parameterized algorithms and kernels for almost induced matching abstract the almost induced matching problem asks whether we can delete at most k vertices from the input graph such that each vertex in the remaining graph has a degree exactly one this paper studies parameterized algorithms for this problem by taking the size k of the deletion set as the parameter we give a 7k vertex kernel and an o 1 7485 k time and polynomial space algorithm both of which are the best known results the linear vertex kernel is obtained by using an extended crown decomposition and careful analysis and the parameterized algorithm is based on a branch and search paradigm

randomized divide and conquer improved path matching and packing algorithms we propose a randomized divide and conquer technique that leads to improved randomized and deterministic algorithms for np hard path matching and packing problems for the parameterized max path problem our randomized algorithm runs in time o 4 k k 2 7 m and polynomial space where m is the number of edges in the input graph improving the previous best randomized algorithm for the problem that runs in time o 5 44 k km and exponential space our randomized algorithms for the parameterized max r d matching and max r set packing problems run in time 4 r 1 k n o 1 and polynomial space improving the previous best algorithms for the problems that run in time 10 88 rk n o 1 and exponential space moreover our randomized algorithms can be derandomized to result in significantly improved deterministic algorithms for the problems and they can be extended to solve other matching and packing problems

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

model order reduction for nonlinear dynamical systems based on trajectory piecewise linear approximations in this paper we analyze and expand a recently developed approach to model order reduction mor for nonlinear dynamical systems based on trajectory piecewise linear tpwl approximations error estimates are given for solutions computed with tpwl reduced order models and problems of preserving stability and passivity are examined since the tpwl method has limited a priori guarantees on global accuracy its effectiveness is demonstrated on a range of examples including a micromachined switch two nonlinear electronic circuits and shock propagation modeled by burgers equation

nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time ts fuzzy models a new approach the discrete time uncertain nonlinear models are considered in a takagi sugeno form and their stabilization is studied through a non quadratic lyapunov function the classical conditions consider a one sample variation here the main results are obtained considering k samples variation i e deltak v x t v x t k v x t the results are shown to always include the classical cases and several examples illustrate the effectiveness of the approach

lower dimensional reductions of gl m c self dual yang mills equation solutions with break of wave profiles any matrix self dual type s integrable partial differential equation pde possesses a family of lower dimensional reductions represented by the matrix quasilinear first order pdes solvable by the method of characteristics these pdes admit two types of particular solutions a explicit solutions and b implicit solutions represented by a system of nondifferential equations the latter solutions exhibit the break of wave profile 2 1 and 3 1 dimensional gl m c self dual yang mills equations have been considered as examples

the evolution partial differential equation ut uxxx 3 uxxu2 3u2xu 3uxu4 the evolution equation ut uxxx 3 uxxu2 3u2xu 3uxu4 u u x t is integrable it can be exactly linearized by an appropriate change of dependent variable hence several explicit solutions of the partial differential equation pde can be exhibited some of them display a remarkable solitronic phenomenology

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

soliton dynamics in the complex modified kdv equation with a periodic potential abstract we study the existence and stability of stationary and moving solitary waves in a periodically modulated system governed by an extended cmkdv complex modified korteweg de vries equation the proposed equation describes in particular the co propagation of two electromagnetic waves with different amplitudes and orthogonal linear polarizations in a liquid crystal waveguide the stronger nonlinear wave actually carrying the soliton while the other a nearly linear one creates an effective periodic potential a variational analysis predicts solitons pinned at minima and maxima of the periodic potential and the vakhitov kolokolov criterion predicts that some of them may be stable numerical simulations confirm the existence of stable stationary solitary waves trapped at the minima of the potential and show that persistently moving solitons exist too the dynamics of pairs of interacting solitons is also studied in the absence of the potential the interaction is drastically different from the behavior known in the nls nonlinear schrodinger equation as the force of the interaction between the cmkdv solitons is proportional to the sine rather than cosine of the phase difference between the solitons in the presence of the potential two solitons placed in one potential well form a persistently oscillating bound state

