chains of darboux transformations for the matrix schrodinger equation chains of darboux transformations for the matrix schr odinger equation are considered a matrix generalization of the well known for the scalar equation crum krein formulae for the resulting action of such chains is given

an improved path following method for mixed h _ 2 h _ infty controller design among the few methods available to solve bilinear matrix inequalities bmis occurring in control design the path following method published some years ago appears to be one of the best ones as far as linearization methods are concerned however few details are given in the literature about its implementation and limits in this technical note this method is applied to the design of mixed h 2 h infin controllers with full details of the algorithm and some improvements over the one which has been published a few years ago the results obtained with the numerical example given in that same publication as well as with some other examples are compared with those given by other methods including a direct bmi solving program

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

non local continuity equations and binary darboux transformation of noncommutative anti self dual yang mills equations we present an infinite number of non local continuity equations of noncommutative anti self dual yang mills nc a sdym equations using the induction method of brezin et al 1979 phys lett b 82 442 and relate it to the lax pair and the parametric backlund transformation of the system from the lax pair we derive a binary darboux transformation to generate solutions of the nc a sdym equations

noncommutative instantons and twistor transform recently n nekrasov and a schwarz proposed a modification of the adhm construction of instantons which produces instantons on a noncommutative deformation of 4 in this paper we study the relation between their construction and algebraic bundles on noncommutative projective spaces we exhibit one to one correspondences between three classes of objects framed bundles on a noncommutative 2 certain complexes of sheaves on a noncommutative 3 and the modified adhm data the modified adhm construction itself is interpreted in terms of a noncommutative version of the twistor transform we also prove that the moduli space of framed bundles on the noncommutative 2 has a natural hyperkahler metric and is isomorphic as a hyperkahler manifold to the moduli space of framed torsion free sheaves on the commutative 2 the natural complex structures on the two moduli spaces do not coincide but are related by an so 3 rotation finally we propose a construction of instantons on a more general noncommutative 4 than the one considered by nekrasov and schwarz a q deformed 4

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

with a cole hopf transformation to solutions of the noncommutative kp hierarchy in terms of wronski matrices in the case of the kp hierarchy where the dependent variable takes values in an arbitrary associative algebra it is known that there are solutions which can be expressed in terms of quasideterminants of a wronski matrix which solves the linear heat hierarchy we obtain these solutions without the help of quasideterminants in a simple way via solutions of matrix kp hierarchies over and by use of a cole hopf transformation for this class of exact solutions we work out a correspondence with weakly nonassociative algebras

a fault detection observer design for lpv systems in finite frequency domain this paper addresses the fault detection observer design problem for linear parameter varying systems two finite frequency performance indexes are introduced to measure the fault sensitivity and the disturbance robustness first the h index fault sensitivity condition in finite frequency domain is obtained by generalised kalman yakubovich popov lemma and new linearisation techniques then with the aid of kalman yakubovich popov lemma and projection lemma the stability and robustness conditions are derived it turns out that the non convexity problem which is caused by dealing with the above three conditions can be translated into a bilinear matrix inequality optimisation problem by increasing the dimensions of slack variable matrix an iterative linear matrix inequality algorithm is proposed to get the solution the effectiveness of the filter is shown via three numerical examples

on a direct approach to quasideterminant solutions of a noncommutative kp equation a noncommutative version of the modified kp equation and a family of its solutions expressed as quasideterminants are discussed the origin of these solutions is explained by means of darboux transformations and the solutions are verified directly we also verify directly an explicit connection between quasideterminant solutions of the noncommutative mkp equation and the noncommutative kp equation arising from the miura transformation

monodromy of the matrix schrodinger equations and darboux transformations a schrodinger operator with a matrix valued rational potential u z is said to have trivial monodromy if all the solutions of the corresponding schrodinger equations are single valued in the complex plane for any a local criterion of this property in terms of the laurent coefficients of the potential u near its singularities which are assumed to be regular is found it is proved that any such operator with a potential vanishing at infinity can be obtained by a matrix analogue of the darboux transformation from the schrodinger operator this generalizes the well known duistermaat grunbaum result to the matrix case and gives the explicit description of the schrodinger operators with trivial monodromy in this case

backlund transformations for the anti self dual yang mills equations beginning from any given local solution of the gl n c anti self dual yang mills asdym equations on minkowski space a simple technique for the generation of large classes of solutions perhaps in some sense all is given the origin of this technique is described in terms of two versions of the ward construction the resulting description of backlund transformations is sufficiently simple that it is then possible to identify the group generated by the collection of all such backlund transformations and the space on which it acts in terms of concrete functions

scale preserving smoothing of polygons a smoother version of a polygon is defined as a polygon which approximates according to a given criterion and which simultaneously has no more edges than itself in this paper a scale preserving smoothing algorithm is presented the input to the algorithm is a polygon and the output is its smoothed version which contains all the scale information that contains is called the linear minimum perimeter polygon lmpp of within a tolerance of using the quantity the degree of with approximates can be controlled from the lmpp a representation for a polygon approximating can be procured which is invariant to scale and translation changes examples of smoothing maps and characters have been presented

