optimal h model reduction via linear matrix inequalities continuous and discrete time cases necessary and sufficient conditions are derived for the existence of a solution to the continuous time and discrete time h model reduction problems these conditions are expressed in terms of linear matrix inequalities lmis and a coupling non convex rank constraint set in addition an explicit parametrization of all reduced order models that correspond to a feasible solution is provided in terms of a contractive matrix these results follow from the recent solution of the h control design problem using lmis particularly simple conditions and a simple parametrization of all solutions are obtained for the zeroth order h approximation problem and the convexity of this problem is demonstrated computational issues are discussed and an iterative procedure is proposed to solve the h model reduction problem using alternating projections although global convergence of the algorithm is not guaranteed

an improved suboptimal model reduction for singular systems an improved suboptimal model reduction for singular systems is proposed the proposed method is based on silverman ho algorithm as in wang et al 2004 a full parametrization of reduced order models is provided unlike the technique of wang et al 2004 where in only partial parametrization is presented the proposed method is illustrated by a numerical example and is compared with the method of wang et al 2004

characterization of the solution to the optimal h model reduction problem abstract in this paper the h norm approximation of a given stable proper rational transfer function by a lower order stable proper rational transfer function is studied the solution method is based on the authors observation that the h model reduction problem can be converted into a hankel norm model reduction problem a simple characterization of the solution to the optimal h model reduction problem is developed

h suboptimal model reduction for singular systems the model reduction problem was investigated for singular systems in this paper to solve the problem the silverman ho algorithm was given and based on this algorithm an optimal model reduction method for the fast subsystem was presented to obtain reduced order stable models for singular systems sequentially the suboptimal model reduction algorithm was obtained for singular systems the advantage of the presented algorithm is that the impulsive nature of singular system is preserved in the reduced order models then some necessary and sufficient conditions for the existence of a stable reduced order system were given and these conditions can be verified numerically finally illustrative examples were given to show the effectiveness of the proposed approach

positive filtering for continuous time positive systems under l 1 performance in this paper we address the positive filtering problem for positive continuous time systems under the l1 induced performance a pair of positive filters with error bounding feature is proposed to estimate the output of positive systems a novel characterisation is first obtained to ensure that the filtering error system is asymptotically stable with a prescribed l1 induced performance then necessary and sufficient conditions for the existence of required filters are presented and the obtained results are expressed in terms of linear programming problems which can be easily checked by standard software finally a numerical example is given to illustrate the effectiveness of the proposed design procedures

hankel norm model reduction with fixed modes a constrained hankel norm approximation problem is considered the reduced order model is required to retain as a subset of its poles some prescribed eigenvalues from the original system the constraint approximation problem is solved with an optimal hankel norm criterion and an l sup infinity error bound for the approximation error is provided the proposed method for model reduction can be described as a partial eigenvalue preservation method the reduced order model is allowed to have a set of free poles in addition to eigenvalues which are preserved from the original system because of physical considerations although the method can be used in conjunction with the dominant mode concept it is equally feasible to retain some eigenvalues of particular interest but otherwise nondominant and let the free poles take care of the dominant characteristics of the system

controller reduction with error performance continuous and discrete time cases this paper is concerned with the problem of controller reduction for linear systems both continuous and discrete time cases are considered with necessary and sufficient conditions obtained for the existence of desired reduced order controllers in solving this problem two approaches are presented the first approach is based on the projection lemma where the admissible controllers can be parameterized after a set of conditions are satisfied and the second one directly incorporates the controller matrices to be determined into a set of conditions by introducing new techniques and thus no parameterization procedure is needed these necessary and sufficient conditions are formulated in terms of linear matrix inequalities lmis plus some equality constraints since these conditions are not convex the cone complementarity linearization ccl idea is exploited to cast them into sequential minimization problems subject to lmi constraints which can be readily solved by standard numerical software a num

weighted inequalities for commutators of fractional integrals on spaces of homogeneous type abstract let 0 1 b be a bmo function and i b m the commutator of order m for the fractional integral we prove two type of weighted l p inequalities for i b m in the context of the spaces of homogeneous type the first one establishes that for a weights the operator i b m is bounded in the weighted l p norm by the maximal operator m m m where m is the fractional maximal operator and m m is the hardy littlewood maximal operator iterated m times the second inequality is a consequence of the first one and shows that the operator i b m is bounded from l p m p m m 1 p w x d x to l p w x d x where m 1 p is the integer part of m 1 p and no condition on the weight w is required from the first inequality we also obtain weighted l p l q estimates for i b m generalizing the classical results of muckenhoupt and wheeden for the fractional integral operator

