descriptor discrete time systems with random abrupt changes stability and stabilisation this paper deals with the class of linear discrete time systems with random abrupt changes also known as class of markovian jump singular systems the problems of stochastic stability and the stochastic stabilisation using state feedback control and static output feedback control are tackled conditions in the lmi setting to design the appropriate gains of the controllers are developed it is shown that all the addressed problems can be solved if the corresponding developed linear matrix inequalities lmis are feasible numerical examples are employed to show the usefulness of the proposed results

composite anti disturbance control for markovian jump nonlinear systems via disturbance observer this paper is concerned with the problems of composite disturbance observer based control dobc and control for markovian jump systems with nonlinearity and multiple disturbances our aim is to design a disturbance observer to estimate the disturbance generated by an exogenous system then construct the control scheme by integrating the output of the disturbance observer with state feedback control law such that the closed loop system can be guaranteed to be stochastically stable and different types of disturbances can be attenuated and rejected by constructing a proper stochastic lyapunov krasovskii functional sufficient conditions for the existence of the desired observer and the state feedback controller are established in terms of linear matrix inequalities lmis which can be readily solved by standard numerical software finally a numerical example is provided to show the effectiveness of the proposed approaches

brief paper control for discrete singular hybrid systems the problems of stability state feedback control and static output feedback control for a class of discrete time singular hybrid systems are investigated in this paper a new sufficient and necessary condition for a class of discrete time singular hybrid systems to be regular causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict lmis respectively finally two illustrative examples are provided to demonstrate the applicability of the proposed approach

fault detection for uncertain fuzzy systems an lmi approach this paper studies the problem of designing a robust fault detection system for uncertain takagi sugeno fuzzy models the worst case fault sensitivity measure is formulated in terms of linear matrix inequalities the existence of a robust fault detection system that guarantees i the l2 gain from a fault signal to a residual signal greater than a prescribed value and ii the l2 gain from an exogenous input to a residual signal less than a prescribed value is given in terms of the solvability of linear matrix inequalities numerical examples are used to illustrate the effectiveness of the proposed design techniques

gain constrained recursive filtering with stochastic nonlinearities and probabilistic sensor delays this paper is concerned with the gain constrained recursive filtering problem for a class of time varying nonlinear stochastic systems with probabilistic sensor delays and correlated noises the stochastic nonlinearities are described by statistical means that cover the multiplicative stochastic disturbances as a special case the phenomenon of probabilistic sensor delays is modeled by introducing a diagonal matrix composed of bernoulli distributed random variables taking values of 1 or 0 which means that the sensors may experience randomly occurring delays with individual delay characteristics the process noise is finite step autocorrelated the purpose of the addressed gain constrained filtering problem is to design a filter such that for all probabilistic sensor delays stochastic nonlinearities gain constraint as well as correlated noises the cost function concerning the filtering error is minimized at each sampling instant where the filter gain satisfies a certain equality constraint a new recursive filtering algorithm is developed that ensures both the local optimality and the unbiasedness of the designed filter at each sampling instant which achieving the pre specified filter gain constraint a simulation example is provided to illustrate the effectiveness of the proposed filter design approach

observer based optimal fault detection and diagnosis using conditional probability distributions a new optimal fault detection and diagnosis fdd scheme is studied in this paper for the continuous time stochastic dynamic systems with time delays where the available information for the fdd is the input and the measured output probability density functions pdf s of the system the square root b spline functional approximation technique is used to formulate the output pdf s with the dynamic weightings as a result the concerned fdd problem can be transformed into a robust fdd problem subjected to a continuous time uncertain nonlinear system with time delays feasible criteria to detect and diagnose the system fault are provided by using linear matrix inequality lmi techniques in order to improve fdd performances two optimization measures namely guaranteed cost performance and hinfin performance are applied to optimize the observer design simulations are given to demonstrate the efficiency of the proposed approach

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

a generalization of sylvester s law of inertia abstract we introduce the class of unitoid matrices as those that are diagonalizable by congruence the nondegenerate canonical angles of a unitoid matrix a are the directions of the nonzero entries of a diagonal matrix congruent to a which are shown to be unique sylvester s law states that two hermitian matrices of the same size are congruent if and only if they have the same numbers of positive respectively negative eigenvalues two unitoid matrices are congruent if and only if they have the same nondegenerate canonical angles

