stochastic stability and l1 gain analysis for positive nonlinear semi markov jump systems with time varying delay via t s fuzzy model approach abstract this paper treats the issues of stochastic stability and l 1 gain analysis for continuous time positive fuzzy semi markov jump systems pfsmjss with time varying delay the system under consideration involves semi markov stochastic process related to weibull distribution the practical systems such as lotka volterra population model described by pfsmjss always need to consider the sudden change in the operating process to deal with these problems a sufficient condition for stochastic stability of pfsmjss is established which is dependent of the bound of time varying delay then based on the obtained results l 1 gain performance is analyzed in standard linear programming lp finally lotka volterra population model shows the validity of the conclusions

conjugacy classes in the symplectic renner monoid abstract in this paper we study conjugacy classes of the symplectic renner monoid r and find the following results each element in r is a join of strictly disjoint cycles and strings there is an explicit one to one correspondence between conjugacy classes and symplectic partitions a formula for calculating the number of conjugacy classes is obtained an explicit formula for computing the number of elements in each conjugacy class is given a relationship between conjugacy classes and munn conjugacy classes is described

on the performance advantage of multitaper spectral analysis the performance advantage of multitaper spectral analysis is quantified relative to weighted overlapped segment averaging wosa to make the comparison of these two nonparametric spectral estimators theoretical performance measures are derived in terms of leakage variance and resolution the methods are then compared by evaluating each measure in turn while requiring the other two measures to be equal the results show that multitaper analysis always performs better than wosa for example given the same leakage and resolution multitaper analysis can have three quarters to one half the variance of wosa given the same resolution and variance multitaper analysis can exhibit a 10 20 db leakage advantage over wosa these and other results provide compelling evidence for greater use of multitaper analysis in situations for which a nonparametric spectral estimator is appropriate

extending the bruhat order and the length function from the weyl group to the weyl monoid abstract for a symmetrizable kac moody algebra the category of admissible representations of the category o is an analogue of the category of finite dimensional representations of a semisimple lie algebra the monoid which is associated to this category and the category of restricted duals by a tannaka krein reconstruction contains the kac moody group as open dense unit group it has similar properties as a reductive algebraic monoid in particular there are bruhat and birkhoff decompositions the weyl group replaced by the weyl monoid c mokler an analogue of a reductive algebraic monoid whose unit group is a kac moody group arxiv math ag 0204246 mem amer math soc in press we determine the closure relations of the bruhat and birkhoff cells which give extensions of the bruhat order from the weyl group to the weyl monoid we show that the bruhat and birkhoff cells are irreducible and principal open in their closures we give product decompositions of the bruhat and birkhoff cells we define extended length functions which are compatible with the extended bruhat orders we show a generalization of some of the tits axioms for twin bn pairs

monoids on groups with bn pairs the theory of linear algebraic monoids has been developed in the last few years by l renner and the author 21 361 as a generalization of the theory of linear algebraic groups 16 40 in applications of the theory of linear algebraic groups one is naturally led to consider groups with bnpairs or tits systems 12 4 9 42 431 this class of groups includes in particular the groups of lie type so that the abstract properties of tits systems are useful in studying the conjugacy classes and representations of groups of lie type see 4 9 our interest is in monoids so let m be a monoid such that the group of units g has a bn pair in general g has very little to do with the rest of m in fact for a given g m g could be an arbitrary semigroup so we introduce three axioms which intimately connect the idempotent structure of m with the structure of g we then say that m is a monoid on g the prime example is a connected regular linear algebraic monoid with zero but there are other natural examples for instance renner 37 is developing a theory of monoids of lie type along the lines of steinberg 41 for groups another example arises from the work of smith 39 and cabanes 3 from their work one can associate with certain irreducible modular representations 4 g gl v a set of idempotents es end v then the monoid m generated by 4 g and e is a monoid on 4 g in the examples we have worked out and very likely in general in the situation of linear algebraic monoids there is a natural type map from the finite lattice of conjugacy classes of idempotents g the lattice of f classes into the power set of the dynkin diagram of g the idea of the type map is due to lex renner and is exploited by renner and the author 31 to show in particular that the system of idempotents can be constructed from the type map in the present situation of monoids on g there is again a type map i which characterizes the system of idempotents 139 0021 8693 89 3 00