an exact approach to the oscillator radiation process in an arbitrarily large cavity starting from a solution of the problem of a mechanical oscillator coupled to a scalar field inside a reflecting sphere of radius r we study the behaviour of the system in free space as the limit of an arbitrarily large radius in the confined solution from a mathematical point of view we show that this way of addressing the problem is not equivalent to considering the system a priori embedded in infinite space in particular the matrix elements of the transformation turning the system to the principal axis do not tend to distributions in the limit of an arbitrarily large sphere as should be the case if the two procedures were mathematically equivalent also we introduce dressed coordinates which allow an exact description of the oscillator radiation process expanding in powers of the coupling constant we recover from our exact expressions the well known decay formulae from perturbation theory

h sub 2 near optimal model reduction this note considers the problem of finding a stable reduced order model for a given stable model so that its h sub 2 model reduction cost differs by less than a prescribed error from the optimal cost which may or may not be achievable it is shown that this new version of the long standing h sub 2 optimal model reduction problem can be reduced to a well posed smooth constrained minimization problem whose global solution is guaranteed to exist in addition a globally convergent algorithm in the form of an ordinary differential equation is derived

logarithmic bump conditions and the two weight boundedness of calderon zygmund operators abstract we prove that if a pair of weights u v satisfies a sharp a p bump condition in the scale of all log bumps or certain loglog bumps then haar shifts map l p v into l p u with a constant quadratic in the complexity of the shift this in turn implies the two weight boundedness for all calderon zygmund operators this gives a partial answer to a long standing conjecture we also give a partial result for a related conjecture for weak type inequalities to prove our main results we combine several different approaches to these problems in particular we use many of the ideas developed to prove the a 2 conjecture as a byproduct of our work we also disprove a conjecture by muckenhoupt and wheeden on weak type inequalities for the hilbert transform this is closely related to the recent counterexamples of reguera scurry and thiele

internal positivity preserved model reduction this article studies model reduction of continuous time stable positive linear systems under the hankel norm h norm and h 2 norm performance the reduced order systems preserve the stability as well as the positivity of the original systems this is achieved by developing new necessary and sufficient conditions of the model reduction performances in which the lyapunov matrices are decoupled with the system matrices in this way the positivity constraints in the reduced order model can be imposed in a natural way as the model reduction performances are expressed in linear matrix inequalities with equality constraints the desired reduced order positive models can be obtained by using the cone complementarity linearisation iterative algorithm a numerical example is presented to illustrate the effectiveness of the given methods

l1 induced norm and controller synthesis of positive systems in this paper the problem of 1 1 induced controller design for discrete time positive systems is investigated with the use of linear lyapunov function an analytical method to compute the exact value of 1 1 induced norm is first presented then a novel characterization for stability and 1 1 induced performance is proposed based on the characterization a necessary and sufficient condition for the existence of desired controllers is derived and an iterative convex optimization approach is developed to solve the condition in addition the synthesis of the state feedback controller for single input multiple output simo positive systems is investigated for this special case an analytic solution is established to show how the optimal 1 1 induced controller can be designed and some links to the spectral radius of the closed loop systems are provided finally the theoretical results are illustrated through a numerical example

a new ap a estimate for calderon zygmund operators in spaces of homogeneous type abstract in this note we study the a p a estimate for calderon zygmund operators in terms of the weak a characteristics in spaces of homogeneous type the weak a class was introduced recently by anderson hytonen and tapiola our estimate is new even in euclidean space

hankel norm approximation of linear systems with time varying delay continuous and discrete cases this paper investigates the problem of hankel norm model reduction for linear systems with time varying delay in the state for a given stable system our attention is focused on the construction of reduced order model which guarantees the corresponding error system to be asymptotically stable and has a specified hankel norm error performance two different approaches are proposed to solve this problem one casts the model reduction into a convex optimization problem by using a linearization procedure and the other is based on the cone complementarity linearization idea which casts the model reduction into a sequential minimization problem subject to linear matrix inequality constraints both continuous and discrete time cases are considered a numerical example is provided to show the effectiveness of the proposed theory

optimal hankel norm approximation for stable systems with first order stable weighting functions abstract given a stable rational transfer function g s and weighting function w s the problem of finding g s of macmillan degree k so as to minimise w g g h is considered this problem is solved for w s s s with no assumptions on the signs of and this gives rise to approximations where w g g can be accurately bounded from above and below in terms of the hankel singular values of wg when 0