fault detection filter design for markovian jump singular systems with intermittent measurements this paper addresses the problem of fault detection filter design for discrete time markovian jump singular systems with intermittent measurements the measurement transmission from the plant to the fault detection filter is assumed to be imperfect and a stochastic variable is utilized to model the phenomenon of data missing our attention is focused on the design of a fault detection filter such that the residual system is stochastically markovian jump admissible and satisfies some expected performances a new necessary and sufficient condition for a class of discrete time markovian jump singular systems to be stochastically markovian jump admissible is proposed in the form of strict linear matrix inequalities sufficient conditions are established for the existence of the fault detection filter finally a numerical example is provided to demonstrate the usefulness and applicability of the developed theoretical results

robust h control of descriptor discrete time markovian jump systems this paper considers the stochastic stability and the robust control of descriptor discrete time systems with markovian jumping parameters in terms of linear matrix inequalities a necessary and sufficient condition is proposed which ensures a discrete time descriptor markovian jump system to be regular causal and stochastically stable a robust admissibility condition and a robust bounded real lemma are also developed based on these a sufficient condition on the existence of a state feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique a robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities finally an example is provided to demonstrate the effectiveness of the proposed approach

stabilization of discrete time markovian jump linear systems via time delayed controllers this paper is concerned with the stabilization problem for a class of discrete time markovian jump linear systems with time delays both in the system state and in the mode signal the delay in the system state may be time varying the delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system we first show that the resulting closed loop system is a time varying delayed markovian jump linear system with extended state space then a sufficient condition is proposed for the design of a controller such that the closed loop system is stochastically stable finally numerical simulation is used to illustrate the developed theory

brief paper sliding mode control for ito stochastic systems with markovian switching this paper deals with the problem of sliding mode control smc for a class of nonlinear uncertain stochastic systems with markovian switching by introducing some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established furthermore the present sliding mode controller including the transition rates of modes can cope with the effect of markovian switching by means of linear matrix inequalities lmis with equality constraint sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with c disturbance attenuation level finally a numerical example is given to illustrate the applicability of the present method

fault detection for fuzzy systems with intermittent measurements this paper investigates the problem of fault detection for takagi sugeno t s fuzzy systems with intermittent measurements the communication links between the plant and the fault detection filter are assumed to be imperfect i e data packet dropouts occur intermittently which appear typically in a network environment and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the unreliable communication links the aim is to design a fuzzy fault detection filter such that for all data missing conditions the residual system is stochastically stable and preserves a guaranteed performance the problem is solved through a basis dependent lyapunov function method which is less conservative than the quadratic approach the results are also extended to t s fuzzy systems with time varying parameter uncertainties all the results are formulated in the form of linear matrix inequalities which can be readily solved via standard numerical software two examples are provided to illustrate the usefulness and applicability of the developed theoretical results

state noise estimator for descriptor systems with application to sensor fault diagnosis for descriptor systems with measurement output noises input disturbances may exist at the same time a new descriptor estimator technique is developed the necessary and sufficient condition for the existence of the present estimator is derived and a systematic design approach is addressed the effect of uncertainties is decoupled completely and the asymptotic estimates of the descriptor system state and the output noise are obtained simultaneously furthermore a normal state disturbance estimator is also given for a class of nonlinear descriptor systems with both output noises and input uncertainties a nonlinear descriptor estimator is derived by using the proposed design approach together with the linear matrix inequality technique the existence and convergence of the nonlinear descriptor estimator is proven the asymptotic estimates of the descriptor nonlinear system state and the output noise are obtained at the same time the present estimators are applied to the sensor fault diagnosis and hence the sensor fault can be estimated asymptotically finally two numerical examples are included to illustrate the proposed design procedures and applications

variance constrained cal h _ infty filtering for a class of nonlinear time varying systems with multiple missing measurements the finite horizon case this paper is concerned with the robust h finite horizon filtering problem for a class of uncertain nonlinear discrete time varying stochastic systems with multiple missing measurements and error variance constraints all the system parameters are time varying and the uncertainty enters into the state matrix the measurement missing phenomenon occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval the stochastic nonlinearities under consideration here are described by statistical means which can cover several classes of well studied nonlinearities sufficient conditions are derived for a finite horizon filter to satisfy both the estimation error variance constraints and the prescribed h performance requirement these conditions are expressed in terms of the feasibility of a series of recursive linear matrix inequalities rlmis simulation results demonstrate the effectiveness of the developed filter design scheme