improved l2 gain performance controller synthesis for takagi sugeno fuzzy system in this paper an improved l2 gain performance controller synthesis is proposed for takagi sugeno t s fuzzy system the t s fuzzy controller can be easily derived by a three step procedure with the linear matrix inequalities lmis technique first a new t s fuzzy model structure is presented which includes the original t s fuzzy plant with stable pre and post filters on the input and output of the original plant second by using this structure the l2 gain performance controller design problem can be easily transformed into standard lmis formulation compared with the previous results it not only gives us a simple structure of the t s fuzzy controller but also provides us effective lmis based conditions which include a small number of unknown matrix variables consequently less value of l2 gain performance of the closed loop system can be obtained third an augmented t s fuzzy controller which guarantees l2 gain performance is obtained for the original t s fuzzy plant which is composed of the t s controller derived from step two and two stable pre and post filters finally some numerical examples are demonstrated to show the effectiveness of the proposals

multiple scale analysis of discrete nonlinear partial difference equations the reduction of the lattice potential kdv we consider multiple lattices and functions defined on them we introduce slow varying conditions for functions defined on the lattice and express the variation of a function in terms of an asymptotic expansion with respect to the slow varying lattices we use these results to perform multiple scale reduction of the lattice potential korteweg de vries equation

h model reduction for discrete time singular systems this paper investigates the problem of h sub infinity model reduction for linear discrete time singular systems without decomposing the original system matrices necessary and sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities lmis and a coupling non convex rank constraint set when these conditions are feasible an explicit parametrization of the desired reduced order models is given particularly a simple lmi condition without rank constraint is derived for the zeroth order h sub infinity approximation problem finally an illustrative example is provided to demonstrate the applicability of the proposed approach

an extension to balanced truncation with application to structured model reduction balanced truncation is a standard method for model reduction possessing many desirable properties such as preservation of model stability and a priori error bounds balanced truncation is conducted using controllability and observability gramians generalized gramians can be found by solving a set of linear matrix inequalities in this paper we show that these linear matrix inequalities can be extended so that the number of decision variables are at least doubled leading to the concept of extended gramians herein it is shown that the desirable properties of balanced truncation also hold with extended gramians the extended gramians are especially useful for improving error bounds and for models possessing additional structural constraints as is demonstrated by means of examples herein

l_ 2 l_ infty model reduction for switched lpv systems with average dwell time in this note the model reduction problem for a class of discrete time switched linear parameter varying systems under average dwell time switching is investigated a parameterized reduced model is constructed and the corresponding existence conditions of such models are derived via strict lmi formulation the minimal average dwell time among all the subsystems and the desired reduced system are obtained such that the resulting model error system is exponentially stable and has a guaranteed l 2 l infin error performance a numerical example is given to demonstrate the potential and effectiveness of the developed theoretical results

robust stabilization of linear systems with norm bounded time varying uncertainty abstract in this paper robust stabilization of a class of linear systems with norm bounded time varying uncertainties is considered it is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a parameter dependent riccati equation also a construction for the stabilizing feedback law is given in terms of the solution to the riccati equation

parameterized approximation algorithms for packing problems parameterized approximation is a topic of considerable interest in the field of parameterized complexity in the past decade new color coding related techniques including the breakthrough representative sets technique have been proven extremely powerful in the design of fast parameterized algorithms furthermore packing problems which are often solved via color coding related techniques have enjoyed a race towards obtaining the fastest parameterized algorithms that solve them therefore it is natural to ask whether packing problems admit efficient parameterized approximation algorithms in this paper we answer this question affirmatively we present tradeoffs that improve the running times of algorithms for well known special cases of the 3 setk packing problem at the cost of their accuracy consider a packing problem for which there is no known algorithm with approximation ratio and a parameter k if the value of an optimal solution is at least k we seek a solution of value at least k otherwise we seek an arbitrary solution clearly if the best known parameterized algorithm that finds a solution of value t runs in time o f t for some function f we are interested in running times better than o f k our main contribution lies in the adaptation of notions fundamental to the representative sets technique to the design of approximation algorithms we introduce the definition of approximate lopsided universal sets combine partial executions of representative sets based algorithms with approximation algorithms and adapt the iterative expansion framework in the context of representative sets to the design of parameterized approximation algorithms our ideas are intuitive and may be relevant to the design of other parameterized approximation algorithms

