lemma with equality

hamiltonian monodromy and morse theory we show that hamiltonian monodromy of an integrable two degrees of freedom system with a global circle action can be computed by applying morse theory to the hamiltonian of the system our proof is based on takens s index theorem which specifies how the energy h chern number changes when h passes a non degenerate critical value and a choice of admissible cycles in fomenko zieschang theory connections of our result to some of the existing approaches to monodromy are discussed

a new bound for the quadratic assignment problem based on convex quadratic programming we describe a new convex quadratic programming bound for the quadratic assignment problem qap the construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for qap the new bound dominates the well known projected eigenvalue bound and appears to be competitive with existing bounds in the trade off between bound quality and computational effort

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

fractional monodromy in the 1 2 resonance we give an analytic proof of the fractional monodromy theorem for the 1 2 oscillator system with s 1 symmetry formulated by n n nekhoroshev d a sadovskii and b i zhilinskii in c r acad sci paris ser i 335 2002 985 988 our proof is based on an analytic description of the hamiltonian flow on the fibers of the integral map of this system c 2006 elsevier inc all rights reserved

a new look at the robust control of discrete time markov jump linear systems abstractin this paper we make a foray in the role played by a set of four operators on the study of robust h2 and mixed h2 h control problems for discrete time markov jump linear systems these operators appear in the study of mean square stability for this class of systems by means of new linear matrix inequality lmi characterisations of controllers which include slack variables that to some extent separate the robustness and performance objectives we introduce four alternative approaches to the design of controllers which are robustly stabilising and at the same time provide a guaranteed level of h2 performance since each operator provides a different degree of conservatism the results are unified in the form of an iterative lmi technique for designing robust h2 controllers whose convergence is attained in a finite number of steps the method yields a new way of computing mixed h2 h controllers whose conservatism decreases with iteration two numerical examples illustrate the applicability

on the convexity of the multiplicative version of karmarkar s potential function karmarkar s potential function is quasi convex but not convex this note investigates the multiplicative version of the potential function and shows that it is not necessarily convex in general but is strictly convex when the corresponding feasible region is bounded this implies that the multiplicative version of the potential function in karmarkar s algorithm is convex since it works on a simplex

restricted quadratic forms inertia theorems and the schur complement the starting point of this investigation is the properties of restricted quadratic forms x ax x s rm where a is an m m real symmetric matrix and s is a subspace the index theory of hestenes 1951 and maddocks 1985 that treats the more general hilbert space version of this problem is first specialized to the finite dimensional context and appropriate extensions valid only in finite dimensions are made the theory is then applied to obtain various inertia theorems for matrices and positivity tests for quadratic forms expressions for the inertias of divers symmetrically partitioned matrices are described in particular an inertia theorem for the generalized schur complement is given the investigation recovers links and extends several formerly disparate results in the general area of inertia theorems

relationship between nash equilibrium strategies and h_ 2 h_ infty control of stochastic markov jump systems with multiplicative noise this technical note is concerned with discussing the relationship between nash equilibrium strategies and the finite horizon h 2 h control of time varying stochastic systems subject to markov jump parameters and multiplicative noise it is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term furthermore necessary and sufficient conditions for the finite horizon h 2 h control of stochastic markov jump systems are presented via coupled matrix valued equations

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

finite time stability and stabilization of ito stochastic systems with markovian switching mode dependent parameter approach this technical note is concerned about the finite time stability and stabilization for ito stochastic systems with markovian switching a mode dependent parameter approach is proposed to give a sufficient condition for finite time stability and its superiority to common parameter approach is analyzed moreover the finite time stabilization is studied and two new sufficient conditions for the existence of state and output feedback controllers are presented in terms of coupled matrix inequalities a n mode algorithm is given for solving the obtained matrix inequalities arising from finite time stability stabilization finally an example is employed to illustrate the effectiveness of our obtained results

strong duality for a trust region type relaxation of the quadratic assignment problem abstract lagrangian duality underlies many efficient algorithms for convex minimization problems a key ingredient is strong duality lagrangian relaxation also provides lower bounds for non convex problems where the quality of the lower bound depends on the duality gap quadratically constrained quadratic programs qqps provide important examples of non convex programs for the simple case of one quadratic constraint the trust region subproblem strong duality holds in addition necessary and sufficient strengthened second order optimality conditions exist however these duality results already fail for the two trust region sub problem surprisingly there are classes of more complex non convex qqps where strong duality holds one example is the special case of orthogonality constraints which arise naturally in relaxations for the quadratic assignment problem qap in this paper we show that strong duality also holds for a relaxation of qap where the orthogonality constraint is replaced by a semidefinite inequality constraint using this strong duality result and semidefinite duality we develop new trust region type necessary and sufficient optimality conditions for these problems our proof of strong duality introduces and uses a generalization of the hoffman wielandt inequality