brief an lmi approach to design robust fault detection filter for uncertain lti systems in this paper the robust fault detection filter design problem for uncertain linear time invariant lti systems with both unknown inputs and modelling errors is studied the basic idea of our study is to use an optimal residual generator assuming no modelling errors as the reference residual model of the robust fault detection filter design for uncertain lti systems with modelling errors and based on it to formulate the robust fault detection filter design as an h model matching problem by using some recent results of h optimization a solution of the optimization problem is then presented via a linear matrix inequality lmi formulation the main results include the development of an optimal reference residual model the formulation of robust fault detection filter design problem the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the lmi solution parameters the determination of adaptive threshold for fault detection an illustrative design example is employed to demonstrate the effectiveness of the proposed approach

technical communique new bounded real lemma for discrete time singular systems in this paper the problem of bounded real lemma for discrete time singular system with strict matrix inequalities is investigated it is proved that the bounded real lemma for discrete singular system can be described by a strict matrix inequality the results lead to more tractable and reliable computation when applying them to design control systems

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

stochastic stabilization of singular systems with markovian switchings this paper studies the stochastic stabilization problem for a class of singular markovian jump system the aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular markovian jump system smjs a new kind of stochastic controller only in the diffusion part is proposed such that the closed loop system has a unique solution and is almost surely exponentially admissible new sufficient condition for the existence of such a controller is given as linear matrix inequalities lmis based on this more extensions to transition probability matrix tpm with elements partially unknown and system states partially observable are developed a numerical example is used to demonstrate the effectiveness of the proposed methods

robust h sub spl infin filtering for stochastic time delay systems with missing measurements in this paper the robust hinfin filtering problem is studied for stochastic uncertain discrete time delay systems with missing measurements the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution we aim to design filters such that for all possible missing observations and all admissible parameter uncertainties the filtering error system is exponentially mean square stable and the prescribed hinfin performance constraint is met in terms of certain linear matrix inequalities lmis sufficient conditions for the solvability of the addressed problem are obtained when these lmis are feasible an explicit expression of a desired robust hinfin filter is also given an optimization problem is subsequently formulated by optimizing the hinfin filtering performances finally a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

decentralized adaptive fuzzy control for nonlinear large scale systems with random packet dropouts sensor delays and nonlinearities abstract this paper investigates the adaptive fuzzy decentralized control problem for a class of uncertain nonlinear large scale systems different from the conventional backstepping based adaptive output feedback control technique the output measurements are imperfect and considered to suffer random packet dropouts rpds random sensor delays rsds and random sensor nonlinearities rsns which result typically from a network environment such as sensor networks a novel sensor model is established for describing the random phenomena within a unified representation by introducing a multi markovian variable based on this sensor model two main difficulties arise first is that the system output cannot be used directly for controller design due to the randomly occurring phenomena second is how to deal with the complex nonlinear stochastic terms with unknown interconnections unknown time varying delays and unknown sensor nonlinearities entangled together with the help of new coordinate transformations and mean value theorem by using appropriate lyapunov krasovskii functionals a new adaptive decentralized memoryless output feedback controller is designed it is proved that the constructed controller ensures the boundedness in probability of all the closed loop signals in presence of rpds rsds and rsns the simulation results are presented to show the effectiveness of the proposed scheme

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

algebraic bethe ansatz for 19 vertex models with reflection conditions in this work we solve the 19 vertex models with the use of algebraic bethe ansatz for diagonal reflection matrices sklyanin k matrices the eigenvectors eigenvalues and bethe equations are given in a general form quantum spin chains of spin one derived from the 19 vertex models were also discussed

quantum spin chain with soliton non preserving boundary conditions we consider the case of an integrable quantum spin chain with soliton non preserving boundary conditions this is the first time that such boundary conditions have been considered in the spin chain framework we construct the transfer matrix of the model we study its symmetry and we find explicit expressions for its eigenvalues moreover we derive a new set of bethe ansatz equations by means of the analytical bethe ansatz method

congruential automorphism groups of general matrices for a mn c aut a the congruential automorphism group of a is the set of all non singular c mn c such that c ac a here the a for which aut a is bounded are described and this allows the characterization of pairs a b for which the set of matrices carrying the congruence of a to b is compact this characterization is in terms of non singular unitoid matrices in which certain configurations of canonical angles are forbidden

distributed filtering for a class of time varying systems over sensor networks with quantization errors and successive packet dropouts this paper is concerned with the distributed finite horizon filtering problem for a class of time varying systems over lossy sensor networks the time varying system target plant is subject to randomly varying nonlinearities rvns caused by environmental circumstances the lossy sensor network suffers from quantization errors and successive packet dropouts that are described in a unified framework two mutually independent sets of bernoulli distributed white sequences are introduced to govern the random occurrences of the rvns and successive packet dropouts through available output measurements from not only the individual sensor but also its neighboring sensors according to the given topology a sufficient condition is established for the desired distributed finite horizon filter to ensure that the prescribed average filtering performance constraint is satisfied the solution of the distributed filter gains is characterized by solving a set of recursive linear matrix inequalities a simulation example is provided to show the effectiveness of the proposed filtering scheme