h_ infty positive filtering for positive linear discrete time systems an augmentation approach in this note we address the reduced order positive filtering problem of positive discrete time systems under the h performance commonly employed approaches such as linear transformation and elimination technique may not be applicable in general due to the positivity constraint of the filter to cope with the difficulty we first represent the filtering error system as a singular system by means of the system augmentation approach which will facilitate the consideration of the positivity constraint two necessary and sufficient conditions are obtained in terms of matrix inequalities under which the filtering error system has a prescribed h performance then a necessary and sufficient condition is proposed for the existence of the desired positive filters and an iterative linear matrix inequality lmi algorithm is presented to compute the filtering matrices which can be easily checked by standard software finally a numerical example to illustrate the effectiveness of the proposed design procedures is presented

exponential stability and l1 gain analysis for positive time delay markovian jump systems with switching transition rates subject to average dwell time abstract the paper deals with the problems of exponential stability and l 1 gain analysis for positive time delay markovian jump systems mjss with switching transition rates another set of useful regime switching model is given which extends fixed transition rates to time varying transition rates by resorting to the linear co positive lyapunov function and average dwell time sufficient conditions for exponential stability are proposed in terms of standard linear programming based on the obtained results l 1 gain performance is analyzed finally an example is proposed to illustrate the validity of the main results

conjugacy decomposition of reductive monoids we study the decomposition of a reductive monoid related to conjugacy classes and obtain a description of the associated finite poset open image in new window this poset is constructed via the gauss jordan elements of the renner monoid r for mn k the poset can be identified with the lattice of all partitions of m 0 m n where the order is an extension of the dominance order on partitions of n

reliable mixed h passive control for t s fuzzy delayed systems based on a semi markov jump model approach abstract this paper investigates the problem of the reliable mixed h passive control for takagi sugeno t s fuzzy delayed systems based on a semi markov jump model smjm approach the focus is to design a fuzzy fault tolerant controller such that the resulting closed loop system is stochastically stable with a prescribed mixed h passive performance level even if the actuator failures appear a semi markov process is employed to describe the encountered failures of the actuator by applying the lyapunov krasovskii method in combination with some novel inequalities some conditions on the performance analysis are established where some negative quadratic terms are fully considered to reduce the conservatism based on the conditions an explicit expression for the desired controller is given three numerical examples are presented to show the effectiveness and reduced conservatism of the proposed method

static output feedback control of nonhomogeneous markovian jump systems with asynchronous time delays this paper investigates the problem of static output feedback control for a class of nonhomogeneous markovian jump system nmjs with asynchronous time delays atds since the atds subject to uncertain transition probabilities tps are taking into account in a practical phenomenon new approaches are introduced to deal with the atds characterized by nonhomogeneous markov processes it is assumed that the communication links are not perfect due to its detrimental effect on the performance of systems stochastic variables are presented to characterize the data transmission which are depending on operation modes and satisfying the bernoulli distribution sets of slack variables are adopted to decouple the product terms between system matrices and lyapunov matrices based on an extended lyapunov function combined with finsler inequality approach the robust static output feedback controller is designed for the closed loop nmjs finally a numerical example is provided to verify the design method

conjugacy classes of renner monoids abstract in this paper we describe conjugacy classes of a renner monoid r with unit group w the weyl group we show that every element in r is conjugate to an element ue where u w and e is an idempotent in a cross section lattice denote by w e and w e the centralizer and stabilizer of e in w respectively let w e act by conjugation on the set of left cosets of w e in w we find that ue and ve u v w are conjugate if and only if u w e and v w e are in the same orbit as consequences there is a one to one correspondence between the conjugacy classes of r and the orbits of this action we then obtain a formula for calculating the number of conjugacy classes of r and describe in detail the conjugacy classes of the renner monoid of some j irreducible monoids we then generalize munn conjugacy on a rook monoid to any renner monoid and show that munn conjugacy coincides with semigroup conjugacy action conjugacy and character conjugacy we also show that the number of inequivalent irreducible representations of r over an algebraically closed field of characteristic zero equals the number of munn conjugacy classes in r

l gain analysis for positive systems with distributed delays this paper addresses the l gain analysis problem of positive linear systems with distributed delays by virtue of the positivity and linearity of the system we first study the monotonic and asymptotic property of the system with distributed delays then by resorting to an auxiliary system without time delay an explicit expression of the l gain of positive systems with distributed delays is given in terms of system matrices moreover the results are extended to positive systems with distributed delays over a bounded time varying interval finally a necessary and sufficient condition on the l gain of an asymptotically stable positive system with distributed delays is presented via linear programming