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

h_ infty model reduction in the stochastic framework this paper investigates the problems of h infty model reduction for both continuous and discrete stochastic systems in terms of certain linear matrix inequalities lmis and a coupling nonconvex rank constraint necessary and sufficient conditions for the existence of solutions to such problems are obtained an explicit parametrization of all reduced order models corresponding to a feasible solution is also proposed in particular when a zeroth order h infty approximation is desired conditions are obtained using lmis only without any rank constraints and a parametrization of all solutions is also presented finally an illustrative example is provided to demonstrate the effectiveness of the proposed approach

stabilization of discrete time switched positive linear systems via weak switched linear copositive lyapunov function abstract by introducing a class of weak switched linear copositive lyapunov functions this paper designs new time dependent switching signals guaranteeing asymptotic stability of discrete time switched positive linear systems whose subsystems are only marginally stable our results have advantages over some existing ones in the literature moreover the main results have been extended to the general switched linear time varying system with disturbance numerical examples well demonstrate the superiority of the obtained results

a state space algorithm for the superoptimal hankel norm approximation problem it has been demonstrated by n t young nato asi series f34 springer verlag berlin new york 1987 that given a stable matrix valued function g 0 s and a nonnegative integer k there exists a unique superoptimal approximation phi s with no more than k poles in the left half plane that minimizes the sequence s 1 infty g 0 phi s 2 infty g 0 phi cdots with respect to lexicographic ordering where s i infty g 0 phi sup omega s i g 0 phi j omega and s i cdot are the singular values in descending order of magnitude this paper presents a constructive state space algorithm that evaluates the superoptimal approximating matrix function the procedure recursively minimizes each frequency dependent singular value with the aid of all pass transformations constructed from the kth schmidt pairs of a sequence of hankel operators the algorithm may be stopped after an arbitrary number of say l leqq min m p steps the representation formula at the

two weight extrapolation via the maximal operator abstract we give several extrapolation theorems for pairs of weights of the form w m k w and w mw w r w where w is any non negative function r 1 and m k is the k th iterate of the hardy littlewood maximal operator as an application we show that our results can be used to extend and sharpen results for square functions and singular integral operators by chang et al 1985 comment math helv 60 217 246 chanillo and wheeden 1987 indiana univ math j 36 277 294 wilson 1987 duke math j 55 879 887 1989 trans amer math soc 314 661 692 1989 illinois j math 33 361 366 and uchiyama 1995 studia math 115 135 149 in the process we prove a conjecture due to wilson

weighted sobolev morrey estimates for hypoelliptic operators with drift on homogeneous groups abstract let x 0 x 1 x q be left invariant real vector fields on the homogeneous group g and assume that x 1 x q are homogeneous of degree one and x 0 is homogeneous of degree two in this paper we consider the following hypoelliptic operator with drift l i j 1 q a i j x i x j a 0 x 0 where a i j is a constant matrix satisfying the elliptic condition in r q and a 0 0 and obtain weighted sobolev morrey estimates and morrey estimates with two weights of l by establishing boundedness of several singular integrals and interpolation lemmas on g

path integral approach to quantum brownian motion abstract we apply the influence functional method of feynman and vernon to the study of brownian motion at arbitrary temperature by choosing a specific model for the dissipative interaction of the system of interest with its environment we are able to evaluate the influence functional in closed form and express it in terms of a few parameters such as the phenomenological viscosity coefficient we show that in the limit h 0 the results obtained from the influence functional formalism reduce to the classical fokker planck equation in the case of a simple harmonic oscillator with arbitrarily strong damping and at arbitrary temperature we obtain an explicit expression for the time evolution of the complete density matrix x x t when the system starts in a particular kind of pure state we compare our results with those of other approaches to the problem of dissipation in quantum mechanics