nonlinear schrodinger type equations from multiscale reduction of pdes ii necessary conditions of integrability for real pdes the multiscale method has been applied in j math phys 41 6399 2000 to evolution pdes to obtain various nonlinear schrodinger type equations here these results are exploited to derive necessary conditions of integrability for nonlinear real evolution pdes in 1 1 dimensions these conditions are given by explicit formulas and several examples are detailed

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

graph editing problems with extended regularity constraints graph editing problems offer an interesting perspective on sub and supergraph identification problems for a large variety of target properties they have also attracted significant attention in recent years particularly in the area of parameterized complexity as the problems have rich parameter ecologies in this paper we examine generalisations of the notion of editing a graph to obtain a regular subgraph in particular we extend the notion of regularity to include two variants of edge regularity along with the unifying constraint of strong regularity we present a number of results with the central observation that these problems retain the general complexity profile of their regularity based inspiration when the number of edits k and the maximum degree r are taken together as a combined parameter the problems are tractable i e in fpt but are otherwise intractable we also examine variants of the basic editing to obtain a regular subgraph problem from the perspective of parameterizing by the treewidth of the input graph in this case the treewidth of the input graph essentially becomes a limiting parameter on the natural k r parameterization

edge disjoint packing of stars and cycles abstract we study the parameterized complexity of two graph packing problems edge disjoint k packing of s stars and edge disjoint k packing of s cycles with respect to the choice of parameters we show that although the two problems are fpt with both k and s as parameters they are unlikely to be fixed parameter tractable when parameterized by only k or only s in terms of kernelization complexity we show that edge disjoint k packing of s stars has a kernel with size polynomial in both k and s but in contrast unless np conp poly edge disjoint k packing of s cycles does not have a kernel with size polynomial in both k and s and moreover does not have a kernel with size polynomial in s for any fixed k we also show that edge disjoint k packing of 4 cycles admits a 96 k 2 kernel in general graphs and a 96 k kernel in planar graphs

multiscale reduction of discrete korteweg de vries equations we show how through a multiscale reduction technique performing the analysis at orders beyond the nonlinear schrodinger equation one can effectively prove if some nonlinear partial difference equation is not integrable the example is carried out on a symmetric discretization of the kdv equation and is compared to a similar reduction performed on the integrable lattice potential kdv equation

on h sub spl infin model reduction using lmis in this note we deal with the problem of approximating a given nth order linear time invariant system g by an rth order system g sub r where r n it is shown that lower bounds of the h sub spl infin norm of the associated error system can be analyzed by using linear matrix ineqaulity lmi related techniques these lower bounds are given in terms of the hankel singular values of the system g and coincide with those obtained in the previous studies where the analysis of the hankel operators plays a central role thus this note provides an alternative proof for those lower bounds via simple algebraic manipulations related to lmis moreover when we reduce the system order by the multiplicity of the smallest hankel singular value we show that the problem is essentially convex and the optimal reduced order models can be constructed via lmi optimization

a discrete linearizability test based on multiscale analysis in this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad graph by the multiple scale reduction around their harmonic solution we show that the a1 a2 and a3 linearizability conditions restrain the number of the parameters which enter into the equation a subclass of the equations which pass the a3 c integrability conditions can be linearized by a mobius transformation

h sub spl infin model reduction with application to flexible systems in this note h sub spl infin model reduction of continuous time linear systems is revisited the main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem the quality of the proposed suboptimal solution is assessed through comparisons performed via simulation with the already classical balanced truncation method leading to the conclusion that the proposed method performs significantly better finally the proposed method is applied to the determination of a reduced order model of a flexible bar

