eigenvalue based algorithms for testing positive realness of siso systems a computational test for scalar positive real and strictly positive real functions is proposed in this paper the input for this algorithm is state space representation not necessarily minimal it is derived for the discrete time problem based on numerical stable eigenvalue computations the test can be used in the continuous counterpart which is in fact an improvement of an algorithm posed by bai and freund differences between the discrete and continuous time problems are also pointed out

a study of boundedness in probabilistic normed spaces probabilistic normed spaces have been redefined by alsina schweizer and sklar we give a detailed analysis of various boundedness notions for linear operators between such spaces and we study the relationship among them and also with the notion of continuity

the complexity probabilistic quasi metric space we introduce and study a probabilistic quasi metric on the set of complexity functions which provides an efficient framework to measure the distance from a complexity function f to another one g in the case that f is asymptotically more efficient than g in this context we also obtain a version of the banach fixed point theorem which allows us to show that the functionals associated both to divide and conquer algorithms and quicksort algorithms have a unique fixed point

design of strictly positive real systems using constant output feedback the authors present a linear matrix inequality lmi approach to the strictly positive real spr synthesis problem find an output feedback k such that the closed loop system t s is spr the authors establish that if no such constant output feedback k exists then no dynamic output feedback with a proper transfer matrix exists to make the closed loop system spr the existence of k to guarantee the spr property of the closed loop system is used to develop an adaptive control scheme that can stabilize any system of arbitrary unknown order and unknown parameters

gradient elasticity in statics and dynamics an overview of formulations length scale identification procedures finite element implementations and new results in this paper we discuss various formats of gradient elasticity and their performance in static and dynamic applications gradient elasticity theories provide extensions of the classical equations of elasticity with additional higher order spatial derivatives of strains stresses and or accelerations we focus on the versatile class of gradient elasticity theories whereby the higher order terms are the laplacian of the corresponding lower order terms one of the challenges of formulating gradient elasticity theories is to keep the number of additional constitutive parameters to a minimum we start with discussing the general mindlin theory that in its most general form has 903 constitutive elastic parameters but which were reduced by mindlin to three independent material length scales further simplifications are often possible in particular the aifantis theory has only one additional parameter in statics and opens up a whole new field of analytical and numerical solution procedures we also address how this can be extended to dynamics an overview of length scale identification and quantification procedures is given finite element implementations of the most commonly used versions of gradient elasticity are discussed together with the variationally consistent boundary conditions details are provided for particular formats of gradient elasticity that can be implemented with simple linear finite element shape functions new numerical results show the removal of singularities in statics and dynamics as well as the size dependent mechanical response predicted by gradient elasticity

robust stabilization with positive real uncertainty beyond the small gain theory in many applications of feedback control phase information is available concerning the plant uncertainty for example lightly damped flexible structures with colocated rate sensors and force actuators give rise to positive real transfer functions closed loop stability is thus guaranteed by means of negative feedback with strictly positive real compensators in this paper the properties of positive real transfer functions are used to guarantee robust stability in the presence of positive real but otherwise unknown plant uncertainty these results are then used for controller synthesis to address the problem of robust stabilization in the presence of positive real uncertainty one of the principal motivations for these results is to utilize phase information in guaranteeing robust stability in this these sense results go beyond the usual limitations the small gain theorem and quadratic lyapunov functions which may be conservative when phase information is available the results of this paper are based upon a riccati equation formulation of the positive real lemma and thus are in the spirit of recent riccati based approaches to bounded real h control

the topological structure of a certain menger space in this paper we will reconsider the topological structure of menger probabilistic normed spaces briefly pn spaces under the t norm m we will prove that this topology is compatible with the topology induced by a countable and separating family of semi norms and hence the well known theorems of classical functional analysis such as the principle of uniform boundedness open mapping and closed graph theorems are valid in this context also we will meanwhile obtain a method by which one may construct easily a large class of pn spaces finally using this method we see that a certain subspace of bounded linear operators between pn spaces i e the class of strongly bounded linear operators has a natural pn structure

tractions balances and boundary conditions for nonsimple materials with application to liquid flow at small length scales using a nonstandard version of the principle of virtual power we develop general balance equations and boundary conditions for second grade materials our results apply to both solids and fluids as they are independent of constitutive equations as an application of our results we discuss flows of incompressible fluids at small length scales in addition to giving a generalization of the navier stokes equations involving higher order spatial derivatives our theory provides conditions on free and fixed boundaries the free boundary conditions involve the curvature of the free surface among the conditions for a fixed boundary are generalized adherence and slip conditions each of which involves a material length scale we reconsider the classical problem of plane poiseuille flow for generalized adherence and slip conditions

probabilistic lp spaces abstract in this paper we define the notion of a probabilistic valued measure and the corresponding l p spaces with suitable interpretations we also prove holder s inequality these results give us sufficient motivations to define probabilistic dual spaces and probabilistic inner product spaces for which the probabilistic l 2 space serves as a model