constructive epsilon nash equilibria for nonzero sum differential games in this paper a class of infinite horizon nonzero sum differential games and their nash equilibria are studied and the notion of epsilon alpha nash equilibrium strategies is introduced dynamic strategies satisfying partial differential inequalities in place of the hamilton jacobi isaacs partial differential equations associated with the differential games are constructed these strategies constitute local epsilon alpha nash equilibrium strategies for the differential game the proposed methods are illustrated on a differential game for which the nash equilibrium strategies are known and on a lotka volterra model with two competing species simulations indicate that both dynamic strategies yield better performance than the strategies resulting from the solution of the linear quadratic approximation of the problem

a note on the augmented hessian when the reduced hessian is semidefinite certain matrix relationships play an important role in optimality conditions and algorithms for nonlinear and semidefinite programming let h be an n n symmetric matrix a an m n matrix and z a basis for the null space of a in a typical optimization context h is the hessian of a smooth function and a is the jacobian of a set of constraints when the reduced hessian zthz is positive definite augmented lagrangian methods rely on the known existence of a finite bar rho ge 0 such that for all rho bar rho the augmented hessian h rho ata is positive definite in this note we analyze the case when zthz is positive semidefinite i e singularity is allowed and show that the situation is more complicated in particular we give a simple necessary and sufficient condition for the existence of a finite bar rho so that h rho ata is positive semidefinite for rho ge bar rho a corollary of our result is that if h is nonsingular and indefinite while zthz is positive semidefinite and singular no such bar rho exists

a new lower bound via projection for the quadratic assignment problem new lower bounds for the quadratic assignment problem qap are presented these bounds are based on the orthogonal relaxation of qap the additional improvement is obtained by making efficient use of a tractable representation of orthogonal matrices having constant row and column sums the new bound is easy to implement and often provides high quality bounds under an acceptable computational effort

reduced order h sub spl infin filtering for stochastic systems this paper deals with the reduced order h sub spl infin filtering problem for stochastic systems necessary and sufficient conditions are obtained for the existence of solutions to the continuous time and discrete time problems in terms of certain linear matrix inequalities lmis and a coupling nonconvex rank constraint condition furthermore when these conditions are feasible an explicit parametrization of all desired reduced order filters corresponding to a feasible solution is given in particular when the reduced order filter is restricted to be a static one then simple conditions expressed by lmis only without any rank constraints are derived and a parametrization of all solutions is also given finally an illustrative example is provided to show the effectiveness of the proposed approach

generalized convexity on affine subspaces with an application to potential functions second order conditions for the pseudo convexity of a function restricted to an affine subspace are obtained by extending those already known for functions on n these results are then used to analyse the pseudo convexity of potential functions of the type introduced by karmarkar

adaptive tracking for stochastic nonlinear systems with markovian switching the problem of the adaptive tracking for a class of stochastic nonlinear systems with stationary markovian switching is considered in this note an ito formula is proposed for stochastic integral equations with an integral about martingale measure an adaptive backstepping controller is designed such that the closed loop system has a unique solution that is globally bounded in probability and l4 norm of the tracking error converges to an arbitrarily small neighborhood of zero a simulation example demonstrates the efficiency of the proposed scheme

integral input to state stability for hybrid delayed systems with unstable continuous dynamics this paper considers integral input to state stability iiss for a class of hybrid time delay systems discrete dynamics includes impulsive and switching signals and continuous dynamics is not necessarily stable based on multiple lyapunov krasovskii functionals a dwell time bound is explicitly given to guarantee iiss of the hybrid delayed system compared with existing results on related problems the obtained stability criteria can be applied to a larger class of hybrid delayed systems moreover the obtained dwell time bound is less conservative than existing ones at last an example related to networked control systems ncss is provided to illustrate the effectiveness of the proposed result

dynamics near the p q resonance abstract we study the dynamics near the truncated p q resonant hamiltonian equilibrium for p q coprime the critical values of the momentum map of the liouville integrable system are found the three basic objects reduced period rotation number and non trivial action for the leading order dynamics are computed in terms of complete hyperelliptic integrals a relation between the three functions that can be interpreted as a decomposition of the rotation number into geometric and dynamic phase is found using this relation we show that the p q resonance has fractional monodromy finally we prove that near the origin of the 1 q resonance the twist vanishes

input to state stability of impulsive stochastic delayed systems under linear assumptions in this paper the input to state stability iss integral iss iiss and stochastic iss siss are investigated for impulsive stochastic delayed systems by means of the lyapunov krasovskii function and the average impulsive interval approach the conditions for iss type properties are derived under linear assumptions respectively for destabilizing and stabilizing impulses it is shown that if the continuous stochastic delayed system is iss and the impulsive effects are destabilizing then the hybrid system is iss with respect to a lower bound of the average impulsive interval moreover it is unveiled that if the continuous stochastic delayed system is not iss the impulsive effects can successfully stabilize the system for a given upper bound of the average impulsive interval an improved comparison principle is developed for impulsive stochastic delayed systems which facilitates the derivations of our results for iss iiss siss an example of networked control systems is provided to illustrate the effectiveness of the proposed results