principal component analysis in linear systems controllability observability and model reduction kalman s minimal realization theory involves geometric objects controllable unobservable subspaces which are subject to structural instability specifically arbitrarily small perturbations in a model may cause a change in the dimensions of the associated subspaces this situation is manifested in computational difficulties which arise in attempts to apply textbook algorithms for computing a minimal realization structural instability associated with geometric theories is not unique to control it arises in the theory of linear equations as well in this setting the computational problems have been studied for decades and excellent tools have been developed for coping with the situation one of the main goals of this paper is to call attention to principal component analysis hotelling 1933 and an algorithm golub and reinsch 1970 for computing the singular value decompositon of a matrix together they form a powerful tool for coping with structural instability in dynamic systems as developed in this paper principal component analysis is a technique for analyzing signals singular value decomposition provides the computational machinery for this reason kalman s minimal realization theory is recast in terms of responses to injected signals application of the signal analysis to controllability and observability leads to a coordinate system in which the internally balanced model has special properties for asymptotically stable systems this yields working approximations of x c x bar o the controllable and unobservable subspaces it is proposed that a natural first step in model reduction is to apply the mechanics of minimal realization using these working subspaces

the structures and interactions of solitary waves in a 2 1 dimensional coupled nonlinear extension of the reaction diffusion equation the complete integrability of a 2 1 dimensional coupled nonlinear extension of the reaction diffusion cnlerd equation using the technique of painlev p analysis is investigated using the formalism of weiss et al 1983 j math phys 24 522 the arbitrariness of the expansion coefficients are proved besides following the hirota s formalism hirota r 1980 direct methods in soliton theory soliton berlin springer combined to weiss et al s methodology weiss et al 1984 j math phys 25 13 the consistency of the truncation is shown thus without the use of kruskal s simplification the bcklund transformation bt of the equations is obtained via the truncation procedure taking into account the arbitrariness of the expansion coefficients in the foregoing truncation a typical spectrum of localized coherent structures may be unearthed the scattering behavior of such structures is also investigated

the multicomponent eckhaus equation the n component eckhaus equation is c integrable here the dependent variable is an n vector and and are two constant matrices restricted by the condition that both and be hermitian some special cases and some explicit solutions are displayed

extended multilinear variable separation approach and multivalued localized excitations for some 2 1 dimensional integrable systems the multilinear variable separation approach and the related universal formula have been applied to many 2 1 dimensional nonlinear systems starting from the universal formula abundant 2 1 dimensional localized excitations have been found in this paper the universal formula is extended in two different ways one is obtained for the modified nizhnik novikov veselov equation such that two universal terms can be combined linearly and this type of extension is also valid for the 2 1 dimensional symmetric sine gordon system the other is for the dispersive long wave equation the broer kaup kupershmidt system the higher order broer kaup kupershmidt system and the burgers system where arbitrary number of variable separated functions can be involved because of the existence of the arbitrary functions in both the original universal formula and its extended forms the multivalued functions can be used to construct a new type of localized excitations folded solitary waves fsws and foldons the fsws

nonlinear schrodinger type equations from multiscale reduction of pdes i systematic derivation in this article we begin a systematic investigation via multiscale expansions of nonlinear evolution pdes partial differential equations in this first article we restrict consideration to a single autonomous but otherwise generic pde in 1 1 variables space time of first order in time whose linear part is dispersive and to solutions dominated by a single plane wave satisfying the linear part of the pde the expansion parameter is an assumedly small coefficient multiplying this plane wave the main indeed asymptotically exact effect of the weak nonlinearity is then to cause a modulation of the amplitude of the plane wave and of its harmonics which is generally described in appropriately defined coarse grained time and space variables by evolution equations of nonlinear schrodinger type a systematic analysis of such equations is presented corresponding to various assumptions on the resonances occurring for the first few harmonics

c integrable nonlinear partial differential equations iii a technique based on a change of dependent variables used in a previous paper to generate c integrable nonlinear partial differential equations pdes i e nonlinear pdes linearizable by an appropriate change of variables in 1 1 dimensions one time and one space variables is extended to the case of more than one space dimension several examples of evolution c integrable pdes in 1 2 dimensions one time and two space variables are exhibited

