complexity of matrix problems in representation theory the classification problem is called wild if it contains the problem of classifying pairs of matrices up to simultaneous similarity we show in an explicit form that the last problem contains all classification matrix problems given by quivers or posets then we prove that this problem does not contain but is contained in the problem of classifying three valent tensors hence every wild classification problem given by a quiver or poset has the same complexity moreover a solution of one of them implies a solution of each of the remaining problems the problem of classifying three valent tensors is more complicated

robust finite time h control of singular stochastic systems via static output feedback abstract this paper addresses the problem of robust finite time stabilization of singular stochastic systems via static output feedback firstly sufficient conditions of singular stochastic finite time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time varying norm bounded disturbance then the results are extended to singular stochastic h finite time boundedness for the class of singular stochastic systems designed algorithm for static output feedback controller is provided to guarantee that the underlying closed loop singular stochastic system is singular stochastic h finite time boundedness in terms of strict linear matrix equalities with a fixed parameter finally an illustrative example is presented to show the validity of the developed methodology

fuzzy model based admissibility analysis and output feedback control for nonlinear discrete time systems with time varying delay abstract this paper is concerned with the admissibility analysis and stabilization problems for singular fuzzy discrete time systems with time varying delay the novelty of this paper comes from the consideration of a new summation inequality which is less conservative than the usual jensen inequality the abel lemma based inequality and the seuret inequality based on the inequality sufficient conditions are established to ensure the systems to be admissible moreover the corresponding conditions for the existence of desired static output feedback controller gains are derived to guarantee that the closed loop system is admissible the conditions can be solved by a modified cone complementarity linearization ccl algorithm examples are given to show the effectiveness of the proposed method

control design for fuzzy systems based on relaxed nonquadratic stability and h_ infty performance conditions in this paper new approaches to hinfin controller design for a class of discrete time nonlinear fuzzy systems are proposed based on a relaxed approach in which basis dependent lyapunov functions are used first two relaxed conditions of nonquadratic stability with h infin norm bound are presented for this class of systems the two relaxed conditions are shown to be useful in designing fuzzy control systems by introducing some additional instrumental matrix variables the two relaxed conditions are used to develop hinfin controllers in the control design the first relaxed condition has fewer inequality constraints but only admits a common additional matrix variable while the second one can admit multiple additional matrix variables finally two examples are given to demonstrate the applicability of the proposed approach

unified continuum description for sub diffusion random walks on multi dimensional comb model abstract the anisotropic sub diffusion random walks on multi dimensional comb structure model have been studied in the continuum approximation the problem is that in the considered model mean square displacements on different directions have different power temporal dependencies so this case essentially differs from usual anisotropic diffusion case and it is not obviously how to describe such a diffusion by a unified way nevertheless the unified continuum description for such random walks has been developed as result the new generalization of fick s law for diffusion current has been obtained for anisotropic anomalous sub diffusion random walks in multi dimensional case namely it has been shown that the effective diffusion coefficient in the generalized fick s law has new operator form components of diffusion tensor instead of constant values have the fractional order temporal derivatives

robust fuzzy filter design for a class of nonlinear stochastic systems this paper describes the robust hinfin fuzzy filtering design for a class of nonlinear stochastic systems the system dynamic is modelled by itocirc type stochastic differential equations for general nonlinear stochastic systems the hinfin filter can be obtained by solving a second order nonlinear hamilton jacobi inequality in general it is difficult to solve the second order nonlinear hamilton jacobi inequality in this paper using fuzzy approach takagi sugeno t s fuzzy model the hinfin fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities lmis instead of a second order hamilton jacobi inequality when the worst case fuzzy disturbance is considered a near minimum variance fuzzy filtering problem is also solved by minimizing the upper bound on the variance of the estimation error the near minimum variance fuzzy filtering problem under the worst case fuzzy disturbance is also characterized in terms of linear matrix inequality problem lmip which can be efficiently solved by the convex optimization techniques simulation examples are provided to illustrate the design procedure and expected performance

observer based controller design for stochastic descriptor systems with brownian motions in the paper a complete proof of the properness and mean square exponential stability for stochastic brownian systems is firstly addressed which lays a solid foundation for system analysis and control synthesis for this kind of stochastic systems observer based controller for the descriptor system with brownian motions is then investigated it is noticed that the system dynamics and observer dynamics are both subjected to state brownian fluctuation which makes it challenging either to design observer gain and controller gain simultaneously or design the observer and control gains by using a complete separation design technique a sequential design technique is proposed to calculate the control and observer gains by solving linear matrix inequalities the proposed design methods are readily extended to the case for stochastic descriptor systems with multiple brownian motions a numerical example is finally given to illustrate the design techniques and simulated results have demonstrated the efficiency

