convex analysis of invariant sets for a class of nonlinear systems we study the invariance of the convex hull of an invariant set for a class of nonlinear systems satisfying a generalized sector condition the generalized sector is bounded by two odd symmetric functions which are convex concave in the right half plane in a recent paper we showed that for this class of systems the convex hull of a group of invariant ellipsoids is invariant this paper shows that the convex hull of a general invariant set need not be invariant and that the convex hull of a contractively invariant set is however invariant

α continuity properties of one dimensional quasicrystals we apply the jitomirskaya last extension of the gilbert pearson theory to discrete one dimensional schrodinger operators with potentials arising from generalized fibonacci sequences we prove for certain rotation numbers that for every value of the coupling constant there exists an 0 such that the corresponding operator has purely continuous spectrum this result follows from uniform upper and lower bounds for the l norm of the solutions corresponding to energies from the spectrum of the operator

singular continuous spectrum for palindromic schrodinger operators we give new examples of discrete schrodinger operators with potentials taking finitely many values that have purely singular continuous spectrum if the hullx of the potential is strictly ergodic then the existence of just one potentialx inx for which the operator has no eigenvalues implies that there is a generic set inx for which the operator has purely singular continuous spectrum a sufficient condition for the existence of such anx is that there is az x that contains arbitrarily long palindromes thus we can define a large class of primitive substitutions for which the operators are purely singularly continuous for a generic subset inx the class includes well known substitutions like fibonacci thue morse period doubling binary non pisot and ternary non pisot we also show that the operator has no absolutely continuous spectrum for allx x ifx derives from a primitive substitution for potentials defined by circle maps x n 1 j 0 n we show that the operator has purely singular continuous spectrum for a generic subset inx for all irrational and every half open intervalj

improved delay dependent stability criteria for uncertain lur e systems with sector and slope restricted nonlinearities and time varying delays abstract this paper deals with the absolute stability analysis for uncertain time delay lur e systems that have time varying delays and sector and slope restricted nonlinearities new delay dependent stability criteria are derived via linear matrix inequality lmi formulation that can be easily solved by various optimization techniques sector bounds and slope bounds are employed to the lyapunov krasovskii functional through convex representation of the nonlinearities so that less conservative stability conditions are obtained numerical examples show effectiveness of the proposed stability condition

eigenfunctions transfer matrices and absolutely continuous spectrum of one dimensional schrodinger operators on l r and its half line problem h on l2 0 with u 0 0 boundary conditions we will focus on a new approach to the absolutely continuous spectrum ac h and more generally ac h the essential support of the a c part of the spectral measures what is new in our approach is that it relies on estimates on the transfer matrix that is the 2 2 matrix te n m which takes u m 1 u m to u n 1 u n for solutions u of hu eu in the continuum case use u x u x instead of u x 1 u x we let te n te n 0 for example we will prove the following

a less conservative stability test for second order linear time varying vector differential equations system stability and stability bounds play an essential role in control theory this note is concerned with the exponential stability of a class of second order linear time varying vector differential equations with real piecewise continuous coefficient matrices a less conservative explicit condition for stability of such a system is derived using the matrix measure theory and a more accurate upper bound for the decay exponent of its stable solution is established examples are included for illustration

recurrence of the eigenstates of a schrodinger operator with automatic potential we consider the schrodinger eigenvalue problem in the discrete case with a potential assuming two values distributed according to the automatic sequence of prouhet thue morse we show that there are no localized states and that the generalized eigenvectors are recurrent on a geometrical set stemming from the hierarchical nature of the potential

the spectrum of a quasiperiodic schrodinger operator the spectrum h of the tight binding fibonacci hamiltonian hmn m n 1 m 1 n m n v n v n chi omega 3 omega 2 n 1 1 is the golden number is shown to coincide with the dynamical spectrum the set on which an infinite subsequence of traces of transfer matrices is bounded the point spectrum is absent for any and h is a cantor set for 4 combining this with casdagli s earlier result one finds that the spectrum is singular continuous for 16

