parameter dependent lmis in robust analysis characterization of homogeneous polynomially parameter dependent solutions via lmi relaxations this note investigates the robust stability of uncertain linear time invariant systems in polytopic domains by means of parameter dependent linear matrix inequality pd lmi conditions exploiting some algebraic properties provided by the uncertainty representation a systematic procedure to construct a family of finite dimensional lmi relaxations is provided the robust stability is assessed by means of the existence of a lyapunov function more specifically a homogeneous polynomially parameter dependent lyapunov hppdl function of arbitrary degree for a given degree if an hppdl solution exists a sequence of relaxations based on real algebraic properties provides sufficient lmi conditions of increasing precision and constant number of decision variables for the existence of an hppdl function which tend to the necessity alternatively if an hppdl solution of degree exists a sequence of relaxations which increases the number of variables and the number of lmis will provide an hppdl solution of larger degree the method proposed can be applied to determine homogeneous parameter dependent matrix solutions to a wide variety of pd lmis by transforming the infinite dimensional lmi problem described in terms of uncertain parameters belonging to the unit simplex in a sequence of finite dimensional lmi conditions which converges to the necessary conditions for the existence of a homogeneous polynomially parameter dependent solution of arbitrary degree illustrative examples show the efficacy of the proposed conditions when compared with other methods from the literature

discretization and event triggered digital output feedback control of lpv systems abstract this paper investigates the problem of discretization and digital output feedback control design for continuous time linear parameter varying lpv systems subject to a time varying networked induced delay the proposed discretization procedure converts a continuous time lpv system into an equivalent discrete time lpv system based on an extension of the taylor series expansion and using an event based sampling the scheduling parameters are continuously measured and modeled as piecewise constant a new transmission of the measured output to the controller is triggered by significant changes in the parameters yielding time varying transmission intervals the obtained discretized model has matrices with polynomial dependence on the time varying parameters and an additive norm bounded term representing the discretization residual error a two step strategy based on linear matrix inequality conditions is then proposed to synthesize a digital static scheduled output feedback control law that stabilizes both the discretized and the lpv model the conditions can also be used to provide robust i e independent of the scheduling parameter static output feedback controllers the viability of the proposed design method is illustrated through numerical examples

gain scheduled output feedback controllers using inexact scheduling parameters for continuous time lpv systems this paper addresses the design problem of gain scheduled output feedback gsof controllers for continuous time linear parameter varying lpv systems in contrast to the conventional problem setting scheduling parameters are supposed to be provided with bounded absolute proportional uncertainties h type problem is tackled and a sufficient condition for our problem is given in terms of parameter dependent linear matrix inequalities pdlmis with a single line search parameter it is also proved that our method is no more conservative than an existing method in proportional uncertainty case

robustness of nonlinear systems with respect to delay and sampling of the controls we consider continuous time nonlinear time varying systems that are globally asymptotically stabilizable by state feedbacks we study the stability of these systems in closed loop with controls that are corrupted by both delay and sampling we establish robustness results through a lyapunov approach of a new type

dynkin like diagrams and representations of the strange superalgebra p n using an extension p n of the noncontragredient superalgebra p n on which a nondegenerate killing form can be constructed simple root systems srss are introduced to each srs is associated a dynkin like diagram then the maximal regular sub super algebras are obtained moreover a procedure to construct highest weight irreducible representations of p n is presented

q oscillator realizations of the quantum superalgebras slq m n andospq m 2n realizations of the quantum superalgebras corresponding to thea m n b m n c n 1 andd m n series are given in terms of the creation and annihilation operators ofq deformed bose and fermi oscillators

output feedback sampled data control design for linear parameter varying systems with delay in this paper we address the sampled data output feedback control design problem for continuous time linear parameter varying systems with time varying delay in the system states due to the combination of the plant s continuous time dynamics and the controller s discrete time dynamics connected through a d and d a converter devices the closed loop system is a hybrid system in order to analyse this hybrid system from stability and performance perspectives we use the input delay approach to map the closed loop system into the continuous time domain with delay in the states this results in a closed loop system containing two types of delays the system internal delay and the one imposed by the mapping next we use delay dependent conditions for analysis of stability and norm performance which result in a sampled data control synthesis procedure the proposed output feedback sampled data controller is obtained based on the solution to a linear matrix inequality optimisation problem using a set of appro