computing lower bounds for the quadratic assignment problem with an interior point algorithm for linear programming an example of the quadratic assignment problem qap is the facility location problem in which n facilities are assigned at minimum cost to n sites between each pair of facilities there is a given amount of flow contributing a cost equal to the product of the flow and the distance between sites to which the facilities are assigned proving optimality of qaps has been limited to instances having fewer than 20 facilities largely because known lower bounds are weak we compute lower bounds for a wide range of qaps using a linear programming based lower bound studied by z drezner 1995 on the majority of qaps tested a new best known lower bound is computed on 87 of the instances we produced the best known lower bound on several instances including some having more the 20 facilities the lower bound is tight the linear programs which can be large even for small qaps are solved with an interior point code that uses a preconditioned conjugate gradient algorithm to compute the interior point directions attempts to solve these instances using the cplex primal simplex algorithm as well as the cplex barrier primal dual interior point method were successful only for the smallest instances

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

input to state stability for nonlinear systems with stochastic impulses abstract in this study the problem of input to state stability iss is systematically investigated for nonlinear systems with stochastic impulses first the iss problem is considered for systems where impulsive strengths are assumed to be stochastic and impulsive intervals are confined by the average impulsive interval then the iss problem is analyzed for nonlinear systems with both stochastic impulsive intensity and density several different cases are considered i e cases where the impulsive instants are satisfied by a renewal process poisson process semi markov chain and markov chain an example of coordination of multi agent systems is provided to illustrate the effectiveness of the proposed new stability criteria

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

recent advances in the solution of quadratic assignment problems the quadratic assignment problem qap is notoriously difficult for exact solution methods in the past few years a number of long open qaps including those posed by steinberg 1961 nugent et al 1968 and krarup 1972 were solved to optimality for the first time the solution of these problems has utilized both new algorithms and novel computing structures we describe these developments as well as recent work which is likely to result in the solution of even more difficult instances

a unified razumikhin type criterion on input to state stability of time varying impulsive delayed systems abstract this paper discusses the problem of input to state stability iss of time varying impulsive delayed systems by introducing a switching parameter and using the notion of average impulsive interval a unified razumikhin type criterion on iss which is simultaneously effective for stabilizing impulses and destabilizing impulses is derived the condition which requires the coefficient of the estimated upper bound of the derivative of a lyapunov function to be constant in the existing results on iss of impulsive systems is weakened the results in this paper allow the coefficient of the derivative of a lyapunov function to be time varying function which can be both positive and negative and may even be unbounded furthermore the impulsive intervals of an impulsive sequence are allowed to have arbitrarily small lower bound and large enough upper bound simultaneously as a by product a unified criterion on iss for time varying impulsive delay free systems is also presented two examples are presented to illustrate the effectiveness of our results

stabilization and destabilization of hybrid systems of stochastic differential equations this paper aims to determine whether or not a stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system new methods are developed and sufficient conditions on the stability and instability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization and destabilization

the linear quadratic optimization problems for a class of linear stochastic systems with multiplicative white noise and markovian jumping in this paper the linear quadratic optimization problem for a class of linear stochastic systems subject both to multiplicative white noise and markovian jumping is investigated two classes of admissible controls are considered one of these classes contains controls with additional property that corresponding trajectories tend to zero in mean square when tends to spl infin while concerning the controls contained in the second class of admissible controls there is not any stability assumption in the optimization problem over the first class of admissible controls the cost functional could have indefinite sign of weights matrices an iterative procedure to compute the maximal solution of the systems of generalized riccati equations is provided a numerical example to illustrate the applicability of the iterative procedure is given

stationary filter for continuous time markovian jump linear systems we derive a stationary filter for the best linear mean square filter blmsf of continuous time markovian jump linear systems mjls it amounts here to obtain the convergence of the error covariance matrix of the blmsf to a stationary value under the assumption of mean square stability of the mjls and ergodicity of the associated markov chain theta t it is shown that there exists a unique solution for the stationary riccati filter equation and this solution is the limit of the error covariance matrix of the blmsf the advantage of this scheme is that it is easy to implement since the filter gain can be performed offline leading to a linear time invariant filter

quadratic assignment problems abstract this paper surveys quadratic assignment problems qap at first several applications of this problem class are described and mathematical formulations of qaps are given then some exact solution methods and good heuristics are outlined their computational behaviour is illustrated by numerical results further recent results on the asymptotic probabilistic behaviour of qaps are outlined

applications of parametric programming and eigenvalue maximization to the quadratic assignment problem we investigate new bounding strategies based on different relaxations of the quadratic assignment problem in particular we improve the lower bound found by using an eigenvalue decomposition of the quadratic part and by solving a linear program for the linear part the improvement is accomplished by applying a steepest ascent algorithm to the sum of the two bounds