some remarks on discrete aperiodic schrodinger operators we consider schrodinger operators onl2 with deterministic aperiodic potential and schrodinger operators on the l2 space of the set of vertices of penrose tilings and other aperiodic self similar tilings the operators onl2 fit into the formalism of ergodic random schrodinger operators hence their lyapunov exponent integrated density of states and spectrum are almost surely constant we show that they are actually constant the lyapunov exponent for one dimensional schrodinger operators with potential defined by a primitive substitution the integrated density of states and the spectrum in arbitrary dimension if the system is strictly ergodic we give examples of strictly ergodic schrodinger operators that include several kinds of almost periodic operators that have been studied in the literature for schrodinger operators on penrose tilings we prove that the integrated density of states exists and is independent of boundary conditions and the particular penrose tiling under consideration

switching stabilizability for continuous time uncertain switched linear systems this paper investigates the switching stabilizability problem for a class of continuous time switched linear systems with time variant parametric uncertainties first a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived under the assumption that the closed loop switched system does not generate sliding motions then an additional condition is introduced to exclude the possibility of unstable sliding motions finally a necessary and sufficient for the asymptotic stabilizability of such continuous time uncertain switched linear systems is presented this result improves upon conditions found in the literature which are either sufficient only or necessary only

singularly continuous spectrum of a self similar laplacian on the half line we investigate the spectrum of the self similar laplacian which generates the so called pq random walk on the integer half line using the method of spectral decimation we prove that the spectral type of the laplacian is singularly continuous whenever p 12 this serves as a toy model for generating singularly continuous spectrum which can be generalized to more complicated settings we hope it will provide more insight into fibonacci type and other weakly self similar models

reduced conservatism in stability robustness bounds by state transformation this note addresses the issue of conservatism in the time domain stability robustness bounds obtained by the lyapunov approach a state transformation is employed to improve the upper bounds on the linear time varying perturbation of an asymptotically stable linear time invariant system for robust stability this improvement is due to the variance of the conservatism of the lyapunov approach with respect to the basis of the vector space in which the lyapunov function is constructed improved bounds are obtained using a transformation on elemental and vector norms of perturbations i e structured perturbations as well as on a matrix norm of perturbations i e unstructured perturbations for the case of a diagonal transformation an algorithm is proposed to find the optimal transformation several examples are presented to illustrate the proposed analysis

brief paper simultaneous schur stability of interval matrices interval matrix structures are ubiquitous in nature and engineering ordinarily in an uncertain system there is associated with a set of coupled interval matrices a basic issue of exploring its asymptotic stability here we introduce the notion of simultaneous schur stability by linking the concepts of the majorant and the joint spectral radius and prove the asymptotic stability of a set of interval matrices governed by simultaneous schur stability the present result may lead to the stability analysis of discrete dynamical interval systems

robustness of uncertain systems in the absence of matching assumptions abstract we consider a class of uncertain dynamical systems containing uncertain elements these may be due to model parameter uncertainty input disturbance and measurement noise we require no a priori information on the uncertain elements except that their restraint sets are assumed to be known and compact this paper describes a general approach for designing controls to assure practical stability in the absence of matching assumptions which most previous results have needed the result is applicable to non linear systems a specialization to linear systems is then given and a comparison is made with previous work

criteria for robust absolute stability of time varying nonlinear continuous time systems the present paper establishes results for the robust absolute stability of a class of nonlinear continuous time systems with time varying matrix uncertainties of polyhedral type and multiple time varying sector nonlinearities by using the variational method and the lyapunov second method criteria for robust absolute stability are obtained in different forms for the given class of systems specifically the parametric classes of lyapunov functions are determined which define the necessary and sufficient conditions of robust absolute stability the piecewise linear lyapunov functions of the infinity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations several simple sufficient conditions of robust absolute stability are given which become necessary and sufficient for special cases two examples are presented as applications of the present results to a particular second order system and to a specific class of systems with time varying interval matrices in the linear part

dynamical upper bounds on wavepacket spreading we derive a general upper bound on the spreading rate of wavepackets in the framework of schrodinger time evolution our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically in time where the rate of this growth is determined by properties of the spectral measure and by spatial properties of solutions of an associated time independent schrodinger equation we also derive a new lower bound on the spreading rate which is strongly connected with our upper bound we apply these new bounds to the fibonacci hamiltonian the most studied one dimensional model of quasicrystals as a result we obtain for this model upper and lower dynamical bounds establishing wavepacket spreading rates which are intermediate between ballistic transport and localization the bounds have the same qualitative behavior in the limit of large coupling