new integrable pdes of boomeronic type novel integrable systems of coupled first order autonomous pdes in 1 1 dimensions space x and time t are presented integrable covariant 2 vector and 3 vector pdes as well as higher order integrable pdes for a single or a couple of scalar dependent variables including an extension of the sine gordon equation and a remarkably neat highly nonlinear third order pde are also obtained by appropriate reductions of the basic matrix equations the lax pairs that characterize the integrable character of the basic matrix pdes are also exhibited as well as their single soliton solutions these solitons generally exhibit the boomeronic and less generically the trapponic phenomenology namely they do not move uniformly but rather in an appropriate reference system come in from one end in the remote past and boomerang back to that same end in the remote future boomerons or are trapped to oscillate around a value fixed by the initial data trappons

kernels for packing and covering problems abstract we show how the notion of combinatorial duality related to the well known notion of duality from linear programming may be used for translating kernel results obtained for packing problems into kernel results for covering problems we exemplify this approach by having a closer look at the problems of packing a graph with vertex disjoint trees or vertex disjoint stars with r edges the case r 2 has been studied in several other papers by establishing a general notion of a crown we show how linear size vertex kernels can be efficiently achieved for the mentioned problems

looking at the stars the problem of packing k vertex disjoint copies of a graph h into another graph g is np complete if h has more than two vertices in some connected component in the framework of parameterized complexity we analyze a particular family of instances of this problem namely the packing of stars we give a quadratic kernel for packing k copies of h k1 s when we consider the special case of s 2 i e h being a star with two leaves we give a linear kernel and an algorithm running in time o 25 301kk2 5 n3

a new fuzzy lyapunov function approach for a takagi sugeno fuzzy control system design in this paper a new fuzzy lyapunov function approach is presented for a class of continuous time takagi sugeno fuzzy control system the proposed fuzzy lyapunov function is formulated as a line integral of a fuzzy vector which is a function of the state and it can be regarded as the work done from the origin to the current state in the fuzzy vector field unlike the approaches using a fuzzy blending of multiple quadratic lyapunov functions the time derivatives of membership functions do not appear in the proposed approach the effectiveness of the proposed approach is shown through numerical examples

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

new multidimensional partially integrable generalization of s integrable n wave equation this paper develops a modification of the dressing method based on the inhomogeneous linear integral equation with integral operator having nonempty kernel the method allows one to construct the systems of multidimensional partial differential equations having differential polynomial structure in any dimension n the associated solution space is not full although it is parametrized by certain number of arbitrary functions of n 1 variables we consider four dimensional generalization of the classical 2 1 dimensional s integrable n wave equation as an example

perturbation theory for the modified nonlinear schrodinger solitons abstract the perturbation theory based on the riemann hilbert problem is developed for the modified nonlinear schrodinger equation which describes the propagation of femtosecond optical pulses in nonlinear single mode optical fibers a detailed analysis of the adiabatic approximation to perturbation induced evolution of the soliton parameter is given the linear perturbation and the raman gain are considered as examples

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

matching and weighted p2 packing algorithms and kernels parameterized algorithms and kernelization algorithms are presented for the weighted p 2 packing problem which is a generalization of the famous graph matching problem the parameterized algorithms are based on the following new techniques and observations 1 new study on structure relationship between graph matchings in general graphs and p 2 packings in bipartite graphs 2 an effective graph bi partitioning algorithm and 3 a polynomial time algorithm for a constrained weighted p 2 packing problem in bipartite graphs the kernelization algorithms are based on the following new techniques 1 the application of graph matching in kernelization 2 a crown reduction structure for weighted problems these techniques lead to randomized and deterministic parameterized algorithms that significantly improve the previous best upper bounds for the problem for both weighted and unweighted versions for the kernelization algorithm by using a weighted version of crown reduction a kernel of size o k 2 is presented where k is the given parameter of the problem