long range deformations for integrable spin chains we present a recursion relation for the explicit construction of integrable spin chain hamiltonians with long range interactions based on arbitrary shortrange e g nearest neighbor integrable spin chains it allows us to construct an infinite set of conserved long range charges we explain the moduli space of deformation parameters by different classes of generating operators the rapidity map and dressing phase in the long range bethe equations are a result of these deformations the closed chain asymptotic bethe equations for long range spin chains transforming under a generic symmetry algebra are derived notably our construction applies to generalizations of standard nearest neighbor chains such as alternating spin chains we also discuss relevant properties for its application to planar d 4 n 4 and d 3 n 6 supersymmetric gauge theories finally we present a map between long range and inhomogeneous spin chains delivering more insight into the structures of these models as well as their limitations at wrapping order

a near optimal multiuser detector for ds cdma systems using semidefinite programming relaxation a multiuser detector for direct sequence code division multiple access systems based on semidefinite programming sdp is proposed it is shown that maximum likelihood ml detection can be carried out by relaxing the associated integer programming problem to a dual sdp problem which leads to a detector of polynomial complexity computer simulations that demonstrate that the proposed detector offers near optimal performance with considerably reduced computational complexity compared with that of existing primal sdp relaxation based detectors are presented

h_ bm infty fuzzy filtering of nonlinear systems with intermittent measurements this paper is concerned with the problem of h infin fuzzy filtering of nonlinear systems with intermittent measurements the nonlinear plant is represented by a takagi sugeno t s fuzzy model the measurements transmission from the plant to the filter is assumed to be imperfect and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the phenomenon of the missing measurements attention is focused on the design of an h infin filter such that the filter error system is stochastically stable and preserves a guaranteed h infin performance a basis dependent lyapunov function approach is developed to design the h infin filter by introducing some slack matrix variables the coupling between the lyapunov matrix and the system matrices is eliminated which greatly facilitates the filter design procedure the developed theoretical results are in the form of linear matrix inequalities lmis finally an illustrative example is provided to show the effectiveness of the proposed approach

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

reduced order h filtering for singular systems abstract this paper solves the problem of reduced order h filtering for singular systems the purpose is to design linear filters with a specified order lower than the given system such that the filtering error dynamic system is regular impulse free or causal stable and satisfies a prescribed h performance level one major contribution of the present work is that necessary and sufficient conditions for the solvability of this problem are obtained for both continuous and discrete singular systems these conditions are characterized in terms of linear matrix inequalities lmis and a coupling non convex rank constraint moreover an explicit parametrization of all desired reduced order filters is presented when these inequalities are feasible in particular when a static or zeroth order h filter is desired it is shown that the h filtering problem reduces to a convex lmi problem all these results are expressed in terms of the original system matrices without decomposition which makes the design procedure simple and directly last but not least the results have generalized previous works on h filtering for state space systems an illustrative example is given to demonstrate the effectiveness of the proposed approach

integrable spin chains associated with slq n and slp q n the hopf structure of the central extension of the uq sl n algebra is considered the intertwine matrix induces new integrable chain models we show the relation of these models and the biparametric spin chain slp q n models the cases n 2 are n 3 are discussed and for n 2 we obtain the model of dasgupta and chowdhury 1993 the case n 3 is solved by the nested bethe ansatz method and the dependence of the bethe equations on the second parameter introduced is demonstrated

extended dissipative filtering for markovian jump interval valued fuzzy systems with uncertain transition rates abstract this paper addresses the problem of the extended dissipative filtering for a class of markovian jump interval valued fuzzy systems with uncertain transition rates first a sufficient condition of stochastic asymptotic stability and extended dissipativity is provided then by introducing some additional matrices the matrices in this sufficient condition can be decomposed into a form with only one part and its transpose containing the unknown parametric matrices of filter which is vitally important for establishing a new sufficient condition and designing an extended dissipative filter via the projection lemma attention is focused on the applications of this projection lemma twice by virtue of the feature of extended dissipative performance which differs from existing work and produces better estimated effects the new sufficient condition is of nonlinear form with respect to some matrix variables which makes the determination of extended dissipative filter difficult fortunately by transforming nonlinear matrix inequalities into a quadratic optimization problem with linear matrix inequality constraints the extended dissipative filter is developed by virtue of a cone complementarity linearization algorithm finally two numerical examples are given to show the effectiveness of our proposed approach