extrapolation from a weights and applications abstract we generalize the a p extrapolation theorem of rubio de francia to a weights in the context of muckenhoupt bases our result has several important features first it can be used to prove weak endpoint inequalities starting from strong type inequalities something which is impossible using the classical result second it provides an alternative to the technique of good inequalities for proving l p norm inequalities relating operators third it yields vector valued inequalities without having to use the theory of banach space valued operators we give a number of applications to maximal functions singular integrals potential operators commutators multilinear calderon zygmund operators and multiparameter fractional integrals in particular we give new proofs which completely avoid the good inequalities of coifman s inequality relating singular integrals and the maximal operator of the fefferman stein inequality relating the maximal operator and the sharp maximal operator and the muckenhoupt wheeden inequality relating the fractional integral operator and the fractional maximal operator

uncertainty principle estimates for vector fields abstract we derive weighted norm estimates for integral operators of potential type and for their related maximal operators these operators are generalizations of the classical fractional integrals and fractional maximal functions the norm estimates are derived in the context of a space of homogeneous type the conditions required of the weight functions involve generalizations of the fefferman phong r bump condition the results improve some earlier ones of the same kind and they also extend to homogeneous spaces some estimates that were previously known to hold only in the classical euclidean setting

the optimal projection equations for model reduction and the relationships among the methods of wilson skelton and moore first order necessary conditions for quadratically optimal reduced order modeling of linear time invariant systems are derived in the form of a pair of modified lyapunov equations coupled by an oblique projection which determines the optimal reduced order model this form of the necessary conditions considerably simplifies previous results of wilson 1 and clearly demonstrates the quadratic extremality and nonoptimality of the balancing method of moore 2 the possible existence of multiple solutions of the optimal projection equations is demonstrated and a relaxation type algorithm is proposed for computing these local extrema a component cost analysis of the model error criterion similar to the approach of skelton 3 is utilized at each iteration to direct the algorithm to the global minimum

positive filtering for positive takagi sugeno fuzzy systems under l 1 performance in this paper the positive filtering problem is addressed for positive takagi sugeno t s fuzzy systems under the 1 induced performance to estimate the output of positive t s fuzzy systems error bounding positive filters are constructed a new performance characterization is first established to guarantee the asymptotic stability of the filtering error system with the 1 induced performance moreover sufficient conditions expressed by linear programming problems are derived to design the required filters finally a numerical example is presented to show the effectiveness of the derived theoretical results

entropy conditions in two weight inequalities for singular integral operators abstract a new type of bumping of the muckenhoupt a 2 condition on weights is introduced it is based on bumping the entropy integral of the weights in particular one gets assuming mild regularity conditions on the corresponding young functions the bump conjecture proved in 20 25 as a corollary of entropy bumping but our entropy bumps cannot be reduced to the bumping with orlicz norms in the solution of bump conjecture they are effectively smaller henceforth we get somewhat stronger results than the one that solves the bump conjecture in 20 25 new results concerning one sided bumping conjecture are obtained all the results hold in the general non homogeneous situation

an approximate approach to h sup 2 optimal model reduction deals with the problem of computing an h sub 2 optimal reduced order model for a given stable multivariable linear system by way of orthogonal projection the problem is formulated as that of minimizing the h sub 2 model reduction cost over the stiefel manifold so that the stability constraint on reduced order models is automatically satisfied and thus totally avoided in the new problem formulation the closed form expression for the gradient of the cost over the manifold is derived from which a gradient flow results as an ordinary differential equation ode a number of nice properties about such a flow are established furthermore two explicit iterative convergent algorithms are developed from the flow one has a constant step size and the other has a varying step size and is much more efficient both of them inherit the properties that the iterates remain on the manifold starting from any orthogonal initial point and that the model reduction cost is decreasing to minima along the iterates a procedure for closing the gap between the original and modified problem is proposed in the symmetric case the two problems are shown to be equivalent numerical examples are presented to illustrate the effectiveness of the proposed algorithms as well as convergence

multiplicative hankel norm approximation of linear multivariable systems abstract in control system design specifications are commonly given in terms of log magnitude quantities i e decibels this description induces a multiplicative or relative error criterion for plant model reduction techniques from the theory of additive hankel norm approximation and spectral factorization are synthesized to produce a multiplicative approximant of a possibly unstable or non square plant it is shown that the reduced order model preserves the unstable poles and right half plane zeros of the original system explicit state space formulae are provided for the construction of the reduced order model and its error properties are discussed the method is illustrated by a numerical example