differential reductions of the kadomtsev petviashvili equation and associated higher dimensional nonlinear pdes we represent an algorithm allowing one to construct new classes of partially inte grable multidimensional nonlinear partial differential equations pdes starting with the special type of solutions to the 1 1 dimensional hierarchy of nonlinear pdes lineariz able by the matrix hopf cole substitution the burgers hierarchy we derive examples of four dimensional nonlinear matrix pdes together with they scalar and three dimensional reductions variants of the kadomtsev petviashvili type and korteweg de vries type equations are represented among them our algorithm is based on the combination of two frobenius type reductions and special differential reduction imposed on the matrix fields of integrable pdes it is shown that the derived four dimensional nonlinear pdes admit arbitrary functions of two variables in their solution spaces which clarifies the in tegrability degree of these pdes

the eckhaus equation in an external potential it is pointed out that the eckhaus nonlinear pde i psi t psi xx 2 mod psi mod 2 x mod psi mod 4 v x psi 0 remains c integrable i e integrable by a change of dependent variable even in the presence of any given external potential v x

a multiple lyapunov function approach to stabilization of fuzzy control systems this paper addresses stability analysis and stabilization for takagi sugeno fuzzy systems via a so called fuzzy lyapunov function which is a multiple lyapunov function the fuzzy lyapunov function is defined by fuzzily blending quadratic lyapunov functions based on the fuzzy lyapunov function approach we give stability conditions for open loop fuzzy systems and stabilization conditions for closed loop fuzzy systems to take full advantage of a fuzzy lyapunov function we propose a new parallel distributed compensation pdc scheme that feedbacks the time derivatives of premise membership functions the new pdc contains the ordinary pdc as a special case a design example illustrates the utility of the fuzzy lyapunov function approach and the new pdc stabilization method

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

the multiscale expansions of difference equations in the small lattice spacing regime and a vicinity and integrability test i we propose an algorithmic procedure i to study the distance between an integrable pde and any discretization of it in the small lattice spacing regime and at the same time ii to test the asymptotic integrability properties of such discretization this method should provide in particular useful and concrete information on how good is any numerical scheme used to integrate a given integrable pde the procedure illustrated on a fairly general ten parameter family of discretizations of the nonlinear schr dinger equation consists of the following three steps i the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in following degasperis et al 1997 physica d 100 187 211 ii the application to such an expansion of the degasperis procesi dp integrability test degasperis a and procesi m 1999 asymptotic integrability symmetry and perturbation theory spt98 ed a degasperis and g gaeta singapore world scientific pp 23 37 degasperis a 2001 multiscale expansion and integrability of dispersive wave equations lectures given at the euro summer school what is integrability isaac newton institute cambridge uk 13 24 august integrability lecture notes in physics vol 767 ed a mikhailov berlin springer to test the asymptotic integrability properties of the discrete system and its distance from its continuous limit iii the use of the main output of the dp test to construct infinitely many approximate symmetries and constants of motion of the discrete system through novel and simple formulas

a systematic approach to improve multiple lyapunov function stability and stabilization conditions for fuzzy systems this paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for takagi sugeno ts systems this approach is based on the idea of multiple lyapunov functions together with simple techniques for introducing slack matrices unlike some previous approaches based on multiple lyapunov functions both the stability and the stabilization conditions are written as linear matrix inequality lmi problems the proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the lmi problems numeric examples illustrate the effectiveness of this method

discrete third order spectral problems and a new toda type equation in this paper we construct the class of equations associated with a discrete spectral problem of third order among the equations of this class we find an integrable differential equation on the lattice with exponential nonlinearity by considering its associated darboux transformation we construct an explicit solution