unitary similarity classes within the cospectral congruence class of a matrix abstract matrix b m n c is c s equivalent resp c e equivalent to a m n c if b is both congruent and similar to resp cospectral with a we are concerned with the number typically one or infinitely many of unitary similarity classes in the c s resp c e equivalence class of a given matrix the case n 2 and the general normal case are fully understood for c s equivalence also the singular case may generally be reduced to the nonsingular case the present work includes four main results 1 if 0 lies in the interior of the field of values of a nonsingular a m n n 3 then the c e equivalence class contains infinitely many unitary similarity classes 2 when 0 is not in the interior general sufficient conditions are given for the c e class and thus the c s class to contain only one unitary class 3 when n 3 these conditions are also necessary and a classification of all c e and c s classes is given 4 for n 3 it is shown that the matrices for which the c s class contains infinitely many unitary similarity classes are dense among all matrices

diagonalisation of gl n invariant transfer matrices and quantum n wave system lee model the algebraic bethe ansatz is constructed for the gl n invariant transfer matrices with arbitrary gl n spin for this purpose the notion of vacuum subspace is introduced it is shown that the gl n magnet can be interpreted as an integrable discrete approximation of vector or matrix nonlinear schrodinger models or of the quantum n wave system

robust fault detection with missing measurements this paper investigates the problem of robust fault detection for uncertain systems with missing measurements the parameter uncertainty is assumed to be of polytopic type and the measurement missing phenomenon which appears typically in a network environment is modelled by a stochastic variable satisfying the bernoulli random binary distribution the focus is on the design of a robust fault detection filter or a residual generation system which is stochastically stable and satisfies a prescribed disturbance attenuation level this problem is solved in the parameter dependent framework which is much less conservative than the quadratic approach both full order and reduced order designs are considered and formulated via linear matrix inequality lmi based convex optimization problems which can be efficiently solved via standard numerical software a continuous stirred tank reactor cstr system is utilized to illustrate the design procedures

h sub spl infin filtering for singular systems this note considers the h sub spl infin filtering problem for linear continuous singular systems the purpose is the design of a linear filter such that the resulting error system is regular impulse free and stable while the closed loop transfer function from the disturbance to the filtering error output satisfies a prescribed h sub spl infin norm bound constraint without decomposing the original system matrices a necessary and sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given finally an illustrative example is presented to demonstrate the applicability of the proposed approach

brief paper robust exponential stabilization for markovian jump systems with mode dependent input delay this paper is concerned with the problem of exponential stabilization for uncertain linear systems with markovian jump parameters and mode dependent input delays sufficient stabilization conditions are developed in terms of matrix inequalities which can be solved by a proposed iterative algorithm based on the cone complementarity linearization ccl method memory controllers are also designed such that the closed loop system is exponentially mean square stable for all admissible uncertainties numerical examples are given to show that the developed method is efficient and less conservative

robust stability and stabilization of discrete singular systems an equivalent characterization this note deals with the problems of robust stability and stabilization for uncertain discrete time singular systems the parameter uncertainties are assumed to be time invariant and norm bounded appearing in both the state and input matrices a new necessary and sufficient condition for a discrete time singular system to be regular causal and stable is proposed in terms of a strict linear matrix inequality lmi based on this the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete time singular systems are introduced necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict lmi and a set of matrix inequalities respectively with these conditions the problems of robust stability and robust stabilization are solved an explicit expression of a desired state feedback controller is also given which involves no matrix decomposition finally an illustrative example is provided to demonstrate the applicability of the proposed approach

integrable su 3 spin chain combining different representations the general expression for the local matrix of a quantum chain with the site space in any representation of su 3 is obtained this is made by generalizing from the fundamental representation and imposing the fulfilment of the yang baxter equation then a non homogeneous spin chain combining different representations of su 3 is solved by developing a method inspired in the nested bethe ansatz the solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled bethe equations a conjecture about the solution of a chain with the site states in different representations of su n is presented the thermodynamic limit of the ground state is calculated

new integrable quantum chains combining different kinds of spins a general procedure to generate new integrable hamiltonians combining to any kind of spins distributed arbitrarily on the line is given as a concrete application anisotropic chains formed by spin 1 2 and spin 1 operators at alternating sites are presented and solved exactly by the bethe ansatz ba the authors compute the ground state and excitation energies and momentum the higher order ba equations are derived depending on the choice these new hamiltonians exhibit or not conformal invariance in their low energy spectrum