endpoint estimates for commutators of singular integral operators abstract we prove endpoint estimates for commutatotrs of singular integrals with bmo functions we first show that they satisfy l log l type inequalities and then that there is a hardy space type estimate where the usual atomic hardy space is replaced by an appropriate subspace

improved lmi representations for the analysis and the design of continuous time systems with polytopic type uncertainty simple modifications to the representation of the bounded real lemma brl in the linear continuous time invariant case are introduced these modifications reduce the overdesign that occurs in the analysis and the design of systems with polytopic type uncertainties a different lyapunov function accompanies each of the vertices of the uncertainty polytope thus eliminating the need for quadratic stability or stabilizability the advantages of these new representations are demonstrated by way of two examples

l2 and l2 l model reduction via linear matrix inequalities necessary and sufficient conditions are derived for the existance of a solution to the continuous time and discrete time suboptimal l2 and l2 l model reduction problems these conditions are expressed in terms of linear matrix inequalities lmis and a coupling non convex rank constraint in addition explicit parametrizations of all reduced order models that correspond to a feasible solution are presented in terms of contractive matrices

dynamic output feedback control for continuous time interval positive systems under l1 performance this paper is concerned with the design of l1 induced dynamic output feedback controller for continuous time positive systems with interval uncertainties a necessary and sufficient condition for stability and l1 induced performance of positive linear systems is proposed in terms of linear inequalities based on this conditions for the existence of robust dynamic output feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions one illustrative example is provided to show the effectiveness and applicability of the theoretical results

fractional integrals potential operators and two weight weak type norm inequalities on spaces of homogeneous type we prove two weight weak type norm inequalities for potential operators and fractional integrals defined on spaces of homogeneous type we show that the operators in question are bounded from lp v to lq u 1 p q provided the pair of weights u v verifies a muckenhoupt condition with a power bump on the weight u

dressed coordinates the path integral approach the recently introduced dressed coordinates are studied in the path integral approach these coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and it is shown that in this model the dressed coordinates appear as a coordinate transformation preserving the path integral functional measure the analysis also generalizes the sum rules established in a previous work

h model reduction of markovian jump linear systems abstract in this paper the h model reduction problem for linear systems that possess randomly jumping parameters is studied the development includes both the continuous and discrete cases it is shown that the reduced order models exist if a set of matrix inequalities is feasible an effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the model reduction solutions using the numerical solutions of the matrix inequalities the reduced order models can be obtained an example is given to illustrate the proposed model reduction method

a characterization of two weight norm inequalities for fractional and poisson integrals caracterisation de deux inegalites de normes ponderees pour les integrales fractionnaires et de poisson applications aux operateurs differentiels elliptiques degeneres

h model reduction for discrete time delay systems delay independent and dependent approaches this paper investigates the problem of h model reduction for linear discrete time state delay systems for a given stable system our attention is focused on the construction of reduced order models which guarantee the corresponding error system to be asymptotically stable and have a prescribed h error performance both delay independent and dependent approaches are developed with sufficient conditions obtained for the existence of admissible reduced order solutions since these obtained conditions are not expressed as strict linear matrix inequalities lmis the cone complementary linearization method is exploited to cast them into sequential minimization problems subject to lmi constraints which can be readily solved in standard numerical software in addition the development of reduced order models with special structures such as delay free models and zeroth order models is also addressed the approximation methods presented in this paper can be further extended to cope with systems with unc

ℋ model reduction for linear parameter varying systems with distributed delay this paper is concerned with the model reduction for linear parameter varying lpv systems with both discrete and distributed delays for a given stable system our attention is focused on the construction of reduced order models which approximate the original system well in an norm sense first a sufficient condition is proposed for the asymptotic stability with an performance of the error system by using the parameter dependent lyapunov functional method then the decoupling technique is applied such that there does not exist any product term between the lyapunov matrices and the system matrices in the parametrised linear matrix inequality plmi constraints thus a new sufficient condition is obtained based on the new condition two different approaches are developed to solve the model reduction problem one is the convex linearisation approach and the other is the projection approach finally a numerical example is provided to demonstrate the effectiveness of the proposed design method

h2 model reduction for negative imaginary systems this paper studies the h2 model reduction problem for negative imaginary ni systems for a given high order system that is stable and ni our goal is to approximate it by a low order ni system so