the h polynomial of an irreducible representation abstract let g be a simple algebraic group associated with the finite dimensional rational representation g end v of g there is the monoid m k g end v and the projective g g embedding p m 0 k one can identify the cases where p is rationally smooth and in such cases it is desirable to calculate the h polynomial h of p in this paper we consider the situation where is irreducible we then determine h explicitly in terms of combinatorial invariants of indeed there is a canonical cellular decomposition for p these cells are defined in terms of idempotents b b orbits and other natural quantities obtained from m furthermore h is obtained by recording the dimension of each of these cells in terms of the descent system of m as a special case we reacquire the well known formula for the poincare polynomial of a wonderful embedding of a simple algebraic group of adjoint type

constrained control of positive systems with delays this technical note addresses controller design for continuous time delayed linear systems the control is under positivity constraint which means that the resulting closed loop systems are not only stable but also positive bounded control is also considered further requiring that the trajectory of the closed loop system is bounded by a prescribed boundary if the initial condition is bounded by the same boundary the contribution lies in three aspects first some necessary and sufficient conditions are presented for the existence of controllers satisfying the positivity constraint second a necessary and sufficient condition is established determining whether the trajectory of a positive system can be bounded by a prescribed boundary provided that the initial condition is bounded by the same boundary third a sufficient condition is presented for bounded control and it is shown to be also necessary if asymptotic stability is not required

on linear copositive lyapunov functions and the stability of switched positive linear systems we consider the problem of common linear copositive lyapunov function existence for positive switched linear systems in particular we present a necessary and sufficient condition for the existence of such a function for switched systems with two constituent linear time invariant systems several applications of this result are also given

the canonical compactification of a finite group of lie type let g be a finite group of lie type we construct a finite monoid m having g as the group of units m has properties analogous to the canonical compactification of a reductive group the complex representation theory of m yields harish chandra s philosophy of cuspidal representations of g the main purpose of this paper is to determine the irreducible modular representations of m we then show that all the irreducible modular representations of g come via the 1942 work of clifford from the one dimensional representations of the maximal subgroups of m this yields a semigroup approach to the modular representation theory of g via the full rank factorizations of the sandwich matrices of m we then determine the irreducible modular representations of any finite monoid of lie type

classification of semisimple rank one monoids consider the classification problem for irreducible normal algebraic monoids with unit group g we obtain complete results for the groups s12 k x k g12 k and pgi2 k x k if g is one of these groups let 4 g denote the set of isomorphy types of normal algebraic monoids with zero element and unit group g our main result establishes a canonical one to one correspondence g q where q is the set of positive rational numbers the classification is achieved in two steps first we construct a class of monoids from linear representations of g that done we show that any other e must already be one of those constructed to do this we devise an extension principle analogous to the big cell construction of algebraic group theory this yields a birational comparison morphism qp er e for some r e q which is ultimately an isomor phism because the monoid er e g is regular

stability and stabilization of discrete time semi markov jump linear systems via semi markov kernel approach this technical note is concerned with the problems of stability and stabilization for a class of discrete time semi markov jump linear systems s mjlss the discrete time semi markov kernel smk is introduced where the probability density function of sojourn time is dependent on both current and next system mode as a consequence different types of distributions and or different parameters in a same type of distribution of sojourn time depending on the target mode towards which the system jumps can coexist in each mode of a smk the underlying s mjlss are therefore more general than those considered in existing studies a new stability concept generalizing the traditional mean square stability is proposed such that numerically testable criteria on the basis of smk are obtained numerical examples are presented to illustrate the validity and advantage of the developed theoretical results

positive observers for linear positive systems and their implications a treatment of the positive observation problem for positive systems is provided for the continuous and discrete time cases the proposed observers are positive that is they ensure that the estimates are nonnegative at any time moreover necessary and sufficient conditions for the existence of such positive observers are formulated in terms of linear programming also we show how positive observers can provide guaranteed bounds on the real states of uncertain positive systems in addition some implications are discussed especially it is shown that it is not possible to stabilise an unstable system using these positive observers finally the applicability of the proposed interval estimation approach is shown for an illustrative application from pharmacokinetics