a jordan canonical form for reachable linear systems abstract we construct a new canonical form for reachable matrix pairs a b under the similarity action the canonical pairs are explicitly characterized by the property that a is in jordan canonical form and b is in a novel block echelon form whose block sizes are determined by the jordan structure of a the reachable pairs are classified by lists of indices and it is shown that the canonical form is continuous on the jordan strata consisting of all reachable pairs with the same index list the jordan strata are characterized topologically and explicit dimension formulas are derived finally we indicate some open problems related to the jordan decomposition of the space of reachable systems

robust h_ infty fuzzy control approach for a class of markovian jump nonlinear systems this paper addresses the problem of stabilizing a class of nonlinear systems subject to markovian jump parameters using a robust stochastic fuzzy controller with hinfin performance the class of jump nonlinear systems considered is described by a fuzzy model composed of two levels a crisp level which represents the jumps and a fuzzy level which represents the system nonlinearities considering the approximation error between the fuzzy model and the jump nonlinear system as norm bounded uncertainties we develop a systematic technique based on a coupled lyapunov function to obtain a robust stochastic fuzzy controller which guarantees the l2 gain of the closed loop system in respect to external inputs to be equal to or less than a prescribed value a simulation example on an industrial power plant operating in a cogeneration scheme is presented to illustrate the effectiveness of the proposed stabilizing controller in reducing oscillations as well as maintaining a desired operation condition in the presence of fluctuations in the local load

on the stabilizer subgroup of a fair of matrices abstract let f g be a pair of matrices defined over an arbitrary field fn n gn m consider the natural action of gln x glm on this pair given by f g gfg 1 ggh 1 where g h gln glm this action is of interest in system theory as well as the representation theory of quivers in this paper we study the stabilizer subgroup of this action stab f g i e g h gl n x gl m gfg 1 f ggh 1 g

subdiffusion in random compressible flows in this work we study the diffusion of admixture particles in a one dimensional velocity field given by a gradient of a random potential this refers us to the case of random compressible flows where previously only scaling estimates were available we develop a general approach which allows to solve this problem analytically with its help we derive the macroscopic transport equation and rigorously show in which cases transport can be subdiffusive we find the fourier laplace transform of the green s function of this equation and prove that for some potential distributions it satisfies the subdiffusive equation with fractional derivative with respect to time

analysis and synthesis of robust control systems using linear parameter dependent lyapunov functions this note provides sufficient robust stability conditions for continuous time polytopic systems they are obtained from the frobenius perron theorem applied to the time derivative of a linear parameter dependent lyapunov function and are expressed in terms of linear matrix inequalities lmi they contain as special cases various sufficient stability conditions available in the literature to date as a natural generalization the determination of a guaranteed h2 cost is addressed a new gain parametrization is introduced in order to make possible the state feedback robust control synthesis using parameter dependent lyapunov functions through linear matrix inequalities numerical examples are included for illustration

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

numerical solution of stochastic differential algebraic equations with applications to transient noise simulation of microelectronic circuits the transient simulation of noise in electronic circuits leads to differential algebraic equations additively disturbed by white noise for these systems we present a mathematical model based on the theory of stochastic differential equations along with an implicit two step method for their numerical treatment this numerical scheme works directly on the given structure of the equations which makes very efficient implementations possible the order of convergence is preserved the theoretical results are verified by numerical noise simulations of benchmark circuits

robust h fuzzy static output feedback control of t s fuzzy systems with parametric uncertainties this paper addresses robust h fuzzy static output feedback control problem for t s fuzzy systems with time varying norm bounded uncertainties sufficient conditions for synthesis of a fuzzy static output feedback controller for t s fuzzy systems are derived in terms of a set of linear matrix inequalities lmis in comparison with the existing literatures the proposed approach not only simplifies the design procedure but also achieves a better h performance three drawbacks existing in the previous papers such as coordinate transformation same output matrices and bmi problem have been eliminated the effectiveness of the proposed design method is demonstrated by an example for the control of a truck trailer system

regular points in system spaces representation theory of quivers is applied to system theory as a result the regular points in system spaces are characterized moreover all prestable points in system spaces are described and another generic property of linear systems is introduced