quantum dynamics via complex analysis methods general upper bounds without time averaging and tight lower bounds for the strongly coupled fibonacci hamiltonian abstract we develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers here we derive upper bounds for non time averaged outside probabilities and moments of the position operator from lower bounds for transfer matrices at complex energies moreover for the time averaged transport exponents we present improved lower bounds in the special case of the fibonacci hamiltonian these bounds lead to an optimal description of the time averaged spreading rate of the fast part of the wavepacket in the large coupling limit this provides the first example which demonstrates that the time averaged spreading rates may exceed the upper box counting dimension of the spectrum

absolute stability with a generalized sector condition this paper generalizes the linear sector in the classical absolute stability theory to a sector bounded by concave convex functions this generalization allows more flexible or more specific description of the nonlinearity and will thus reduce the conservatism in the estimation of the domain of attraction we introduce the notions of generalized sector and absolute contractive invariance for estimating the domain of attraction of the origin necessary and sufficient conditions are identified under which an ellipsoid is absolutely contractively invariant in the case that the sector is bounded by piecewise linear concave convex functions these conditions can be exactly stated as linear matrix inequalities moreover if we have a set of absolutely contractively invariant aci ellipsoids then their convex hull is also aci and inside the domain of attraction we also present optimization technique to maximize the absolutely contractively invariant ellipsoids for the purpose of estimating the domain of attraction the effectiveness of the proposed method is illustrated with examples

uniform cantor singular continuous spectrum for nonprimitive schrodinger operators it is shown that some schrodinger operators with nonprimitive substitution potentials have pure singular continuous cantor spectrum with null lebesgue measure for all elements in the respective hulls

singular continuous spectrum on a cantor set of zero lebesgue measure for the fibonacci hamiltonian it is rigorously proven that the spectrum of the tight binding fibonacci hamiltonian h mn m n 1 m n 1 m n n 1 n where 5 1 2 and means integer part is a cantor set of zero lebesgue measure for all real nonzero and the spectral measures are purely singular continuous this follows from a recent result by kotani coupled with the vanishing of the lyapunov exponent in the spectrum

robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects this paper focuses on the hybrid effects of parameter uncertainty stochastic perturbation and impulses on global stability of delayed neural networks by using the ito formula lyapunov function and halanay inequality we established several mean square stability criteria from which we can estimate the feasible bounds of impulses provided that parameter uncertainty and stochastic perturbations are well constrained moreover the present method can also be applied to general differential systems with stochastic perturbation and impulses

on stability of interval matrices new sufficient and sometimes necessary and sufficient conditions are obtained for schur and hurwitz stability of interval matrices by relying on the concept of connective stability and m matrices the necessity part is broadened to include interval matrices with mixed signs of the off diagonal elements provided the sign patterns follow that of the morishima matrix the obtained results are extended to cover convex combinations of interval matrices

the fractal dimensions of the spectrum of sturm hamiltonian abstract let 0 1 be irrational and 0 a 1 a 2 be the continued fraction expansion of let h v be the sturm hamiltonian with frequency and coupling v v be the spectrum of h v the fractal dimensions of the spectrum have been determined by fan liu and wen 2011 8 when a n n 1 is bounded the present paper will treat the most difficult case i e a n n 1 is unbounded we prove that for v 24 dim h v s v and dim b v s v where s v and s v are lower and upper pre dimensions respectively by this result we determine the fractal dimensions of the spectrums for all sturm hamiltonians we also show the following results s v and s v are lipschitz continuous on any bounded interval of 24 the limits s v ln v and s v ln v exist as v tends to infinity and the limits are constants only depending on s v 1 if and only if lim sup n a 1 a n 1 n which can be compared with the fact s v 1 if and only if lim inf n a 1 a n 1 n liu and wen 2004 13

simple criteria for stability of interval matrices in this paper the simple sufficient conditions are presented for the stability of a constant real matrix whose elements are not known precisely but we know the upper and lower bounds of intervals in which the elements of matrix a are confined these conditions are also applied in determining the stability and the degree of stability of a matrix

lyapunov function construction by linear programming in this paper the lyapunov function given by the infinity norm is considered a new proof of the theorem of molchanov and pyatintskii 1986 is given the presented proof enables us to give an explicit calculation of the matrix which was only demonstrated to exist in the original paper combining the obtained result with the idea of scaling faces of a polytope gives the method of fitting the shape of level surfaces of the lyapunov function given by the infinity norm to the specified demands

upper bounds in quantum dynamics of course the case of main interest is where h is given by l2 rd or 2 zd h is a schr dinger operator of the form a v and ip 0 is a localized wavepacket under the time evolution 1 the wavepacket i t will in general spread out with time finding quantitative bounds for this spreading in concrete cases and developing methods for proving such bounds has been the objective of a great number of papers in recent years one is often interested in the growth behavior of the moments of the position operator that is the function 11 x p 2 i 2 these questions are particularly complicated and interesting in situations where singular continuous spectra occur the discovery of the occurrence of such spectra for many models of physical relevance has triggered some activity on the quantum dynamical side for models with absolutely continuous spectra on the other hand quantum dynamical questions have been investigated much earlier in the context of scattering theory and have been answered to a great degree of satisfaction models with point spectrum or more restrictively models exhibiting anderson localization have also been investigated from a quantum dynamical point of view while it is not true in general that spectral localization implies dynamical localization 26 73 it has been shown that the three main approaches to spectral localization the fractional moment method 3 4 5 multi scale analysis 28 27 75 and the bourgain goldstein schlag method 12 37 yield dynamical localization as a by product 2 13 22 31 34 quantum dynamics for schr dinger operators with singular continuous spectra is much less understood the two primary examples motivated by physics are the harper model also known as the almost mathieu operator at critical cou pling which describes a bloch electron in a constant magnetic field with irrational flux through a unit cell and the fibonacci model which describes a standard one dimensional quasicrystal both models have been studied heavily in both the physics and mathematics communities

robustness of stability of time varying linear systems abstract this paper introduces the concept of stability radius for time varying linear systems invariance properties of the stability radius are analysed for the group of bohl transformations we also explore the relationship between the stability radius the norm of a certain perturbation operator and the solvability of a nonstandard differential riccati equation as an application we construct robust lyapunov functions and show how they can be used to analyze robustness with respect to nonlinear perturbations

continuity properties of the electronic spectrum of 1 d quasicrystals in this paper we consider operatorsh x defined onl 2 by h alpha x psi n sum limits m in mathbb z t m circ phi n alpha x psi n m where x x t m is in the algebra of bounded periodic functions on 2 generated by the characteristic functions of the sets phi n left alpha x in mathbb r 2 left left 1 alpha leqq x alpha bmod 1 right right right this class of hamiltonian includes the kohmoto model numerically computed by ostlund and kim where the potential is given by upsilon alpha x n lambda chi 1 alpha 1 x n alpha n in mathbb z x lambda alpha in mathbb r see b i s t we prove that the spectrum as a set ofh x varies continuously with respect to near each irrational for anyx we also show that the various strong limits obtained as converges to a rational numberp q describe either a periodic medium or a periodic medium with a localized impurity the corresponding spectrum has eigenvalues in the gaps and the right and left limits as p q do not coincide for the kohmoto model the results are obtained throughc algebra techniques

diagonal stability of interval matrices and applications abstract let a i a r n n a a a be an interval matrix and 1 p we introduce the concept of schur and hurwitz diagonal stability relative to the holder p norm of a i abbreviated as sds p and hds p respectively this concept is formulated in terms of a matrix inequality using the p norm which must be satisfied by the same positive definite diagonal matrix for all a a i the inequality form is different for sds p and hds p the particular case of p 2 is equivalent to the condition of quadratic stability of a i the sds 2 inequality is equivalent to the stein inequality a a i a t pa p 0 and the hds 2 inequality is equivalent to the lyapunov inequality a a i a t p pa 0 in both cases p is a positive definite diagonal matrix and the notation 0 means negative definite the first part of the paper provides sds p and hds p criteria presents methods for finding the positive definite diagonal matrix requested by the definition of sds p and hds p analyzes the robustness of sds p and hds p and explores the connection with the schur and hurwitz stability of a i the second part shows that the sds p or hds p of a i is equivalent to the following properties of a discrete or continuous time dynamical interval system whose motion is described by a i the existence of a strong lyapunov function defined by the p norm and the existence of exponentially decreasing sets defined by the p norm that are invariant with respect to system s trajectories

uniform spectral properties of one dimensional quasicrystals i absence of eigenvalues we consider discrete one dimensional schrodinger operators with sturmian potentials for a full measure set of rotation numbers including the fibonacci case we prove absence of eigenvalues for all elements in the hull

power law growth for the resistance in the fibonacci model many one dimensional quasiperiodic systems based on the fibonacci rule such as the tight binding hamiltonianh n n 1 n 1 v n n ne el2 e wherev n n 1 n x denoting the integer part ofx and the golden mean sqrt 5 1 2 give rise to the same recursion relation for the transfer matrices it is proved that the wave functions and the norm of transfer matrices are polynomially bounded critical regime if and only if the energy is in the spectrum of the hamiltonian this solves a conjecture of kohmoto and sutherland on the power law growth of the resistance in a one dimensional quasicrystal

transport exponents of sturmian hamiltonians 2015 elsevier inc we consider discrete schrodinger operators with sturmian potentials and study the transport exponents associated with them under suitable assumptions on the frequency we establish upper and lower bounds for the upper transport exponents as an application of these bounds we identify the large coupling asymptotics of the upper transport exponents for frequencies of constant type we also bound the large coupling asymptotics uniformly from above for lebesgue typical frequency a particular consequence of these results is that for most frequencies of constant type transport is faster than for lebesgue almost every frequency we also show quasi ballistic transport for all coupling constants generic frequencies and suitable phases

a numerical technique for the stability analysis of linear switched systems in this paper the ray gridding approach a new numerical technique for the stability analysis of linear switched systems is presented it is based on uniform partitions of the state space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance in this framework the existence of a polyhedral lyapunov function that is common to a family of asymptotically stable subsystems can be checked efficiently via simple iterative algorithms the technique can be used to prove the stability of switched linear systems classes of linear time varying systems and linear differential lnclusions we also present preliminary results on another related problem namely the construction of multiple polyhedral lyapunov functions for the specification of stabilizing switching sequences for a switched system constructed from a family of stable linear subsystems

criteria of robust stability for time varying 2d wang mitchel differential systems integral funnel method abstracttwo dimensional nonlinear systems with parametrical interval uncertainty are studied differential geometric extremal deviations method is developed its basic elements are integral funnels ifs and their boundaries extreme matrix valued functions determining the branches of the boundaries of ifs are synthesised typical phase portraits of considered uncertain systems with different oscillatory properties are presented analytical criteria of robust stability for different oscillatory classes of uncertain systems are formulated

stability robustness in linear state space models with structured time varying uncertainties in this paper we analyse the stability robustness of linear continuous time and discrete time systems with structured time varying uncertainties the system to be controlled is described by the usual state space formulation but includes time varying uncertainties the first new robust stability sufficient condition we have derived in this paper may become the necessary and sufficient condition of system stability in some situations the second new condition is always less conservative than the sufficient condition recently proposed by sobel et al 1989 the third new condition using the similarity transformation provides the possibility of getting even less conservative results in deriving these new conditions we also present some new lemmas which are valuable in related research the results are extended to linear discrete time systems and some illustrative examples are given

power law bounds on transfer matrices and quantum dynamics in one dimension we present an approach to quantum dynamical lower bounds for discrete one dimensional schrodinger operators which is based on power law bounds on transfer matrices it suffices to have such bounds for a nonempty set of energies we apply this result to various models including the fibonacci hamiltonian

uniform spectral properties of one dimensional quasicrystals iii α continuity we study the spectral properties of one dimensional whole line schrodinger operators especially those with sturmian potentials building upon the jitomirskaya last extension of the gilbert pearson theory of subordinacy we demonstrate how to establish continuity of a whole line operator from power law bounds on the solutions on a half line however we require that these bounds hold uniformly in the boundary condition

comments on assessing the stability of linear time invariant continuous interval dynamic systems the first part of this note identifies and analyzes two weak points of the commented paper i example 1 reports an incorrect result for which we provide a complete explanation and correction ii the practical use of theorem 1 reveals major drawbacks such as a severe limitation in the applicability due to the restrictive conditions requested by the hypothesis and a relatively low accuracy of the results i e rough values for the right outer bounds of the eigenvalue ranges of interval matrices the second part of the note presents three methods that circumvent the use of theorem 1 and provide the following information about the eigenvalue range of an interval matrix a right outer bound relying on an inequality proved by j rohn see references the right end point by solving a constrained global maximization problem a right outer bound for arbitrary interval matrices and the right end point for some classes of interval matrices by calculating the spectral abscissa of a constant matrix that majorizes the considered interval matrix for illustration by numerical examples throughout the note we use three interval matrices related to example 1 from the commented paper

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

spectral properties of one dimensional quasi crystals in this paper we prove that the one dimensional schrodinger operator onl 2 with potential given by upsilon n lambda chi 1 alpha 1 x n alpha alpha notin mathbb q has a cantor spectrum of zero lebesgue measure for any irrational and any 0 we can thus extend the kotani result on the absence of absolutely continuous spectrum for this model to all mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepge9fr xfr x frpewzqaaeaabigaciaacaqabeaadaqaaqaaaoqaaiaadihaiiaacq wfiiiztuudjxwak1uy0hmmaehbfv3yslgzg0uy0hgiud3bagqbbiab nj8ubaa 4628 x in mathbb t

robust absolute stability of lur e control systems in parameter space abstract this paper deals with the problem of robust absolute stability analysis for nonlinear lur e control systems in the presence of system parameter variations the well known popov criterion for absolute stability is used in order to characterize the boundary of the region of absolute stability in the parameter plane when the coefficients of the transfer function of the linear plant are polynomial functions of the uncertain parameters for a scalar parameter a method is given to determine the maximal interval of variation around a fixed nominal value preserving absolute stability this result is also used to derive a technique for checking absolute stability of lur e systems with parameters in given planar uncertainty sets numerical examples showing the application of the method are reported

almost periodic schrodinger operators along interval exchange transformations it is shown that schrodinger operators with potentials along the shift embedding of irreducible interval exchange transformations in a dense set have pure singular continuous spectrum for lebesgue almost all points of the interval such potentials are natural generalizations of the sturmian case

absence of localization in a class of schrodinger operators with quasiperiodic potential we prove that a class of discrete schrodinger operators with a quasiperiodic potential taking only a finite number of values exhibits purely continuous spectrum in particular they cannot have localized eigenvectors

criteria of asymptotic stability of differential and difference inclusions encountered in control theory abstract for a class of differential inclusions to which many of the practically important control systems can be reduced necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of lyapunov functions similar results are obtained for the corresponding class of difference inclusions

a new class of universal lyapunov functions for the control of uncertain linear systems the authors analyze the problem of synthesizing a state feedback control for the class of uncertain continuous time linear systems affected by time varying memoryless parametric uncertainties they consider as candidate lyapunov functions the elements of the class spl sigma sub p sup z which is formed by special homogeneous positive definite functions they show that this class is universal in the sense that a lyapunov function exists if and only if there exists a lyapunov function in spl sigma sub p sup z they prove this result in a constructive way showing that such a lyapunov function can always be obtained by smoothing a polyhedral function for which construction algorithms are available the authors show that unlike the polyhedral lyapunov functions these functions allow us to derive explicit formulas for the stabilizing controller

on robustness of lurie systems with multiple non linearities abstract the robustness of absolute stability of lurie systems with multiple non linearities with respect to model variations is considered two approaches for robustness analysis are developed one is based on the popov frequency domain criterion and the other on the algebraic criterion for the absolute stability it is shown that there exist finite perturbations in the system model which admit certain norm bounds so that the stability of the system is not affected computationally the method is very feasible it involves a very simple numerical algorithm two illustrative examples are worked out the theory is applied to characterize the robustness properties of a steam boiler example of a yugoslav thermal power plant

robust stability of linear time varying delta operator formulated discrete time systems some earlier results on robust stability of continuous time and discrete time control systems are extended to a class of linear time varying delta operator formulated discrete time systems

spectral properties of one dimensional schrodinger operators with potentials generated by substitutions we investigate one dimensional discrete schrodinger operators whose potentials are invariant under a substitution rule the spectral properties of these operators can be obtained from the analysis of a dynamical system called the trace map we give a careful derivation of these maps in the general case and exhibit some specific properties under an additional easily verifiable ypothesis concerning the structure of the trace map we present an analysis of their dynamical properties that allows us to prove that the spectrum of the underlying schrodinger operator is singular and supported on a set of zero lebesgue measure a condition allowing to exclude point spectrum is also given the application of our theorems is explained on a series of examples

solitary solutions periodic solutions and compacton like solutions using the exp function method in this paper the exp function method is used for seeking solitary solutions periodic solutions and compacton like solutions of nonlinear differential equations the combined kdv mkdv equation and the liouville equation are chosen to illustrate the effectiveness and convenience of the proposed method

structured dissipativity and absolute stability of nonlinear systems the paper considers a problem of absolute stability for a nonlinear uncertain system with structured uncertainty an s procedure for nonlinear systems is established and using this the paper shows that the absolute stability problem is equivalent to an absolute stability problem for a nonlinear uncertain system with unstructured uncertainty the paper also introduces a new notion of structured dissipativeness for nonlinear systems this notion extends the standard notion of dissipativeness in that it allows for multiple supply functions the paper shows that a nonlinear uncertain system containing structured uncertainties will be absolutely stable if and only if a corresponding structured dissipativeness condition is satisfied it is also shown that structured dissipativeness is equivalent to the standard notion of dissipativeness with a parameter dependent supply function

spectral and quantum dynamical properties of the weakly coupled fibonacci hamiltonian we consider the spectrum of the fibonacci hamiltonian for small values of the coupling constant it is known that this set is a cantor set of zero lebesgue measure here we study the limit as the value of the coupling constant approaches zero of its thickness and its hausdorff dimension we prove that the thickness tends to infinity and consequently the hausdorff dimension of the spectrum tends to one we also show that at small coupling all gaps allowed by the gap labeling theorem are open and the length of every gap tends to zero linearly moreover for a sufficiently small coupling the sum of the spectrum with itself is an interval this last result provides a rigorous explanation of a phenomenon for the fibonacci square lattice discovered numerically by even dar mandel and lifshitz finally we provide explicit upper and lower bounds for the solutions to the difference equation and use them to study the spectral measures and the transport exponents

n soliton solutions of the kp equation by exp function method abstract in this paper the exp function method is generalized to determine the 1 soliton 2 soliton and 3 soliton solutions of the kadomtsev petviashvili kp equation then the uniform formula of n soliton solutions is derived the method is simple and straightforward in constructing the n soliton of the nonlinear evolution equation in mathematical physics

spectral properties of a tight binding hamiltonian with period doubling potential we study a one dimensional tight binding hamiltonian with a potential given by the period doubling sequence we prove that its spectrum is purely singular continuous and supported on a cantor set of zero lebesgue measure for all nonzero values of the potential strength moreover we obtain the exact labelling of all spectral gaps and compute their widths asymptotically for small potential strength

on the application of the exp function method to the kp equation for n soliton solutions abstract we observe that the form of the kadomstev petviashvili equation studied by yu 2011 s yu n soliton solutions of the kp equation by exp function method appl math comput 2011 doi 10 1016 j amc 2010 12 095 is incorrect we claim that the n soliton solutions obtained by means of the basic exp function method and some of its known generalizations do not satisfy the equation considered we emphasize that yu s results except only one cannot be solutions of the correct form of the kadomstev petviashvili equation in addition we provide some correct results using the same approach

necessary and sufficient conditions for the hurwitz and schur stability of interval matrices establishes a set of new sufficient conditions for the hurwitz and schur stability of interval matrices the authors use these results to establish necessary and sufficient conditions for the hurwitz and schur stability of interval matrices the authors relate the above results to the existence of quadratic lyapunov functions for linear time invariant systems with interval valued coefficient matrices using the above results the authors develop an algorithm to determine the hurwitz and the schur stability properties of interval matrices the authors demonstrate the applicability of their results by means of two specific examples

application of exp function method for 3 1 dimensional nonlinear evolution equations in this paper the exp function method is used to construct solitary and periodic solutions of nonlinear partial differential equations we choose an example which includes kadomstev petviashvili equation and potantial ytsf equation to illustrate the method the method is straightforward and concise and its applications are promising the exp function method presents a wider applicability for handling nonlinear wave equations

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

almost sure frequency independence of the dimension of the spectrum of sturmian hamiltonians we consider the spectrum of discrete schrodinger operators with sturmian potentials and show that for sufficiently large coupling its hausdorff dimension and its upper box counting dimension are the same for lebesgue almost every value of the frequency

palindromic richness for languages invariant under more symmetries for a given finite group g consisting of morphisms and antimorphisms of a free monoid a we study infinite words with language closed under the group g we focus on the notion of g richness which describes words rich in generalized palindromic factors i e in factors w satisfying q w w for some antimorphism email protected g we give several equivalent descriptions which are generalizations of known characterizations of rich words in the terms of classical palindromes and show two examples of g rich words

an improvement on the exp function method when balancing the highest order linear and nonlinear terms abstract the exp function method has been widely used to solve different kinds of nonlinear partial differential equations these nonlinear partial differential equations are transformed first into nonlinear ordinary differential equations and then the ansatz of the exp function method u n c p a n exp n m d q b m exp m is applied to obtain the solution however a part of the solution using this method is to construct the relations between c p d and q by balancing the highest order linear term with the highest order nonlinear term it is proved in the present paper that c d and p q are the only relations that can be obtained by applying this method to any nonlinear ordinary differential equation therefore the additional calculations of balancing the highest order linear term with the highest order nonlinear term are not longer required in future hence the method becomes more straightforward

multiple soliton solutions for the kp equation by hirota s bilinear method and by the tanh coth method abstract in this work we use the hirota s direct method combined with the simplified version of this method to determine the n soliton solutions n 1 2 3 4 5 for the kadomtsev petviashvili kp equation the one soliton solutions will be handled by the tanh coth method the work emphasizes the power of the two methods that will be used

absolutely continuous convolutions of singular measures and an application to the square fibonacci hamiltonian author s damanik d gorodetski a solomyak b abstract 2015 we prove for the square fibonacci hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants this is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact dimensional measures

singular continuous spectrum for the period doubling hamiltonian on a set of full measure we consider the discrete one dimensional schrodinger operator with potential generated by the period doubling substitution we show that for almost every element in the hull with respect to the unique ergodic measure on there are no eigenvalues combining this with a result proven by kotani we establish purely singular continuous spectrum on a set of full measure

resistance of one dimensional quasicrystals abstract one dimensional quasiperiodic systems are often based on an inflation rule giving rise to a recursion formula on the transfer matrices it is shown in a general setting that the norm growth of these matrices can be evaluated a consequence is for instance a purely critical regime namely polynomial bounds in function of the sample size for the electrical resistance when the energy is in the spectrum this solves a conjecture by sutherland and kohmoto

dynamical upper bounds for one dimensional quasicrystals abstract following the killip kiselev last method we prove quantum dynamical upper bounds for discrete one dimensional schrodinger operators with sturmian potentials these bounds hold for sufficiently large coupling almost every rotation number and every phase

hierarchical structures in sturmian dynamical systems the paper is concerned with hierarchical stuctures in subshifis over a finite alphabet in particular we present a hierarchy based approach to sturmian systems this approach is then used to characterize the linearly repetitive sturmian systems among the sturmian systems by uniform positivity of certain weights more generally we discuss various bounds on weights and their relationship finally we combine hierarchies and bounds on a weights to study a thermodynamic formalism for lattice gas models associated to arbitrary linearly repetitive subshifts