multiple scale perturbation beyond the nonlinear schroedinger equation i abstract we consider the effect of weak nonlinearity on the propagation of one dimensional strongly dispersive waves in the standard quasi monochromatic approximation it is well known that the first order amplitude modulation satisfies the nonlinear schroedinger equation in slow variables with the assumption that this amplitude modulation has no discrete spectrum component i e no soliton we explore the higher order effects and provide a well defined procedure to compute all coefficients of the perturbative expansion as relatively bounded functions no secularity effects of slow variables the main effect of this procedure is that the leading amplitude modulation satisfies at higher orders the nonlinear schroedinger hierarchy of evolution equations in slow variables key ingredient is the integrability of the nonlinear schroedinger equation and its commuting symmetries

c integrable nonlinear partial differential equations in n 1 dimensions two techniques are introduced which are suitable to manufacture c integrable nonlinear pdes i e nonlinear pdes solvable by an appropriate change of variables in n 1 dimensions several examples are exhibited

a descriptor system approach to fuzzy control system design via fuzzy lyapunov functions there has been a flurry of research activities in the analysis and design of fuzzy control systems based on linear matrix inequalities lmis this paper presents a descriptor system approach to fuzzy control system design using fuzzy lyapunov functions the design conditions are still cast in terms of lmis but the proposed approach takes advantage of the redundancy of descriptor systems to reduce the number of lmi conditions which leads to less computational requirement to obtain relaxed lmi conditions new types of fuzzy controller and fuzzy lyapunov function are proposed a salient feature of the lmi conditions derived in this paper is to relate the feasibility of the lmis to the switching speed of each linear subsystem to be exact to the lower bounds of time derivatives of membership functions to illustrate the validity and applicability of the proposed approach two design examples are provided the first example shows that the lmi conditions based on the fuzzy lyapunov function are less conservative than those based on a common standard lyapunov function the second example illustrates the utility of the fuzzy lyapunov function approach in comparison with a piecewise lyapunov function approach

multicomponent integrable wave equations i darboux dressing transformation the darboux dressing transformations are applied to the lax pair associated with systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both bright and dark soliton solutions the general formalism is set up and the relevant equations are explicitly solved several instances of multicomponent wave equations of applicative interest such as vector nonlinear schrodinger type equations and three resonant wave equations are considered

universal c integrable nonlinear partial differential equation in n 1 dimensions a nonlinear partial differential equation of evolution in n 1 dimensions is exhibited which is c integrable namely integrable via an appropriate change of variables and which also possesses an element of universality as it is obtained by applying a limiting procedure to a class of nonlinear partial differential equations since this limiting procedure corresponds to physical conditions likely to prevail in some phenomenological circumstances it is expected that this equation shall have applicative relevance but this possibility is not pursued in this paper the method whereby this equation has been obtained as well as its integrable character qualify it as a n 1 dimensional analog of the eckhaus equation to which it does indeed reduce for n 1

the korteweg de vries hierarchy and long water waves by using the multiple scale method with the simultaneous introduction of multiple times we study the propagation of long surface waves in a shallow inviscid fluid as a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion we show that the korteweg de vries hierarchy equations do play a role in the description of such waves finally we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by kodama and taniuti

multiple scale analysis of dynamical systems on the lattice we propose a new approach to the multiple scale analysis of difference equations in the context of the finite operator calculus we derive the transformation formulae that map any given dynamical system continuous or discrete into a rescaled discrete system by generalizing a classical result due to jordan under suitable analytical hypotheses on the function space we consider the rescaled equations are of finite order our results are applied to the study of multiple scale reductions of dynamical systems and in particular to the case of a discrete nonlinear harmonic oscillator

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

a descriptor takagi sugeno approach to nonlinear model reduction abstract in this note the problem of nonlinear model reduction is addressed it consists in approximating a given nth order nonlinear system by a kth order nonlinear system where k n the goal is to compute the reduced order system minimizing the l 2 gain from the input to the difference between the outputs of the original and the reduced systems for this purpose the nonlinear system generating the approximation error is written under the takagi sugeno formalism and is studied with the use of a multiple lyapunov function based on the descriptor approach the obtained results are expressed in terms of linear matrix inequalities lmi and the matrices defining the reduced order system are obtained as a result of lmi problem uncertain nonlinear system reduction is also addressed