a wild quiver in linear systems theory abstract we study the action t l a b t 1 at t 1 bl of the group gl n k gl m k of linear state and input transformations on the space u n m of control systems a b k n n k n m with n different eigenvalues k an algebraically closed field this action is of interest in systems theory as well as the representation theory of quivers we construct a canonical form for on u n m and determine completely its stabilizer subgroups the results are based on an analysis of the scaling action d e b d 1 be of the group of diagonal matrices d n k d m k on k n m we construct a canonical form for this action by graph theoretic methods and determine the adherence order of the underlying stratification of k n m

generalized nonquadratic stability of continuous time takagi sugeno models this paper provides generalized nonquadratic stability conditions for continuous time nonlinear models in the takagi sugeno ts form obtained by sector nonlinearity approach should global quadratic stability fail for a given nonlinear model the proposed approach allows the obtaining of progressively better estimations of the stability domain via local asymptotic conditions in the form of linear matrix inequalities lmis which are efficiently solved by convex optimization techniques illustrative examples are presented to emphasize the broadening capabilities of the new stability analysis

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

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

two dimensional representations of the free group in two generators over an arbitrary field abstract working over an arbitrary field we classify all two dimensional representations of the free group with two generators

solutions for a schrodinger equation with a nonlocal term we obtain time dependent solutions for a schrondiger equation in the presence of a nonlocal term by using the green function approach these solutions are compared with recent results obtained for the fractional schrodinger equation as well as for the usual one the nonlocal term incorporated in the schrodinger equation may also be related to the spatial and time fractional derivative and introduces different regimes of spreading of the solution with the time evolution

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

quaternionic matrices unitary similarity simultaneous triangularization and some trace identities abstract we construct six unitary trace invariants for 2 2 quaternionic matrices which separate the unitary similarity classes of such matrices and show that this set is minimal we have discovered a curious trace identity for two unit speed one parameter subgroups of sp 1 a modification gives an infinite family of trace identities for quaternions as well as for 2 2 complex matrices we were not able to locate these identities in the literature we prove two quaternionic versions of a well known characterization of triangularizable subalgebras of matrix algebras over an algebraically closed field finally we consider the problem of describing the semi algebraic set of pairs x y of quaternionic n n matrices which are simultaneously triangularizable even the case n 2 which we analyze in more detail remains unsolved

mean square admissibility for stochastic ts fuzzy singular systems based on extended quadratic lyapunov function approach the mean square admissibility problem of stochastic ts fuzzy singular systems via an extended quadratic lyapunov function is investigated in this paper comparing with the existing quadratic lyapunov function method the extended quadratic lyapunov function method can relax stabilization conditions firstly the sufficient condition is given for the mean square admissibility of stochastic ts fuzzy singular systems based on an extended quadratic lyapunov function approach secondly two sufficient conditions for mean square admissibility of closed loop systems via the parallel distributed compensation pdc fuzzy controller and non parallel distributed compensation non pdc fuzzy controller are proposed furthermore through the extended quadratic lyapunov function method and non pdc fuzzy controller the less conservative mean square admissibility conditions on solving fuzzy controllers are derived in terms of linear matrix inequalities lmis finally some simulation examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology

versal deformations of invariant subspaces we describe a miniversal deformation of invariant subspaces with regard to a fixed endomorphism by means of a technique which can be applied to obtain explicitly miniversal deformations in a general orbit space in addition we present an application to the problem of classifying invariant subspaces

filtering and lqg problems for discrete time stochastic singular systems discrete time stochastic singular systems are discussed filtering and linear quadratic gaussian lqg problems are considered the problems are first transformed into the normal form via state augmentation and then solved by utilizing standard results for nonsingular systems the linear unbiased least squares state estimation algorithm and the optimal control law for the lqg problem are given the order of the filtering algorithm obtained in this way is not much increased moreover this algorithm allows the presence of some kinds of control inputs

the codimension of degenerate pencils abstract let dn dn r denote the codimension of the set of pairs of n n hermitian really symmetric matrices a b for which det i a xb p x is a reducible polynomial we prove that dn r n 1 dn n 1 n odd dn n n even we conjecture that the equality holds in all three inequalities we prove this conjecture for n 2 3

robust nonfragile h_ infty filtering of fuzzy systems with linear fractional parametric uncertainties this paper is concerned with the h filtering problem for continuous time takagi sugeno t s fuzzy systems different from existing results for fuzzy h filtering the proposed ones are toward uncertain fuzzy systems with linear fractional parametric uncertainties attention is focused on the design of a fuzzy filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by a descriptor representation approach two sufficient conditions for the h filter design are proposed in terms of linear matrix inequalities lmis when these lmis are feasible an explicit expression of the desired filter is given a simulation example will be given to show the efficiency of the proposed methods