subspace identification of bilinear and lpv systems for open and closed loop data in this paper we present a novel algorithm to identify lpv systems with affine parameter dependence operating under open and closed loop conditions a factorization is introduced which makes it possible to form a predictor that predicts the output which is based on past inputs outputs and scheduling data the predictor contains the lpv equivalent of the markov parameters using this predictor ideas from closed loop lti identification are developed to estimate the state sequence from which the lpv system matrices can be constructed a numerically efficient implementation is presented using the kernel method it turns out that if structure is present in the scheduling sequence the computational complexity reduces even more

on inexact lpv control design of continuous time polytopic systems robust dynamic output design most often relies on nonconvex problems this is precisely the case with linear parameter varying lpv control when the measured varying parameters do not exactly fit the real ones this paper provides a solution in the convex programming framework with the use of linear matrix inequality lmi solvers in the case of polytopic parameter dependence a bounded uncertainty set is defined from the difference between the measured and the true parameters from which lmi stabilization and performance conditions are obtained after bounding as a desired property the proposed conditions reduce to the classical lpv ones whenever the true parameters are available for control synthesis

oscillator realization of the strange superalgebras p n and q n the strange superalgebra p n is realized in terms of bilinear products of oscillators of bosonic and fermionic type the even part is given by sums of bilinears in bosons and fermions and the odd part by bilinears in one boson and one fermion these oscillators can be used to build explicit realizations of some highest weight irreducible representations of p n this procedure is illustrated for p 3 where in particular the case of the adjoint representation of p 3 is worked out in detail finally an oscillator realization of the strange superalgebra q n is also given

transfer matrix study of the adsorption of a flexible self avoiding polymer chain in two dimensions the authors model the polymer as a self avoiding walk on a semi infinite square lattice with an energy contribution in from each step along the lattice boundary the critical adsorption temperature ta and the ordinary and special surface exponents of the walk above and at the adsorption temperature respectively are estimated with transfer matrix finite size scaling methods for the adsorption temperature they obtain exp in kta 2 041 or 0 002 and for the crossover and susceptibility exponents of the special transition phi sp 0 501 or 0 003 and gamma 1sp 1 454 or 0 004

study of the θ point by enumeration of self avoiding walks on the triangular lattice the author reports series expansion analyses of self avoiding walks with nearest neighbour bond interactions the estimates 2 nu t 1 07 or 0 05 and phi 0 64 or 0 05 for the correlation and crossover exponents at the theta point were obtained by examining the number of walks and the end to end distance data up to 16 steps on the triangular lattice

polynomial lpv approach to robust h control of nonlinear sampled data systems this paper addresses l2 gain analysis and robust h control of nonlinear sampled data systems described by a polynomial linear parameter varying plpv model first conditions for l2 gain analysis of sampled data plpv systems are derived using a modified krasovskii functional in which the distance between the real and measured parameters are considered as uncertainties the resulting conditions are formulated in terms of parameterised linear matrix inequalities plmi second a solution approach for satisfying plmi conditions over the set of whole parameters and uncertainties is proposed using the sum of squares decomposition method third conditions for robust h sampled data controller synthesis for nonlinear systems described by plpv models are derived in terms of parameterised bilinear matrix inequalities pbmi with the maximum allowable sampling period as the parameter to make the resulting bilinear matrix inequality bmi problems tractable an iterative algorithm is developed and utilised to s

convergence and equivalence results for the jensen s inequality application to time delay and sampled data systems the jensen s inequality plays a crucial role in the analysis of time delay and sampled data systems its conservatism is studied through the use of the gruss inequality it has been reported in the literature that fragmentation or partitioning schemes allow to empirically improve the results we prove here that the jensen s gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases finally a family of bounds is characterized and a comparison with other bounds of the literature is provided it is shown that the other bounds are equivalent to jensen s and that they exhibit interesting well posedness and linearity properties which can be exploited to obtain better numerical results

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

statistical properties of dynamical systems with some hyperbolicity this paper is about the ergodic theory of attractors and conservative dynamical systems with hyperbolic properties on large parts though not necessarily all of their phase spaces the main results are for discrete time systems to put this work into context recall that for axiom a attractors the picture has been fairly complete since the 1970 s see s1 b r2 since then much progress has been made on two fronts there is a general nonuniform theory that deals with properties common to all diffeomorphisms with nonzero lyapunov exponents o p1 ka ly and there are detailed analyses of specific kinds of dynamical systems including for example billiards 1 dimensional and henon type maps s2 bsc hk j bc2 by1 statistical properties such as exponential decay of correlations are not enjoyed by all diffeomorphisms with nonzero lyapunov exponents the goal of this paper is a systematic understanding of these and other properties for a class of dynamical systems larger than axiom a this class will not be defined explicitly but it includes some of the much studied examples by looking at regular returns to sets with good hyperbolic properties one could give systems in this class a simple dynamical representation conditions for the existence of natural invariant measures exponential mixing and central limit theorems are given in terms of the return times these conditions can be checked in concrete situations giving a unified way of proving a number of results some new and some old among the new results are the exponential decay of correlations for a class of scattering billiards and for a positive measure set of henon type maps

surface critical exponents for models of polymer collapse and adsorption the universality of the theta and theta points the surface critical exponents are estimated both in ordinary and in special regimes from exact series expansions of up to 28 terms for a model of the theta point they are found to be in agreement with those derived for the theta point confirming the conjecture that the theta and theta points lie in the same universality class some essential features of the phase diagram for a self interacting self avoiding polymer in solution are also calculated to a higher degree of accuracy than previously obtained

a realization of generalized deformed oscillators with cyclic symmetry the algebra of generalized deformed oscillators that possess cyclic symmetry is studied the general set of multilinear operator relations is presented which characterizes the multilinear part of the algebra of cyclic extended deformed oscillators the realization scheme of generalized deformed oscillators with cyclic symmetry in terms of those without cyclic symmetry is established it is shown that all generalized deformed oscillators with cyclic symmetry constructed by the scheme are actually equivalent in the viewpoint of mathematics though each generalized deformed oscillator admits its own particular cyclic extended counterpart examples are given to illustrate this peculiar realization scheme

the effect of attractive monomer monomer interactions on adsorption of a polymer chain the authors have used transfer matrix techniques to study a model of polymer adsorption and collapse they consider the conventional model of a self avoiding walk with attractive nearest neighbour interactions on the square lattice and introduce adsorbing boundaries the numerical results are consistent with the existence of a multicritical point where the adsorption and collapse transitions coincide and suggest that the adsorption transition of a collapsed polymer chain in first order there is also clear evidence that the collapse transition lowers the adsorption temperature estimates of the surface scaling dimensions at the ordinary theta transition support the conjecture of seno and stella 1988 that the surface critical behaviour at the theta and theta points belong to different universality classes

a ruelle operator for a real julia set letr be an expanding rational function with a real bounded julia set and let left lg right left x right sum limits ry x frac g left y right left r left y right right 2 be a ruelle operator acting in a space of functions analytic in a neighbourhood of the julia set we obtain explicit expressions for the resolvent function e left x z lambda right left i lambda l right 1 frac 1 z x and in particular for the fredholm determinantd det i l it gives us an equation for calculating the escape rate we relate our results to orthogonal polynomials with respect to the balanced measure ofr two examples are considered

q fermionic operators and quantum exceptional algebras using a q deformation of the usual clifford algebra one constructs a realization of the quantum exceptional algebras e6 e7 e8 and f4 in terms of q fermionic operators

dynamical determinants via dynamical conjugacies for postcritically finite polynomials we give an analogue of levin sodin yuditskii s study of the dynamical ruelle determinants of hyperbolic rational maps in the case of subhyperbolic quadratic polynomials our main tool is to reduce to an expanding situation we do so by applying a dynamical change of coordinates on the domains of a markov partition constructed from the landing ray at the postcritical repelling orbit we express the dynamical determinants d beta z exp sum k geqslant 1 tfrac z k k sum w in text fix f k tfrac 1 f c k w beta tfrac 1 1 tfrac 1 f c k w beta in mathbb z as the product of an entire determinant with an explicit expression involving the postcritical repelling orbit thus explaining the poles in d z

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

q analogues of clifford and weyl algebras spinor and oscillator representations of quantum enveloping algebras we introduceq analogues of clifford and weyl algebras using these we construct spinor and oscillator representations of quantum enveloping algebras of typean 1 bn cn dn andan 1 1 also we discuss the irreducibility and the unitarity of these representations

on the susceptibility function of piecewise expanding interval maps we study the susceptibility function psi z sum n 0 infty int z n x y rho 0 y frac partial partial y varphi f n y dy associated to the perturbation f t f tx circ f of a piecewise expanding interval map f and to an observable 1 is the formal derivative at t 0 of the average mathcal r t int varphi rho t dx of with respect to the srb measure of ft our analysis is based on a spectral description of transfer operators it gives in particular sufficient conditions on f x and which guarantee that z is holomorphic in a disc of larger than one or which ensure that a number may be associated to the possibly divergent series 1 we present examples of f x and so that mathcal r t is not lipschitz at 0 and we propose a new version of ruelle s conjecture

exceptional lie algebras in terms of fermionic creation annihilation operators from the embedding e8 d4 d4 defining fermionic operators which transform respectively as the vectorial and spinorial representations of d4 the algebra of e8 is constructed in terms of a bilinear in the fermionic operators then by embeddings the adjoint and fundamental representations of the other exceptional algebras are explicitly written

output feedback control of lpv sampled data systems in this paper we address the analysis and the output feedback synthesis problems for linear parameter varying lpv sampled data control systems with potentially variable sampling rates we assume that the state space matrices of the plant and the sampling interval depend on parameters that are measurable in real time and vary in a compact set with bounded variation rates we explore criteria such as the stability the energy to energy gain induced l 2 norm and the energy to peak gain induced l 2 to l x norm of such sampled data lpv systems using parameter dependent lyapunov functions based on these analysis results the corresponding sampled data output feedback control synthesis problems are examined both analysis and synthesis conditions are formulated in terms of linear matrix inequalities lmis that can be solved via efficient interior point algorithms

realization of exceptional superalgebras in terms of fermion boson creation annihilation operators operators satisfying clifford algebra fermions and weyl algebra bosons are introduced f 4 and g 3 are realized in terms of bilinears of fermions the even part and bilinears of one boson and one fermion the odd part d 2 1 is realized as bilinears the even part and trilinears the odd part of bosons

deformation of lie algebras in a non chevalley basis and embedding of q algebras a deformation scheme for lie algebras in a basis which manifestly exhibits for q 1 the content of a singular subalgebra is presented this scheme allows to build up embedding chains of q algebras which can be physically interesting the case when the rank of the subalgebra is one unit less than the rank of the algebra is studied and explicit constructions of the algebras are given in terms of q bosonic and or q fermionic oscillators

automated generation and comparison of takagi sugeno and polytopic quasi lpv models in the last decades gain scheduling control techniques have consolidated as an efficient answer to analysis and synthesis problems for non linear systems among the approaches proposed in the literature the linear parameter varying lpv and takagi sugeno ts paradigms have proved to be successful in dealing with the different trials that the analyzer or the designer of a gain scheduled control system has to face despite the strong similarities between the two paradigms research on lpv and ts systems has been performed in an independent way and some results that could be useful for both paradigms were obtained only for one of them however in recent works some clues that there is a very close connection between lpv and ts worlds have been presented the present paper openly addresses the presence of strong analogies between lpv and ts models in an attempt to establish a bridge between these two worlds so far considered different in particular this paper addresses the modeling problem presenting two methods for the automated generation of lpv and ts systems and introducing some measures in order to compare the obtained models a mathematical example is used to illustrate the proposed methods

advanced sampled data synchronization control for complex dynamical networks with coupling time varying delays abstract this study addresses sampled data control in the synchronization problem of complex dynamical networks systems with a coupling time varying delay by constructing the augmented lyapunov krasovskii functionals and using some mathematical techniques a sampled data synchronization criterion is derived as the first result with the framework of linear matrix inequalities based on the first result a sampled data synchronization control method is proposed as the second result finally the effectiveness and superiority of the proposed results will be shown by comparing the maximum sampling period with the established results in two numerical examples

the construction of the q analogues of the harmonic oscillator operators from ordinary oscillator operators the q analogues of boson operators are constructed from ordinary boson operators by an embedding approach accordingly the q deformed quantum algebras su n q can be obtained straightforwardly from corresponding universal enveloping algebras of lie algebra su n

equivalence of deformed fermionic algebras generalized deformations of the fermionic algebra are studied the polynomial representations of these algebras are constructed all the deformation schemes can be realized by the same polynomial basis using the bargmann representation thus proving that all deformed fermionic algebras are isomorphically equivalent to the non deformed fermionic algebra

differentiating the absolutely continuous invariant measure of an interval map f with respect to f let the map f 1 1 1 1 have a c i m absolutely continuous f invariant measure with respect to lebesgue let be the change of corresponding to a perturbation x f f 1 of f formally we have for differentiable a

sampled data piecewise affine differential inclusions this paper addresses exponential stability and stabilization of sampled data piecewise affine differential inclusions pwadi with an unknown nonuniform sampling rate the contributions of this paper are threefold first given a controller sufficient conditions for exponential stability of closed loop sampled data pwadi are presented using a piecewise smooth krasovskii functional second assuming the controller is piecewise linear and the krasovskii functional is piecewise quadratic the stability conditions are cast as linear matrix inequalities lmis third sufficient conditions for sampled data controller synthesis for pwadi are formulated in terms of lmis with the maximum allowable sampling period as a parameter the effectiveness of the approach is shown via a pwadi example that is motivated by a nonlinear system

the thermodynamic formalism for expanding maps letf x x be an expanding map of a compact space small distances are increased by a factor 1 a generating function z is defined which countsf periodic points with a weight one can express in terms of nonstandard fredholm determinants of certain transfer operators which can be studied by methods borrowed from statistical mechanics in this paper we review the spectral properties of the transfer operators and the corresponding analytic properties of z gibbs distributions and applications to julia sets are also discussed some new results are proved and some natural conjectures are proposed

q oscillators realization of fq 4 and gq 3 a realization of the quantum superalgebras corresponding to f 4 and g 3 is given in terms of q deformed bosonic and fermionic oscillators

lmi techniques for optimization over polynomials in control a survey numerous tasks in control systems involve optimization problems over polynomials and unfortunately these problems are in general nonconvex in order to cope with this difficulty linear matrix inequality lmi techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems this survey aims to provide the reader with a significant overview of the lmi techniques that are used in control systems for tackling optimization problems over polynomials describing approaches such as decomposition in sum of squares positivstellensatz theory of moments polya s theorem and matrix dilation moreover it aims to provide a collection of the essential problems in control systems where these lmi techniques are used such as stability and performance investigations in nonlinear systems uncertain systems time delay systems and genetic regulatory networks it is expected that this survey may be a concise useful reference for all readers

intermittency and regularized fredholm determinants we consider real analytic maps of the interval i 0 1 which are expanding everywhere except for a neutral fixed point at 0 we show that on a certain function space the associated perron frobenius operator has a continuous and residual spectrum contained in the line segment c 0 1 and a point spectrum p which has no points of accumulation outside 0 and 1 furthermore points in p 0 1 are eigenvalues of finite multiplicity we construct a regularized fredholm determinant d which has a holomorphic extension to c and can be analytically continued from each side of c to an open neighborhood of c 0 1 on different riemann sheets in c the zero set of d is in one to one correspondence with the point spectrum of through the conformal transformation the function d z extends to a holomorphic function in a domain which contains the unit disc

deformation of the strange superalgebra p n a deformation uq p n pq n of the extended noncontragredient strange superalgebra of p n denoted by p n is proposed a realization of pq n in terms of q bosons and q fermions is presented then a procedure to build up a set of representations of pq n is briefly discussed as a by product a new realization of suq n is obtained

comparison of lpv and nonlinear system theory a realization problem abstract the paper explores the utilization of the nonlinear realization theory to address the problem of transforming linear parameter varying input output lpv io equations into a state space form with static dependence on the so called scheduling parameter the necessary and sufficient solvability conditions are given and three additional subclasses of lpv io equations are suggested that are guaranteed to have a realization of the considered type

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

brief paper a novel stability analysis of linear systems under asynchronous samplings this article proposes a novel approach to assess the stability of continuous linear systems with sampled data inputs the method which is based on the discrete time lyapunov theorem provides easy tractable stability conditions for the continuous time model sufficient conditions for asymptotic and exponential stability are provided dealing with synchronous and asynchronous samplings and uncertain systems an additional stability analysis is provided for the cases of multiple sampling periods and packet losses several examples show the efficiency of the method

sos based solution approach to polynomial lpv system analysis and synthesis problems based on sum of squares sos decomposition we propose a new solution approach for polynomial linear parameter varying lpv system analysis and control synthesis problems instead of solving matrix variables over positive cone the sos approach tries to find a suitable decomposition to verify the positiveness of given polynomials the complexity of the sos based numerical method is polynomial of the problem size and is computationally attractive this approach also leads to more accurate solutions to lpv systems than most existing relaxation methods several examples have been used to demonstrate benefits of the sos based solution approach

gain scheduled controller design an analytic framework directly incorporating non equilibrium plant dynamics a velocity based linearization framework is employed to develop a novel rigorous approach to gain scheduling design the proposed approach enables knowledge concerning the plant dynamics at non equilibrium operating points to be incorporated directly into the controller design since the velocity based linearization framework supports the analysis of the transient response performance considerations can be accommodated the approach retains continuity with linear methods which is central to the existing conventional gain scheduling methodology and since a single type of linearization is employed throughout the design procedure is both straightforward and conceptually appealing