conjugacy classes in algebraic monoids let m be a connected linear algebraic monoid with zero and a reductive group of units g the following theorem is established theorem there exist affne subsets ml mk of m reductive groups g1 gk with antiautomorphisms surjective morphisms 0t mi gi such that 1 every element of m is conjugate to an element of some ms and 2 two elements a b in mi are conjugate in m if and only if there exists x e gi such that x0 a x si b as a consequence it is shown that m is a union of its inverse submonoids introduction the objects of study in this paper are connected linear algebraic monoids m with zero this means by definition that the underlying set of m is an irreducible affine variety and that the product map is a morphism i e a polynomial map we will further assume that the group of units g of m is reductive this means 1 3 that the unipotent radical of g is trivial then by 6 10 m is unit regular i e m e m g where e e m e e mle2 e in this paper we study the conjugacy classes of m an initial study was made by the author 8 where the general problem was reduced to nilpotent elements the approach here is quite different yielding a more complete answer to be precise we show that there exist affine subsets m1 mk of m reductive groups g1 gk with antiautomorphisms surjective morphisms si mi gi i 1 k such that 1 every element of m is conjugate to an element of some mi and 2 if a b e mi then a is conjugate to b in m if and only if there exists x e gi such that xsi a x si b as an application of this result we show that m is a union of its inverse submonoids an inverse semigroup is a semigroup s with the property that for each a e s there exists a unique a e s such that aaa a and aaa a see 2 finally in 3 we use our main results to briefly analyze the conjugacy classes of nilpotent elements 1 preliminaries throughout this paper z will denote the set of all positive integers and k an algebraically closed field let g be a connected linear algebraic group defined over k the radical r g is the maximal closed connected normal solvable subgroup of g and the unipotent radical ru g is the group of unipotent elements of r g we will assume throughout that g is a reductive group i e ru g 1 then r g c c g the center of g moreover g r g go where go g g is a semisimple group i e r go 1 also 3 theorem 27 5 go is a product of the simple closed normal subgroups of g in particular we have the following received by the editors november 3 1986 1980 mathematics subject classification 1985 revision primary 20g99 20m10 c 1987 american mathematical society 0002 9947 87 1 00 25 per page

classification of semisimple algebraic monoids let x be a semisimple algebraic monoid with unit group g associated with e is its polyhedral root system x c where x x t is the character group of the maximal torus t c g c x t is the set of roots and c x t is the character monoid of t c e zariski closure the correspondence e x c is a complete and discriminating invariant of the semisimple monoid e extending the well known classification of semisimple groups in establishing this result monoids with preassigned root data are first constructed from linear representations of g that done we then show that any other semisimple monoid must be isomorphic to one of those constructed to do this we devise an extension principle based on a monoid analogue of the big cell construction of algebraic group theory thls ultimately yields the desired conclusions consider the classification problem for semisimple algebraic monoids over the algebraically closed field k what sort of problem is this first the definition a semisimple algebraic monoid is an irreducible affine algebraic variety e defined over k together with an associative morphlsm m e x e e and a two sided unit 1 e e for m we assume further that e has a 0 the unit group g which is always linear algebraic and dense in e is reductive e g gl k dim zg 1and e is a normal variety the problem then presents us with two familiar objects let t c g be a maximal torus then z t c e zariski closure is an affine torus embedding and g c e is a reductive algebraic group torus embeddings have been introduced by demazure in 6 in his study of cremona groups and are classified numerically using rational polyhedral cones 14 on the other hand reductive groups have been studied at least in principle since the nineteenth century their classification in the modern sense being achieved largely by chevalley 4 that numerical classification uses the now familiar root systems l l chapter 31 of killing that were introduced by him 15 in his penetrating formulation of the classification e cartan s of semisimple lie algebras thus in the classification of semisimple monoids we are compelled to consider the root system x x t t of g and the polyhedral cone c x z c x t of t c z the two objects are canonically related by the weyl group action on x which leaves c stable received by the editors november 16 1984 1980 mathematics subject classification primary 14m99 secondary 20m99

mobius functions and semigroup representation theory ii character formulas and multiplicities abstract we generalize the character formulas for multiplicities of irreducible constituents from group theory to semigroup theory using rota s theory of mobius inversion the technique works for a large class of semigroups including inverse semigroups semigroups with commuting idempotents idempotent semigroups and semigroups with basic algebras using these tools we are able to give a complete description of the spectra of random walks on finite semigroups admitting a faithful representation by upper triangular matrices over the complex numbers these include the random walks on chambers of hyperplane arrangements studied by bidigare hanlon rockmore brown and diaconis applications are also given to decomposing tensor powers and exterior products of rook matrix representations of inverse semigroups generalizing and simplifying earlier results of solomon for the rook monoid

the use of nonparametric noise models extracted from overlapping subrecords for system identification in this paper we study the asymptotic properties consistency and asymptotic efficiency of a frequency domain errors in variables estimator using data extracted from overlapping subrecords while the classical approach without overlap needs six consecutive periods we show in this paper that using overlapping subrecords consistent estimators can be found with only two periods of the steady state response to a periodic excitation this is done using overlapping subrecords moreover the system identification procedure developed for data extracted from independent periods is shown to be valid for data extracted from overlapping subrecords this allows the user to reduce the measurement time considerably without changing the identification procedure

infinite dimensional reductive monoids associated to highest weight representations of kac moody groups abstract starting with a highest weight representation of a kac moody group over the complex numbers we construct a monoid whose unit group is the image of the kac moody group under the representation multiplied by the nonzero complex numbers we show that this monoid has similar properties to those of a j irreducible reductive linear algebraic monoid in particular the monoid is unit regular and has a bruhat decomposition and the idempotent lattice of the generalized renner monoid of the bruhat decomposition is isomorphic to the face lattice of the convex hull of the weyl group orbit of the highest weight

investigating the effects of time delays on stochastic stability and designing l1 gain controllers for positive discrete time markov jump linear systems with time delay this paper is concerned with stochastic stability l1 gain performance analysis and positivity preserving l1 gain controller design for a positive discrete time markov jump linear system with time delay first necessary and sufficient conditions for stochastic stability of the system are derived by constructing a linear co positive stochastic lyapunov functional and establishing a system equation whose state variables consist of the mathematical expectation of the markovianized states and whose coefficient matrices depend on time delay and the transition probability it is revealed that stochastic stability of the positive discrete time markov jump linear system with time delay is influenced by the size of time delay and it is demonstrated by an example that the effect of time delay on stochastic stability can be either positive or negative second exact computation on an l1 gain index of a stochastically stable positive discrete time markov jump linear system with time delay is presented and a necessary and sufficient condition for the l1 gain performance is derived in the form of linear programming third an iterative algorithm is proposed to design a positivity preserving l1 gain controller and in single input case an optimal controller is obtained analytically such that the closed loop system achieves the minimal l1 gain performance then a modified pest s structured population dynamic model is developed to illustrate the effectiveness of the designed method

stochastic stability of positive markov jump linear systems abstract this paper investigates on the stability properties of positive markov jump linear systems pmjls s i e markov jump linear systems with nonnegative state variables specific features of these systems are highlighted in particular a new notion of stability exponential mean stability is introduced and is shown to be equivalent to the standard notion of 1 moment stability moreover various sufficient conditions for exponential almost sure stability are worked out with different levels of conservatism the implications among the different stability notions are discussed it is remarkable that thanks to the positivity assumption some conditions can be checked by solving linear programming feasibility problems

l_1 stochastic stability and l_1 gain performance of positive markov jump linear systems with time delays necessary and sufficient conditions this paper is concerned with l 1 stochastic stability and l 1 gain performance analysis of a continuous time positive markov jump linear system with a time delay by constructing a novel linear co positive stochastic lyapunov functional based on the positivity of the system and characterizing the system equation of the mathematical expectation of the markovianized states some necessary and sufficient delay dependent conditions for l 1 stochastic stability and l 1 gain performance are presented in terms of linear programming a numerical example is provided for showing the effectiveness of the obtained conditions especially for exploring and revealing both the negative effect and the positive effect of the time delay on stochastic stability of the positive markov jump linear system with a time delay

stochastic stability of ito differential equations with semi markovian jump parameters in this note the problem of stochastic stability for linear systems with jump parameters being semi markovian rather than full markovian is further investigated in particular the system under consideration is described by ito type nonlinear stochastic differential equations with phase type semi markovian jump parameters stochastic stability conditions are presented

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

stability and stabilizability criteria for discrete time positive switched systems in this paper we consider the class of discrete time switched systems switching between p autonomous positive subsystems first sufficient conditions for testing stability based on the existence of special classes of common lyapunov functions are investigated and these conditions are mutually related thus proving that if a linear copositive common lyapunov function can be found then a quadratic positive definite common function can be found too and this latter in turn ensures the existence of a quadratic copositive common function secondly stabilizability is introduced and characterized it is shown that if these systems are stabilizable they can be stabilized by means of a periodic switching sequence which asymptotically drives to zero every positive initial state conditions for the existence of state dependent stabilizing switching laws based on the values of a copositive linear quadratic lyapunov function are investigated and mutually related too finally some properties of the patterns of the stabilizing switching sequences are investigated and the relationship between a sufficient condition for stabilizability the existence of a schur convex combination of the subsystem matrices and an equivalent condition for stabilizability the existence of a schur matrix product of the subsystem matrices is explored

controller design for time delay system with stochastic disturbance and actuator saturation via a new criterion abstract this paper deals with the problem of controller design for time delay system with stochastic disturbance and actuator saturation by use of more appropriate lyapunov krasovskii functional lkf and a new criterion for the domain of attraction less conservative conditions for stochastic stability are proposed then the difficulties of the domain of attraction confronted in system analysis and synthesis can be overcome these sufficient conditions are derived in terms of linear matrix inequality lmi finally two practical examples demonstrate the validity of the given results

stochastic stability and stabilization conditions of semi markovian jump systems with mode transition dependent sojourn time distributions this paper is concerned with the stochastic stability and stabilization problem for a class of continuous time semi markovian jump systems s mjss with mode transition dependent sojourn time distributions in contrast to other approaches this paper offers the possibility to explore more refined probability models on the sojourn time by considering the mode transition dependent sojourn time distributions instead of mode dependent ones here to construct a finite set of linear matrix inequalities lmis from sojourn time dependent matrix inequalities a less conservative relaxation method is proposed in such a way that all available constraints on time varying transition rates can be exploited simulation examples report the effectiveness of the proposed method

disturbance attenuation and rejection for stochastic markovian jump system with partially known transition probabilities in this paper the problem of disturbance attenuation and rejection is investigated for stochastic markovian jump system with multiple disturbances which include white noises and disturbances with partially known information a disturbance observer is designed to estimate the disturbances with partially known information based on the estimation value a disturbance observer based attenuation and rejection controller is constructed such that the closed loop system is asymptotically bounded in mean square or asymptotically stable in probability under different conditions finally a numerical example is given to illustrate the effectiveness of the proposed approach

analog of the bruhat decomposition for algebraic monoids ii the length function and the trichotomy 0 introduction the purpose of this paper is to continue the study of b b orbits on a reductive monoidm this was first taken up systematically by the author in 9 where several basic properties analogous to the case of groups were established the b b orbits were identified with a finite monoid r defined in terms of the normalizer of a maximal torus and a direct analysis of these orbits led to an extension of tits axiom br brb b rb to the case of reductive monoids however there is more to this axiom when dealing with monoids obviously

frequency domain system identification using non parametric noise models estimated from a small number of data sets abstract this paper discusses the problem of identifying a linear system from the frequency data when the measurements of the input and the output signals are both disturbed with noise a typical example of such a problem is the identification of a system in a feedback loop it is known that this problem can be solved using errors in varaibles methods if the covariance matrices of the disturbing noise on input and output measurements are a priori known it is shown that the exact covariance matrices can be replaced by the sample covariance matrices the system can be identified from the sample means and sample covariance matrices calculated from a small number m of independently repeated experiments it is shown that under these conditions the estimates are still strongly consistent for an increasing number of data points n in each experiment n if m 4 the loss in efficiency is quantified m 6 and the expected value of the cost function m 4 and its variance m 6 are calculated

state estimation and sliding mode control for semi markovian jump systems with mismatched uncertainties this paper is concerned with the state estimation and sliding mode control problems for phase type semi markovian jump systems using a supplementary variable technique and a plant transformation a finite phase type semi markov process has been transformed into a finite markov chain which is called its associated markov chain as a result phase type semi markovian jump systems can be equivalently expressed as its associated markovian jump systems a sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated markovian jump systems satisfy the reaching condition moreover an observer based sliding mode control problem is investigated sufficient conditions are established for the solvability of the desired observer two numerical examples are presented to show the effectiveness of the proposed design techniques

the probability density of spectral estimates based on modified periodogram averages welch s 1967 method for spectral estimation of averaging modified periodograms has been widely used for decades because such an estimate relies on random data the estimate is also a random variable with some probability density function here the pdf of a power estimate is derived for an estimate based on an arbitrary number of frequency bins overlapping data segments amount of overlap and type of data window given a correlated gaussian input sequence the pdfs of several cases are plotted and found to be distinctly non gaussian the asymptotic result of averaging frequency bins and or data segments using the kullback leibler distance as a measure for limited numbers of frequency bins or data segments the precise pdf is considerably skewed and will be important in applications such as maximum likelihood tests

linear copositive lyapunov functions for continuous time positive switched systems continuous time positive systems switching among p subsystems are introduced and a complete characterization for the existence of a common linear copositive lyapunov function for all the subsystems is provided when the subsystems are obtained by applying different feedback control laws to the same continuous time single input positive system the above characterization leads to a very easy checking procedure

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

shellability in reductive monoids the purpose of this paper is to extend to monoids the work of bjorner wachs and proctor on the shellability of the bruhat chevalley order on weyl groups let m be a reductive monoid with unit group g borel subgroup b and weyl group w we study the partially ordered set of b x b orbits with respect to zariski closure inclusion within a g x g orbit of m this is the same as studying a w x w orbit in the renner monoid r such an orbit is the retract of a universal orbit which is shown to be lexicograhically shellable in the sense of bjorner and wachs

reductive monoids are von neumann regular let k be an algebraically closed field an a e algebraic monoid e is an affme algebraic variety defined over k together with an associative morphism m e x e e and a two sided unit 1 e e for m in categorical terminology an afftne algebraic monoid is a representable functor from the category of afftne varieties to the category of monoids algebraic group theory is concerned mainly with reductive groups and their representations whereas the theory of monoids is concerned largely with von neumann regular monoids the main result of this paper provides a fundamental link between these two objects

welch method revisited nonparametric power spectrum estimation via circular overlap the objective of this paper is twofold the first part provides further insight in the statistical properties of the welch power spectrum estimator a major drawback of the welch method reported in the literature is that the variance is not a monotonic decreasing function of the fraction of overlap selecting the optimal fraction of overlap which minimizes the variance is in general difficult since it depends on the window used we show that the explanation for the nonmonotonic behavior of the variance as reported in the literature does not hold in the second part this extra insight allows one to eliminate the nonmonotonic behavior of the variance for the welch power spectrum estimator pse by introducing a small modification to the welch method the main contributions of this paper are providing extra insight in the statistical properties of the welch pse modifying the welch pse to circular overlap the variance is a monotonically decreasing function of the fraction of overlap making the method more user friendly and an extra reduction of variance with respect to the welch pse without introducing systematic errors this reduction in variance is significant for a small number of data records only

l1 gain performance analysis and positive filter design for positive discrete time markov jump linear systems a linear programming approach abstract this paper is concerned with the l 1 gain performance analysis and positive filter design for a positive discrete time markov jump linear system mjls by using a linear programming lp approach first by constructing a linear stochastic lyapunov function and introducing an equivalent deterministic positive discrete time linear system necessary and sufficient conditions in the form of lp are derived for stochastic stability and l 1 gain performance of the positive discrete time mjls then a sufficient condition on the existence of the desired positive l 1 gain filter is provided the desired positive l 1 gain filter can be designed by solving a standard lp problem the pest s structured population dynamic model is employed to illustrate the effectiveness of the proposed method

analogue of the bruhat chevalley order for reductive monoids the purpose of this paper is to describe the adherence order of w x b b orbits on a reductive algebraic monoid by the results of 10 there is already a perfect analogue of the bruhat decomposition for reductive w x monoids indeed by 10 corollary 5 8 if m is reductive with unit group g and maximal torus t g with borel subgroup b t then the set of two sided b orbits b r mrb is canonically identified with a certain finite inverse monoid r in fact r s n t rt the orbit monoid of the zariski g closure of n t in m by definition for s t g r we define the adherg ence order by s f t if bs b bt b where bt b denotes the zariski closure in m of bt b

orders of the renner monoids abstract in this paper we give a general formula for a renner monoid of a reductive monoid with zero it is based on putcha s type map we apply this formula to find the orders of the renner monoids for j irreducible monoids k g where g is a simple algebraic group over an algebraically closed field k and g gl v is an irreducible representation associated with an arbitrary fundamental dominant weight