unitary and euclidean representations of a quiver abstract a unitary euclidean representation of a quiver is given by assigning to each vertex a unitary euclidean vector space and to each arrow a linear mapping of the corresponding vector spaces we recall an algorithm for reducing the matrices of a unitary representation to canonical form give a certain description of the representations of canonical form and reduce the problem of classifying euclidean representations to the problem of classifying unitary representations we also describe the set of dimensions of all indecomposable unitary euclidean representations of a quiver and establish the number of parameters in an indecomposable unitary representation of a given dimension

canonical forms for linear systems this paper considers canonical forms for the similarity action of gl n on n m a b cn n cn m gl n n m n m h a b hah 1 hb those canonical forms are obtained as an application of a more general method to select canonical elements mc in the orbits om of a matrix group g acting on a set of matrices m cl p we define a total order on cl p different from the lexicographic order l 0l x x 0 but 0 x 0 for x r and consider normalized om elements with a minimal number of parameters min m om m normalized it is shown that the row and column echelon forms the jordan canonical form and nice control canonical forms for reachable a b pairs have a homogeneous interpretation as such minimal orbit elements moreover new canonical forms for the general action are determined via this method

relaxed stabilization conditions for continuous time takagi sugeno fuzzy control systems this paper deals with the stabilization of continuous time takagi sugeno t s fuzzy control systems based on fuzzy lyapunov functions and nonparallel distributed compensation non pdc control laws new stabilization conditions are represented in the form of linear matrix inequalities lmis the theoretical proof shows that the proposed conditions can provide less conservatism than the existing results in the literature moreover in order to demonstrate the effectiveness of the non pdc control laws the problem of h controller design for t s fuzzy systems is also studied simulation examples are given to illustrate the merits of the proposed methods

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

a continuous jacobi like approach to the simultaneous reduction of real matrices abstract the problem of simultaneous reduction of real matrices by either orthogonal similarity or orthogonal equivalence transformations is considered based on the jacobi idea of minimizing the sum of squares of the complementary part of the desired form to which matrices are reduced the projected gradient method is used in this paper it is shown that the projected gradient of the objective function can be formulated explicitly this gives rise to a system of ordinary differential equations that can be readily solved by numerical software the advantages of this approach are that the desired form to which matrices are reduced can be almost arbitrary and that if a desired form is not attainable then the limit point of the corresponding differential equation gives a way of measuring the distance from the best reduced matrices to the nearest matrices that have the desired form the general procedure for deriving these differential equations is discussed the framework can be generalized to the complex valued case some applications are given

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

stabilization of stochastic singular nonlinear hybrid systems abstract this paper deals with the control of the class of singular nonlinear stochastic hybrid systems under some appropriate assumptions results on stochastic stability and stochastic stabilization are developed two state feedback controllers linear and nonlinear that stochastically stabilize the class of systems we are considering are designed lmi sufficient conditions are developed to compute the gains of these controllers

fuzzy descriptor systems and nonlinear model following control this paper defines a fuzzy descriptor system by extending the ordinary takagi sugeno t s fuzzy model several kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matrix inequalities lmis we illustrate an example of defining the fuzzy descriptor system instead of the ordinary t s fuzzy model an lmi design approach is employed to find stable feedback gains and a common lyapunov function in addition this paper presents a nonlinear model following control for the fuzzy descriptor system a new parallel distributed compensation the so called twin parallel distributed compensations tpdc to realize the nonlinear model following control is proposed we present a design technique based on the tpdc the proposed method is a unified approach to nonlinear model following control it contains the regulation and servo control problems as special cases

simultaneous similarity of matrices abstract in this paper we solve completely and explicitly the long standing problem of classifying pairs of n n complex matrices a b under the simultaneous similarity tat 1 tbt 1 roughly speaking the classification decomposes to a finite number of steps in each step we consider an open algebraic set m 0n 2 r mn mn mn the set of n n complex valued matrices here r and are two positive integers then we construct a finite number of rational functions o1 os in the entries of a and b whose values are constant on all pairs similar in m n 2 r to a b the values of the functions oi a b i 1 s determine a finite number at most n 2 r of similarity classes in m n 2 r let sn be the subspace of complex symmetric matrices in mn for a b sn sn we consider the similarity class tatt tbtt where t ranges over all complex orthogonal matrices then the characteristic polynomial i a xb determines a finite number of similarity classes for almost all pairs a b sn sn