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

combining convex concave decompositions and linearization approaches for solving bmis with application to static output feedback a novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality bmi constraints the key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings at each iteration of the algorithm the concave part is linearized leading to a convex subproblem applications to various output feedback controller synthesis problems are presented in these applications the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality lmi constraints the performance of the algorithm has been benchmarked on the data from the compleib library

scattering of plane waves in self dual yang mills theory we consider the classical self dual yang mills equation in 3 1 dimensional minkowski space we have found a new solution it describes the scattering of n plane waves the construction which we use is similar to the quantum inverse scattering method we introduce a monodromy matrix it acts in the direct product of the universal enveloping of su n algebra and an auxiliary linear space in order to obtain the solution of the self dual yang mills equation we take a special matrix element of in the auxiliary space

technical communique on lmi conditions to design observer based controllers for linear systems with parameter uncertainties this paper deals with the problem of observer based stabilization for linear systems with parameter inequality a new design methodology is proposed thanks to a judicious use of the famous young relation this latter leads to a less restrictive synthesis condition expressed in term of linear matrix inequality lmi than those available in the literature numerical comparisons are provided in order to show the validity and superiority of the proposed method

a geometrical approach to polygonal dissimilarity and shape matching two geometrical measures have been proposed to quantify the dissimilarity between two irregular polygons these measures capture the intuitive notion of the dissimilarity between shapes and are related to the minimum value of the intersecting area of the polygons on superposing one on the other in various configurations a more easily computable measure of dissimilarity referred to as the minimum integral square error between the polygons has also been proposed and using the latter measure pattern classification has been performed experimental results involving the classification of the noisy boundaries of the four great lakes erie huron michigan and superior using this measure have been presented

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

backlund transformations and the atiyah ward ansatz for non commutative anti self dual yang mills equations we present backlund transformations for the non commutative anti self dual yang mills equation where the gauge group is g gl 2 and use it to generate a series of exact solutions from a simple seed solution the solutions generated by this approach are represented in terms of quasi determinants we also explain the origins of all the ingredients of the backlund transformations within the framework of non commutative twistor theory in particular we show that the generated solutions belong to a non commutative version of the atiyah ward ansatz

non linear multi plane wave solutions of self dual yang mills theory new solutions of self dual yang mills sdym equations are constructed in minkowski space time for the gauge groupsl 2 after proposing a lorentz covariant formulation of yang s equations a set of ansatze for exact non linear multiplane wave solutions are proposed the gauge fields are rational functions ofex ki ki2 0 1 i n for these ansatze at least three families of multisoliton type solutions are derived explicitly their asymptotic behaviour shows that non linear waves scatter non trivially in minkowski sdym

extraction of trend lines and extrema from multiscale curves abstract multiscale planar curves are curves conveying information at several levels of detail to extract polygonal approximations of such curves at different resolutions we propose a parallel method based on connecting locally computed centroids the implementation makes use of a new pyramidal data structure the chain pyramid coarser and coarser approximations are obtained through a hierarchy of increasingly coarse tessellations significant extrema of the curves are localized at the highest resolution by segmenting at a natural scale and employing the structure of the chain pyramid for down projection

on solutions to the non abelian hirota miwa equation and its continuum limits in this paper we construct grammian like quasideterminant solutions of a non abelian hirota miwa equation through continuum limits of this non abelian hirota miwa equation and its quasideterminant solutions we construct a cascade of non commutative differential difference equations ending with the non commutative kp equation for each of these systems the quasideterminant solutions are constructed as well

on a non abelian hirota miwa equation a generalization of the hirota miwa equation to an abstract non abelian associative algebra is considered this system is integrable in the sense that it arises as compatibility condition for a linear system and has solutions constructed by means of the application of an arbitrary number of darboux transformations these solutions are in general expressed in terms of quasideterminants

quantisation of twistor theory by cocycle twist we present the main ingredients of twistor theory leading up to and including the penrose ward transform in a coordinate algebra form which we can then quantise by means of a functorial cocycle twist the quantum algebras for the conformal group twistor space mathbb cp 3 compactified minkowski space mathbb cm and the twistor correspondence space are obtained along with their canonical quantum differential calculi both in a local form and in a global algebra formulation which even in the classical commutative case provides a useful alternative to the formulation in terms of projective varieties we outline how the penrose ward transform then quantises as an example we show that the pull back of the tautological bundle on mathbb cm pulls back to the basic instanton on s 4 subset mathbb cm and that this observation quantises to obtain the connes landi instanton on deformed s4 as the pull back of the tautological bundle on our deformed mathbb cm we likewise quantise the fibration mathbb cp 3 rightarrow s 4 and use it to construct the bundle on deformed mathbb cp 3 that maps over under the transform to the deformed instanton