l induced output feedback controller synthesis for positive nonlinear systems via t s fuzzy model approach abstract this paper investigates the l induced output feedback controller synthesis problem for positive takagi sugeno t s fuzzy systems for positive t s fuzzy systems a sufficient condition for stability and l induced performance is first put forward using a group of linear inequalities then on the basis of these inequalities the conditions on which static output feedback controllers exist are set up and to solve these conditions a method of iterative convex optimization is provided moreover a complete solution to the synthesis problem of the controller is proposed based on linear programming for positive t s fuzzy systems with single output or input finally two examples are presented to illustrate and verify the effective and applicable methods derived in this paper

weighted nonlinear potential theory the potential theoretic idea of the thinness of a set at a given point is extended to the weighted nonlinear potential theoretic setting the weights representing in general singularities degeneracies and conditions on these weights are given that guarantee when two such notions are equivalent at the given point when applied to questions of boundary regularity for solutions to degenerate elliptic second order partial differential equations in bounded domains this result relates the boundary wiener criterion for one operator to that of another and in the linear case gives conditions for boundary regular points to be the same for various operators the methods also yield two weight norm inequalities for riesz potentials j llq p 1 p q oo which at least in the first order case a 1 have found some use in a number of places in analysis

sharp weighted inequalities for the vector valued maximal function we prove in this paper some sharp weighted inequalities for the vector valued maximal function mq of fefferman and stein defined by 00 llq mqf x mfi o q where m is the hardy littlewood maximal function as a consequence we derive the main result establishing that in the range 1 a jf x jq mw x dx a rn where c is a constant independent of a 1 motivation and description of the main results the purpose of this paper is to obtain some sharp weighted inequalities for the vector valued maximal function mq which are not within the scope of the standard ap theory for vector valued singular integrals as can be found in rrt we start with a review of some of the classical estimates and then we shall state the main results 1 1 background let m be the hardy littlewood maximal function and let mq be the vector valued maximal operator defined by mq f x e m fi x q this nonlinear operator was introduced by c fefferman and e m stein in fs as a generalization of both the scalar maximal function m and the classical integral of marcinkiewicz and since then it has played an important role in the development of modern harmonic analysis we recall the two basic estimates obtained in fs for 1 q oo received by the editors may 19 1997 1991 mathematics subject classification primary 42b20 42b25 42b15 this work was partially supported by dgicyt grant pb940192 spain 2000 american mathematical society 3265 this content downloaded from 207 46 13 102 on sat 30 jul 2016 04 48 12 utc all use subject to http about jstor org terms

classification of four dimensional estimation algebras of central importance in nonlinear filtering theory is the classification of finite dimensional estimation algebras through which we can construct recursive filters we classify all t dimensional estimation algebras t spl les 4 for arbitrary state space dimension

on h2 model reduction of bilinear systems the h 2 model reduction problem for continuous time bilinear systems is studied in this paper by defining the h 2 norm of bilinear systems in terms of the state space matrices the h 2 model reduction error is computed via the reachability or observability gramian necessary conditions for the reduced order bilinear models to be h 2 optimal are given the gradient flow approach is used to obtain the solution of the h 2 model reduction problem the formulation allows certain properties of the original models to be preserved in the reduced order models the model reduction procedure developed can also be applied to finite dimensional linear time invariant systems a numerical example is employed to illustrate the effectiveness of the proposed method

delay dependent and decay rate dependent conditions for exponential mean stability and non fragile controller design of positive markov jump linear systems with time delay abstract this paper proposes some new sufficient conditions and necessary conditions for exponential mean stability with prescribed decay rate and sufficient conditions for non fragile controller design of both continuous time and discrete time positive markov jump linear systems with time delay first sufficient stability conditions are derived by constructing novel linear stochastic co positive lyapunov krasovskii functionals second the corresponding necessary conditions are established by applying a model transformation technique and analyzing the relationship between stochastic stability of the transformed systems and exponential mean stability with given decay rate of the original systems compared with the existing conditions the proposed stability conditions are not only delay dependent but also decay rate dependent and the sufficient conditions plus the necessary conditions can be used to judge the system stability more precisely third based on the new sufficient conditions non fragile controllers are designed by solving linear programming problems such that the closed loop systems are positive and exponentially mean stable with an expected decay rate finally by numerical examples the effects of both time delay and decay rate on exponential mean stability are exploited and the validity of the non fragile controller design conditions is demonstrated

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory