a pathway to matrix variate gamma and normal densities a general real matrix variate probability model is introduced here which covers almost all real matrix variate densities used in multivariate statistical analysis through the new density introduced here a pathway is created to go from matrix variate type 1 beta to matrix variate type 2 beta to matrix variate gamma to matrix variate gaussian or normal densities other densities such as extended matrix variate student t f cauchy density will also come in as particular cases connections to the distributions of quadratic forms and generalized quadratic forms in the new matrix are established the present day analysis of these problems is mainly confined to gaussian random variables thus through the new distribution all these theories are extended connections to certain geometrical probability problems such as the distribution of the volume of a random parallelotope in euclidean space is also established

robust observer design under measurement noise with gain adaptation and saturated estimates abstract we use incremental homogeneity gain adaptation and incremental observability for proving new results on robust observer design for systems with noisy measurement and bounded trajectories a state observer is designed by dominating the incrementally homogeneous nonlinearities of the observation error system with its linear approximation while gain adaptation and incremental observability guarantee an asymptotic upper bound for the estimation error depending on the limsup of the norm of the measurement noise a characteristic and innovative feature of this observer is the mixed low high gain structure in combination with saturated state estimates and dynamically tuned gains and saturation levels the gain adaptation is implemented as the output of a stable filter using the squared norm of the measured output estimation error and the mismatch between each estimate and its saturated value

smooth output feedback stabilization of planar systems without controllable observable linearization this note considers the problem of global stabilization by output feedback for a family of planar systems whose jacobian linearization is neither controllable nor observable the problem cannot be dealt with by existing output feedback design methods most of them are based on the separation principle under appropriate growth conditions we propose an output feedback control scheme that does not rely on the separation principle and achieves global asymptotic stabilization the novelty of our control scheme lies in the explicit design of a dynamic output compensator which combines a nonlinear gain observer design and the technique of adding a power integrator as a consequence an interesting global stabilization result by output feedback can be obtained for feedback linearizable systems in a triangular form which turns out to be new even in the two dimensional case

discrete time homogeneity robustness and approximation in this paper we study robustness properties of discrete time homogeneous systems we also analyse stability and robustness properties of a more general class of nonlin ear discrete time systems that can be approximated by homogeneous ones we apply the results to the investigation of stability properties of discretized continuous time systems

optimal controllers and output feedback stabilization abstract in this paper the output feedback stabilizability problem is explored in terms of control lyapunov functions sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem our main results extends those developed in 31 and generalize a theorem due to sontag 23

a local stabilization theorem for interconnected systems abstract we prove that if a nonlinear control system is locally asymptotically stabilizable at its equilibrium by means of a continuous feedback then adding an integrator the resulting system is also locally asymptotically stabilizable by means of a feedback law which is smooth except possibly at the equilibrium our approach is based on previous works of arstein sontag and the author

a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

adding one power integrator a tool for global stabilization of high order lower triangular systems a new feedback design tool called adding a power integrator is introduced and used to solve the problem of global robust stabilization for a significant class of uncertain nonlinear systems that are of a lower triangular form but neither necessarily feedback linearizable fully or partially nor affine in the control input and therefore cannot be dealt with via conventional approaches sufficient conditions are presented under which a globally stabilizing smooth state feedback control law can be explicitly constructed using repeatedly the adding one power integrator technique this novel design technique permits removal of the feedback linearizability and linearity of the control input which have been two common assumptions so far in the literature of nonlinear control

modelling temporal decay of aftershocks by a solution of the fractional reactive equation abstract we propose a new analytical perspective to explain the behavior of the number of seismic events observed post an intense earthquake as time elapses through the application of a fractional solution of the reactive equation according to the results obtained a double power law model shows the number density decay in several possible ways among which is a particular case the modified version of omori law proposed by utsu in 1961

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

fractional differential operators in the complex matrix variate case abstract there are many applications for fractional integrals fractional derivatives and fractional differential equations in the real scalar variable cases however when it comes to fractional integrals in the real and complex matrix variate cases there are not many papers the author has given some definitions and properties for fractional integrals and fractional derivatives in the real matrix variate cases recently some situations of fractional derivatives in the complex matrix variate case are discussed in the present article along with the definitions for fractional derivatives in the complex matrix variate case the definition introduced here enables us to handle certain types of derivatives of real valued scalar functions of matrix argument in the complex domain it is not universally applicable fractional derivatives in the riemann liouville and caputo senses are evaluated when the arbitrary function is compatible with right and left sided fractional integrals in the complex matrix variate cases kober operators of the first and second kind in the complex matrix variate cases are also examined here

gamma function to beck cohen superstatistics abstract in this paper we show a mathematical construction of beck cohen superstatistics in the bayesian point of view with the help of the two representations of a gamma function furthermore it is shown how some results for superstatistics are related to each other

on an output feedback finite time stabilization problem studies the problem of finite time output feedback stabilization for the double integrator system a class of output feedback controllers that can achieve global finite time stability for the double integrator system are constructed based on a finite time separation principle furthermore it is shown that the closed loop system resulting from our control law can maintain its local finite time stability regardless of some nonlinear perturbations thus our control law actually applies to a large class of nonlinear second order systems

continuous finite time stabilization of the translational and rotational double integrators a class of bounded continuous time invariant finite time stabilizing feedback laws is given for the double integrator lyapunov theory is used to prove finite time convergence for the rotational double integrator these controllers are modified to obtain finite time stabilizing feedback that avoid unwinding

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

pathway model superstatistics tsallis statistics and a generalized measure of entropy abstract the pathway model of mathai a pathway to matrix variate gamma and normal densities linear algebra appl 396 2005 317 328 is shown to be inferable from the maximization of a certain generalized entropy measure this entropy is a variant of the generalized entropy of order considered in mathai and rathie basic concepts in information theory and statistics axiomatic foundations and applications wiley halsted new york and wiley eastern new delhi 1975 and it is also associated with shannon boltzmann gibbs renyi tsallis and havrda charvat entropies the generalized entropy measure introduced here is also shown to have interesting statistical properties and it can be given probabilistic interpretations in terms of inaccuracy measure expected value and information content in a scheme particular cases of the pathway model are shown to be tsallis statistics c tsallis possible generalization of boltzmann gibbs statistics j stat phys 52 1988 479 487 and superstatistics introduced by beck and cohen superstatistics physica a 322 2003 267 275 the pathway model s connection to fractional calculus is illustrated by considering a fractional reaction equation

some complex matrix variate statistical distributions on rectangular matrices abstract in a recent survey olkin the 70th anniversary of the distribution of random matrices a survey linear algebra appl 354 2002 231 243 has looked into 70 years of development on random matrices giving special attention to rectangular matrices gupta and richards multivariate liouville distributions j multivariate anal 23 1987 233 256 have looked into generalizations of the dirichlet family of distributions for the multivariate case mathai an introduction to geometrical probability distributional aspects with applications gordon and breach scientific publishers new york 1999 developed a gamma type distribution on rectangular matrices in connection with the distributional aspects of random volumes this idea is developed further in the present article to define rectangular matrix variate gamma type beta type and dirichlet type distributions with location and scale matrices connections among these distributions and various properties are pointed out this paper discusses the complex matrix variate cases and the corresponding real cases are also listed along with each result the complex rectangular matrix variate t and cauchy distributions are obtained as particular cases

lyapunov design of stabilizing controllers for cascaded systems the design of a state feedback law for an affine nonlinear system to render a as small as possible compact neighborhood of the equilibrium of interest globally attractive is discussed following z artstein s theorem 1983 the problem can be solved by designing a so called control lyapunov function for systems which are in a cascade form a lyapunov function meeting artstein s conditions is designed assuming the knowledge of a control law stabilizing the equilibrium of the head nonlinear subsystem in particular for planar systems this gives sufficient and necessary conditions for a compact neighborhood of the equilibrium to be stabilized

arctic octahedron in three dimensional rhombus tilings and related integer solid partitions three dimensional integer partitions provide a convenient representation of codimension one three dimensional random rhombus tilings calculating the entropy for such a model is a notoriously difficult problem we apply transition matrix monte carlo simulations to evaluate their entropy with high precision we consider both free and fixed boundary tilings our results suggest that the ratio of free and fixed boundary entropies is free fixed 3 2 and can be interpreted as the ratio of the volumes of two simple nested polyhedra this finding supports a conjecture by linde moore and nordahl concerning the arctic octahedron phenomenon in three dimensional random tilings

stabilizability does not imply homogeneous stabilizability for controllable homogeneous systems this paper presents an example of a homogeneous planar controllable system which is stabilizable while not stabilizable by homogeneous feedback addition of an integrator to the system provides a three dimensional it affine system with the same properties

global stabilization of discrete time homogeneous systems abstract the feedback stabilization of continuous time r homogeneous systems has been studied by several authors see for instance dayawansa and martin proceedings of the 28th c d c tampa florida december 1989 hermes j differential equations 92 1991 76 89 hermes systems control lett 24 1995 7 11 kawski proceedings of the 27th c d c texas 1988 texas kawski control theory and advanced technology vol 6 mita press tokyo 1996 pp 497 516 sepulchre and aeyels math control signal systems 9 1996 34 58 in kawski analysis of controlled dynamical systems birkhauser basel 1991 kawski proceedings of ifac nolcos 1995 kawski gave an intrinsic concept of homogeneity with respect to general smooth dilations in this note we define the homogeneity of transition maps w r t continuous dilations and we show how one can construct a global stabilizing feedback control for discrete time homogeneous systems which are locally asymptotically stabilizable

multivariate and matrix variate analogues of maxwell boltzmann and raleigh densities abstract the maxwell boltzmann and raleigh densities are basic densities in many problems in physics a multivariate analogue and a rectangular matrix variate analogue of these densities are explored in this article the results may become useful in extending the usual theories where these densities for the real scalar variable case occur to multivariate and matrix variable situations various properties are studied and connection to the volumes of parallelotopes determined by p linearly independent random points in euclidean n space n p is also established structural decompositions of these random determinants and pathway extensions of maxwell boltzmann and raleigh densities are also considered

dimers belonging to three orientations on plane honeycomb lattices it is well known that there are three types of dimers belonging to the three different orientations in a honeycomb lattice and in each type all dimers are mutually parallel based on a previous result we can compute the partition function of the dimer problem of the plane free boundary honeycomb lattices with three different activities by using the number of its pure dimer coverings perfect matchings the explicit expression of the partition function and free energy per dimer for many types of plane honeycomb lattices with fixed shape of boundaries is obtained in this way for a shape of plane honeycomb lattices the procedure that the size goes to infinite corresponds to a way that the honeycomb lattice goes to infinite from these results an interesting phenomena is observed in the case of the regions of the plane honeycomb lattice has zero entropy per dimer when its size goes to infinite though in the thermodynamic limit there is no freedom in placing a dimer at all but if we distinguish three types of dimers with nonzero activities then its free energy per dimer is nonzero furthermore a sufficient condition for the plane honeycomb lattice with zero entropy per dimer when the three activities are equal to 1 is obtained finally the difference between the plane honeycomb lattices and the plane quadratic lattices is discussed and a related problem is proposed

stretched exponentials from superstatistics abstract distributions exhibiting fat tails occur frequently in many different areas of science a dynamical reason for fat tails can be a so called superstatistics where one has a superposition of local gaussians whose variance fluctuates on a rather large spatio temporal scale after briefly reviewing this concept we explore in more detail a class of superstatistics that hasn t been subject of many investigations so far namely superstatistics for which a suitable power of the local inverse temperature is 2 distributed we show that 0 leads to power law distributions while 0 leads to stretched exponentials the special case 1 corresponds to tsallis statistics and the special case 1 to exponential statistics of the square root of energy possible applications for granular media and hydrodynamic turbulence are discussed

some physical features of the burr type xii distribution aspects related to driven nonequilibrium systems considered in beck cohen superstatistics bcs formalism and in addition the unbiased maximum entropy density estimation show the pertinence of considering the three parameter burr type xii distribution as a suitable way to describe stationary states of complex and nonequilibrium systems the above is shown following a variant to the procedure presented in the formulation of bcs which consists of the incorporation of an expanded boltzmann factor through the mittag leffler function on the other hand maximization of shannon boltzmann gibbs entropy and other generalized forms of entropy show that the burr type xii distribution may emerge as the least informative distribution for the mentioned systems

robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization this paper investigates the problem of robust output feedback stabilization for a family of uncertain nonlinear systems with uncontrollable unobservable linearization to achieve global robust stabilization via smooth output feedback we introduce a rescaling transformation with an appropriate dilation which turns out to be very effective in dealing with uncertainty of the system using this rescaling technique combined with the nonseparation principle based design method we develop a robust output feedback control scheme for uncertain nonlinear systems in the p normal form under a homogeneous growth condition the construction of smooth state feedback controllers and homogeneous observers uses only the knowledge of the bounding homogeneous system rather than the uncertain system itself the robust output feedback design approach is then extended to a class of uncertain cascade systems beyond a strict triangular structure examples are provided to illustrate the results of the paper

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

asymptotically stabilizing feedback controls abstract the problem considered is the existence and construction of an asymptotically stabilizing feedback control for a rest solution of an n dimensional single input affine control system the method is to construct high order homogeneous approximations of the vector fields defining the control system which then describe an approximating control system such that an asymptotically stabilizing control of the latter system is a local asymptotically stabilizing control of the original system unlike linear approximations there are many possible nonlinear homogeneous approximations these are constructed from lie algebra filtrations obtained by assigning various weights to the defining vector fields one seeks a weighting hence an approximating system which satisfies the various known necessary conditions for the existence of an asymptotically stabilizing feedback control and for which such a control can be constructed as the solution to a homogeneous hamilton jacobi bellman equation associated with an optimization regulator problem

on input output linearization of discrete time nonlinear systems abstract we consider a nonlinear discrete time system of the form x t 1 f x t u t y t h x t where x r n u r m y r q and f and h are analytic necessary and sufficient conditions for local input output linearizability are given we show that these conditions are also sufficient for a formal solution to the global input output linearization problem finally we show that zeros at infinity of can be obtained by the structure algorithm for locally input output linearizable systems

stabilisation of nonlinear systems by discontinuous dynamic state feedback in this paper a dynamic state feedback that stabilizes general nonlinear affine in the control systems is proposed it is deduced from the solution of an hamilton jacobi like equality with two boundary conditions the asymptotic stability of the closed loop system is proved and some examples are given an interesting feature of this method is that the so obtained feedback takes the form of a generalised sliding mode control in the sense that it is a dynamic feedback on one half part of the space and a static feedback on the other half with eventually a discontinuity on the surface dividing the space

generalized superstatistics of nonequilibrium markovian systems abstract the paper is devoted to the construction of the superstatistical description for nonequilibrium markovian systems it is based on kirchhoff s diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes the latter feature enables us to introduce equivalence classes called channels within which detailed balance holds individually then stationary probability as well as flux distributions are represented as some sums over the channels the latter construction actually forms the superstatistical description which however deals with a certain superposition of equilibrium subsystems rather than a formal expansion of the nonequilibrium steady state distribution into terms of the boltzmann type

stabilization of non linear control systems the role of newton diagrams abstract the stabilization of two dimensional non linear control systems is treated although the main technique is applicable to more general systems it combines the theory of centre manifolds and singularities of algebraic functions to design continuous but not necessarily lipschitz stabilizing feedback control laws in particular the devices known as the newton diagram and the newton or puiseux polygon are employed to construct uniformizing transformations finally remarks are made about systems for which no continuous stabilizing feedback control law exists

homogeneous lyapunov function for homogeneous continuous vector field the goal of this article is to provide a construction of a homogeneous lyapunov function p associated with a system of differential equations j f x x r n 1 under the hypotheses 1 f c r n vanishes at x 0 and is homogeneous 2 the zero solution of this system is locally asymptotically stable moreover the lyapunov function v x tends to infinity with 1 x i and belongs to c r 0 r n cp with p e as large as wanted as application to the theory of homogeneous systems we present two well known results of robustness in a slightly extended form and with simpler proofs

what should a statistical mechanics satisfy to reflect nature there is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual boltzmann gibbs prescriptions more specifically ubiquitous natural and artificial systems exhibit generic stationary states which are not ergodic nor close to it in any geometrically simple subset of the a priori allowed phase space in any even extended trivial sense a vast class of such systems appears nevertheless to be tractable within thermostatistical methods completely analogous to the usual ones the question posed in the title arises then naturally some answer to this complex question is advanced in the present review of nonextensive statistical mechanics and its recent connections

generalized boltzmann factors induced by weibull type distributions abstract the inverse mellin transform technique is utilized to obtain closed form representations of the generalized boltzmann factors associated with several weibull type models such as the generalized gamma maxwell rayleigh and half normal distributions the results complement those already available in the physics literature in connection with the distribution of certain variables affecting the behavior of nonequilibrium systems subject to complex dynamics which include for instance computable expressions for the generalized boltzmann factors induced by the gamma f uniform and lognormal statistical models

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

on generalized entropy measures and pathways abstract product probability property known in the literature as statistical independence is examined first then generalized entropies are introduced all of which give generalizations to shannon entropy it is shown that the nature of the recursivity postulate automatically determines the logarithmic functional form for shannon entropy due to the logarithmic nature shannon entropy naturally gives rise to additivity when applied to situations having product probability property it is argued that the natural process is non additivity important for example in statistical mechanics c tsallis possible generalization of boltzmann gibbs statistics j stat phys 52 1988 479 487 e g d cohen boltzmann and einstein statistics and dynamics an unsolved problem pramana 64 2005 635 643 even in product probability property situations and additivity can hold due to the involvement of a recursivity postulate leading to a logarithmic function generalized entropies are introduced and some of their properties are examined situations are examined where a generalized entropy of order leads to pathway models exponential and power law behavior and related differential equations connection of this entropy to kerridge s measure of inaccuracy is also explored

asymptotically stabilizing feedback controls and the nonlinear regulator problem continuous asymptotically stabilizing feedback controls are constructed for two dimensional and certain three dimensional small time locally controllable affine systems the lie products which de

controllability of nonlinear discrete time systems a lie algebraic approach this paper presents a geometric study of controllability for discrete time nonlinear systems various accessibility properties are characterized in terms of lie algebras of vector fields some of the results obtained are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

random tilings of high symmetry ii boundary conditions and numerical studies we perform numerical studies including monte carlo simulations of high rotational symmetry random tilings for computational convenience our tilings obey fixed boundary conditions in regular polygons such tilings are put in correspondence with algorithms for sorting lists in computer science we obtain statistics on path counting and vertex coordination which compare well with predictions of mean field theory and allow estimation of the configurational entropy which tends to the value 0 568 per vertex in the limit of continuous symmetry tilings with phason strain appear to share the same entropy as unstrained tilings as predicted by mean field theory we consider the thermodynamic limit and argue that the limiting fixed boundary entropy equals the limiting free boundary entropy although these differ for finite rotational symmetry

random tilings concepts and examples we introduce a concept for random tilings which comprising the conventional one is also applicable to tiling ensembles without height representation in particular we focus on the random tiling entropy as a function of the tile densities in this context and under rather mild assumptions we prove a generalization of the first random tiling hypothesis which connects the maximum of the entropy with the symmetry of the ensemble explicit examples are obtained through the re interpretation of several exactly solvable models this also leads to a counterexample to the analogue of the second random tiling hypothesis about the form of the entropy function near its maximum

almost disturbance decoupling for a class of high order nonlinear systems the problem of almost disturbance decoupling with internal stability add is formulated in terms of an l sub 2 l sub 2p instead of an l sub 2 gain for a class of high order nonlinear systems which consist of a chain of power integrators perturbed by a lower triangular vector field a significant feature of the systems considered in the paper is that they are neither feedback linearizable nor affine in the control input which have been two basic assumptions made in all the existing add nonlinear control schemes using the technique of adding a power integrator we solve the add problem via static smooth state feedback under a set of growth conditions that can be viewed as a high order version of the feedback linearization conditions we also show how to explicitly construct a smooth state feedback controller that attenuates the disturbance s effect on the output to an arbitrary degree of accuracy with internal stability

boundary effects in the dimer problem on a non bravais lattice the dimer problem on the hexagonal lattice is solved for various boundary shapes the number of arrangements of dimers in the asymptotic limit of large lattices proves to be very sensitive to the precise form of the lattice boundary if n is the number of lattice points and for large n wn 2 the number of dimer configurations then the molecular freedom w reduces to 1 in the case of standard boundaries parallelogram rectangle and there is in the thermodynamic limit no freedom in placing a dimer at all but in the case of a hexagonal lattice which has been given the shape of a macroscopic honeycomb and which thus exhibits the symmetry properties of the unit cell the molecular freedom is found to tend to w 3 4 3 1 299 for n investigating various other boundary forms the regular hexagon proves to be a convenient surface shape with a maximum molecular freedom which differs markedly from the known value w 1 381 for the hexagonal lattice wrapped on a torus

proportional reversed hazard rates weighted frailty model abstract in this paper a proportional reversed hazards weighted frailty model is considered the model is treated by the concept of weighted distributions where a natural alteration in the baseline distribution in the ordinarily proportional reversed hazards model illustrates the formation of the model stochastic variation of the model based on some stochastic orders is discussed finally the model is motivated with several expository examples by which the model is potentially applied to analyze parallel systems with different formations of lifetime components data analysis of the model for a physical distribution is carried out

evaluation of matrix variate gamma and beta integrals as multiple integrals and koberfractional integral operators in the complex matrix variate case explicit evaluations of matrix variate gamma and beta integrals in the complex domain by using conventional procedures is extremely difficult such an evaluation will reveal the structure of these matrix variate integrals in this article explicit evaluations of matrix variate gamma and beta integrals in the complex domain for the order of the matrix p 1 2 are given then fractional integral operators of the kober type are given for some specific cases of the arbitrary function a formal definition of fractional integrals in the complex matrix variate case was given by the author earlier as the m convolution of products and ratios where kober operators become a special class of fractional integral operators

fractional integral operators involving many matrix variables abstract fractional integral operators of the first and second kind in many and complex matrix variate cases are the main topic of discussion here after discussing fractional integral operators in the real scalar variable case the ideas are extended to fractional integral operators involving one matrix variable in the real and complex cases then these ideas are extended to define fractional integrals of the first and second kinds in many matrix variables in the real as well as complex cases

output feedback stabilization the stabilization of control systems using output feedback is addressed necessary and sufficient lyapunov conditions are established generalizing the artstein s stabilization theorem for linear control systems a necessary and sufficient lyapunov condition is provided for stabilization by means of a linear output feedback law

some properties of q logarithm and q exponential functions in tsallis statistics we present some formulae which q logarithmic and q exponential functions introduced in tsallis statistics satisfy exact expression of the mellin transform of q exponential function is given moreover the q generalization of the digamma function is presented

feedback linearization of discrete time systems abstract we give necessary and sufficient conditions for a nonlinear discrete time system to be locally linearizable by a change of state coordinates and a feedback the conditions are expressed in terms of controllability distributions associated to the system

remarks on asymptotic controllability and sampled data feedback stabilization for autonomous systems a weak concept of sampled data feedback stabilization for the case of autonomous systems is presented and its lyapunov characterization is established sufficient conditions are derived for the existence of a time varying sampled data feedback exhibiting global stabilization for certain class of nonlinear systems

on the relation between local controllability and stabilizability for a class of nonlinear systems the problem of local stabilizability of locally controllable nonlinear systems is considered it is well known that contrary to the linear case local controllability does not necessarily imply stabilizability a class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static state feedback is described as for this class of systems the well known hermes controllability condition is necessary and sufficient for local controllability

asymptotic stabilization of two dimensional real analytic systems abstract we investigate the local asymptotic stabilizability of a real analytic control system around an equilibrium point and give necessary and sufficient conditions for local asymptotic stabilization using continuous feedback

h control stabilization and input output stability of nonlinear systems with homogeneous properties new relations are established between h control and stabilization and between input output stability and lyapunov stability of nonlinear systems with homogeneous properties these results can be applied to h controller design and stability analysis

an extension of artstein s theorem on stabilization by using ordinary feedback integrators abstract we prove that under suitable lyapunov like conditions a single input nonlinear system although it may not be stabilized by an ordinary state feedback law is dynamically stabilize by means of an ordinary feedback integrator

random volumes under a general matrix variate model abstract the convex hull generated by p linearly independent points in euclidean n space n p will almost surely determine a p simplex and the corresponding p parallelotope the volume of this p parallelotope is v xx 1 2 where the rows of the p n n p matrix of rank p represent the p linearly independent points if the points are random points in some sense then v becomes a random volume the distribution of this random volume v when the matrix x has a very general real rectangular matrix variate density is the topic of this paper the complicated classical procedures based on integral geometry techniques for dealing with such problems are replaced by a simpler procedure based on jacobians of matrix transformations and functions of matrix argument apart from the distribution of v under this general model arbitrary moments of v connection to the likelihood ratio statistic or criterion for testing hypotheses on the parameters of multivariate normal distributions connections to mellin barnes integrals and meijer s g function connection to the concept of generalized variance various structural decompositions of v and special cases are also examined here

adding an integrator for the stabilization problem abstract we study the relationship between the following two properties p1 the system x f x y y v is locally asymptotically stabilizable and p2 the system x f x u is locally asymptotically stabilizable where x r n y r dayawansa martin and knowles have proved that these properties are equivalent if the dimension n 1 here using the so called control lyapunov function approach a we propose another more constructive and somewhat simpler proof of dayawansa martin and knowles s result b we show that in general p1 does not imply p2 for dimensions n larger than 1 c we prove that p2 implies p1 if some extra assumptions are added like homogeneity of the system by using the latter result recursively we obtain a sufficient condition for the local asymptotic stabilizability of systems in a triangular form

analogues of reliability analysis for matrix variate cases abstract an attempt is made in this paper to extend various aspects of reliability analysis in the real scalar variable case to the corresponding real matrix variate cases probability of a matrix random variable being bigger than a given matrix is defined in terms of norms and positive definite matrices then by using these definitions various aspects of reliability analysis are extended to the corresponding matrix variate cases a multivariate in the sense of many real scalar variables pathway model is also defined and some probabilities connected with reliability are also evaluated here

asymptotic stabilization of planar systems abstract sufficient conditions for the existence of a c1 asymptotically stabilizing feedback control for planar affine systems are given the methods are constructive and yield homogeneous feedback controls for homogeneous systems which allow the results to be extended to more general systems

practical output tracking of nonlinear systems with uncontrollable unstable linearization the paper focuses on the problem of having the output of nonlinear systems track a prescribed c sup 1 reference signal it is proved that under mild assumptions global practical output tracking is achievable by smooth state feedback although asymptotic output tracking is usually not possible even locally because the linearized system has uncontrollable modes whose eigenvalues are on the right half plane smooth feedback controllers which solve the problem of global practical output tracking are explicitly constructed based on a modified adding a power integrator approach this feedback design method also leads to solutions to challenging benchmark control problems including practical output tracking of an underactuated unstable two degrees of freedom mechanical system

solution of fractional kinetic equation by a class of integral transform of pathway type solutions of fractional kinetic equations are obtained through an integral transform named p transform introduced in this paper the p transform is a binomial type transform containing many class of transforms including the well known laplace transform the paper is motivated by the idea of pathway model introduced by mathai linear algebra appl 396 317 328 2005 10 1016 j laa 2004 09 022 the composition of the transform with differential and integral operators are proved along with convolution theorem as an illustration of applications to the general theory of differential equations a simple differential equation is solved by the new transform being a new transform the p transform of some elementary functions as well as some generalized special functions such as h function g function wright generalized hypergeometric function generalized hypergeometric function and mittag leffler function are also obtained the results for the classical laplace transform is retrieved by letting 1

a class of asymmetric pathway distributions and an entropy interpretation abstract asymmetric distributions are widely used in probability modeling and statistical analysis recently various asymmetric distributions are being developed by many researchers for modeling various data sets in real life contexts in the present paper we introduce a new class of q type asymmetric distributions which include q analogues of asymmetric laplace exponential power weibull etc and corresponding standard distributions as special cases also we show that this pathway model can be obtained by optimizing mathai s generalized entropy with more general setup which is a generalization of various entropy measures due to shannon and others

finite time stability and stabilization of a class of continuous systems abstract finite time stability is investigated for continuous system x f x which satisfies uniqueness of solutions in forward time a necessary and sufficient condition for finite time stability is given for this class of systems using lyapunov functions then a necessary and sufficient condition is developed for finite time stabilization of class cl k affine systems x f x g x u involving a class cl 0 settling time function for the closed loop system finally an explicit feedback control is addressed by using a control lyapunov function verifying a certain inequality

global stabilization of cascade systems by c sup 0 partial state feedback this paper shows how the nonsmooth but continuous feedback design approach developed recently for global stabilization of nonlinear systems with uncontrollable unstable linearization and the notion and properties of the input to state stability lyapunov function can be effectively coupled resulting in globally stabilizing c sup 0 partial state feedback controllers for a class of cascade systems which may not be smoothly stabilizable even locally

fractional integral operators in the complex matrix variate case abstract a formal definition of fractional integrals in the complex matrix variate case is given here this definition will encompass all the various fractional integral operators introduced by various authors in the real scalar and matrix cases the new definition is introduced in terms of m convolutions of products and ratios of matrices in the complex domain their connections to statistical distribution theory mellin convolutions m transforms and mellin transform are pointed out some basic properties are given and a pathway extension of the new definition is also given the pathway extension will provide a switching mechanism to move among three different families of functions

on generalized fractional kinetic equations abstract in a recent paper saxena et al astro phys space sci 282 2002 281 developed solutions of generalized fractional kinetic equations in terms of mittag leffler functions the object of the present paper is to derive the solution of further generalized fractional kinetic equations their relation to fundamental laws of physics is briefly discussed results are obtained in a compact form in terms of generalized mittag leffler functions and a number of representations of these functions which are widely distributed in the literature are compiled for the first time

stabilizability conditions in terms of critical hamiltonians and symbols symmetric functions of critical hamiltonians called symbols were used in such problems of nonlinear control as the characterization of symmetries and feedback invariants we derive here a stabilizability condition in the class of almost continuous feedback controls based on symbols the methodology proposed consists of defining a selector of the multivalued covector field satisfying an extra degree condition on a sphere close to the origin then the above selector is extended to some neighborhood in order to get an exact differential form integration of that form gives us a control lyapunov function candidate theorem 3 1 the condition proposed is applied to the analysis of a planar control affine system with polynomial homogeneous vector fields unlike known results in the literature we consider the case when each vector field vanishes at the origin and the control is bounded we give stabilizability conditions explicitly in terms of the control system parameters theorem 4 1

an alternative view on quasicrystalline random tilings we apply a framework for the description of random tilings without height representation which was proposed recently to the special case of quasicrystalline random tilings two important examples are discussed thereby demonstrating the consistency of this alternative description with the conventional one we also clarify the latter by deriving a group theoretic criterion for the validity of the first random tiling hypothesis

model predictive control for want of a local control lyapunov function all is not lost we present stability results for unconstrained discrete time nonlinear systems controlled using finite horizon model predictive control mpc algorithms that do not require the terminal cost to be a local control lyapunov function the two key assumptions we make are that the value function is bounded by a k sub spl infin function of a state measure related to the distance of the state to the target set and that this measure is detectable from the stage cost we show that these assumptions are sufficient to guarantee closed loop asymptotic stability that is semiglobal and practical in the horizon length and robust to small perturbations if the assumptions hold with linear or locally linear k sub spl infin functions then the stability will be global or semiglobal for long enough horizon lengths in the global case we give an explicit formula for a sufficiently long horizon length we relate the upper bound assumption to exponential and asymptotic controllability using terminal and stage costs that are controllable to zero with respect to a state measure we can guarantee the required upper bound but we also require that the state measure be detectable from the stage cost to ensure stability while such costs and state measures may not be easy to construct in general we explore a class of systems called homogeneous systems for which it is straightforward to choose them in fact we show for homogeneous systems that the associated k sub spl infin functions are linear thereby guaranteeing global asymptotic stability we discuss two examples found elsewhere in the mpc literature including the discrete time nonholonomic integrator to demonstrate our methods for these systems we give a new result they can be globally asymptotically stabilized by a finite horizon mpc algorithm that has guaranteed robustness we also show that stable linear systems with control constraints can be globally exponentially stabilized using finite horizon mpc without requiring the terminal cost to be a global control lyapunov function

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

quadratic forms in random variables theory and applications textbook for a one semester graduate course for students specializing in mathematical statistics or in multivariate analysis or reference for theoretical as well as applied statisticians confines its discussion to quadratic forms and second degree polynomials in real normal random vectors and matr

two global stabilizability results for homogeneous systems from a local stabilizability assumption in this technical note two problems have been investigated the first one concerns the global asymptotic feedback stabilization of homogeneous systems for these systems it is shown that local asymptotic stabilization implies the global dynamic feedback stabilization one the second problem consists to show that under a weak assumption on the observability if a state affine system is locally asymptotically stabilizable then it becomes globally asymptotically stabilizable by using a discontinuous output feedback

a pathway from bayesian statistical analysis to superstatistics abstract superstatistics and tsallis statistics in statistical mechanics are given an interpretation in terms of bayesian statistical analysis subsequently superstatistics is extended by replacing each component of the conditional and marginal densities by mathai s pathway model and further both components are replaced by mathai s pathway models this produces a wide class of mathematically and statistically interesting functions for prospective applications in statistical physics it is pointed out that the final integral is a particular case of a general class of integrals introduced by the authors earlier those integrals are also connected to kratzel integrals in applied analysis inverse gaussian densities in stochastic processes reaction rate integrals in the theory of nuclear astrophysics and tsallis statistics in nonextensive statistical mechanics the final results are obtained in terms of fox s h function matrix variate analogue of one significant specific case is also pointed out

homogeneous feedback controls for homogeneous systems let x x j 2n aj x xj be a real analytic n dimensional vector field with x 0 0 which is homogeneous of degree m 0 with respect to a dilation erx er1x1 ernxn and y xj we show that control system x x x uy admits a continuous asymptotically stabilizing feedback control u x then a one dimensional dynamic extension of the system admits a homogeneous asymptotically stabilizing dynamic feedback control u x such that the vector field w x 1 m u x 1 j 2aj x xj describing the extended controlled system is homogeneous of degree m with respect to the extended dilation er x e er1x1 ernxn