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

strictly positive real transfer functions revisited the two most commonly used definitions of strictly positive real spr transfer functions are reviewed contrary to what has been suggested in the literature it is proven that the least restrictive weak definition of the two is clearly related to the yacubovich kalman lemma the relationship between time and frequency domain conditions pertaining to the weak definition of spr systems is established

synthesis of strictly positive real ℋ2 controllers using dilated lmis abstractthis paper considers strictly positive real spr controller design via direct minimisation of an upper bound on the closed loop h2 norm to realise a tractable design problem an observer

characterizations of metrizable topological vector spaces and their asymmetric generalizations in terms of fuzzy quasi norms we obtain characterizations of those paratopological vector spaces that are quasi metrizable locally bounded quasi metrizable locally convex and quasi normable respectively in terms of appropriate kinds of fuzzy quasi norms characterizations of distinguished kinds of metrizable topological vector spaces some of them known already are deduced as particular cases of our approach

frequency domain conditions for strictly positive real functions frequency domain conditions for strictly positive real spr functions which appear in literature are often only necessary or only sufficient this point is raised in 1 2 where necessary and sufficient conditions in the s domain are given for a transfer function to be spr in this note the points raised in 1 i2 are clarified further by giving necessary and sufficient conditions in the frequency domain for transfer functions to be spr these frequency domain conditions are easier to test than those given in the s domain or time domain 1 2

some topologies on a serstnev probabilistic normed space abstract in this paper we will introduce two other topologies coarser than the so called strong topology on a class of serstnev probabilistic normed spaces and obtain some important properties of these topologies we will show that under the first topology denoted by 0 our probabilistic normed space is decomposable into the topological direct sum of a normable subspace and the subspace of probably null elements under the second topology which is in fact the inductive limit topology of a family of locally convex topologies the dual space becomes a locally convex topological vector space

low order multivariable adaptive control with application to flexible structures all adaptive controllers require a certain amount of prior information regarding the plant to be controlled to achieve the desired control objectives in the context of multivariable adaptive control not only is the prior information quite significant but also the complexity of the adaptive controller is too high in this paper we introduce a low order multivariable adaptive controller that is easy to implement and requires less prior information than most other adaptive controllers

time domain and frequency domain conditions for strict positive realness the author states various time domain and frequency domain conditions pertaining to multivariate strict positive real systems and establishes the relationship between these conditions their relationship is clarified by means of a three tier diagram each tier represents a set of equivalent conditions successively stronger than the lower tier the main theorem in the present study can be considered as the positive realness lemma for strictly positive real systems

on a class of marginally stable positive real systems a class of marginally stable positive real systems is defined which is less restrictive than the previously published definitions of strictly positive real systems a minimal realization and state space characterization of such systems are presented and it is proven that controllers belonging to this class robustly stabilize positive real plants

on kalman yakubovich popov lemma for stabilizable systems the kalman yakubovich popov kyp lemma has been a cornerstone in system theory and network analysis and synthesis it relates an analytic property of a square transfer matrix in the frequency domain to a set of algebraic equations involving parameters of a minimal realization in time domain this note proves that the kyp lemma is also valid for realizations which are stabilizable and observable

on relationships among passivity positive realness and dissipativity in linear systems the notions of passivity and positive realness are fundamental concepts in classical control theory but the use of the terms has varied for lti systems these two concepts capture the same essential property of dynamical systems that is a system with this property does not generate its own energy but only stores and dissipates energy supplied by the environment this paper summarizes the connection between these two concepts for continuous and discrete time lti systems beyond that relationships are provided between classes of strictly passive systems and classes of positive real systems the more general framework of dissipativity is introduced to connect passivity and positive realness and also to survey other energy based results the frameworks of passivity indices and conic systems are discussed to connect to passivity and dissipativity after surveying relevant existing results some clarifying results are presented these involve connections between classes of passive systems and finite gain l2l2 stability as well as asymptotic stability additional results are given to clarify some of the more subtle conditions between classes of these systems and stability results this paper surveys existing connections between classes of passive and positive real systems and provides results that clarify more subtle connections between these concepts

higher order nonlinear complementary filtering on lie groups nonlinear observer design for systems whose state space evolves on lie groups is considered the proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model and corrects the propagated state estimate using an innovation term on the tangent space of the lie group in the proposed method the innovation term is constructed by passing the gradient of an invariant cost function resolved in a basis of the tangent space through a linear time invariant system the introduction of the linear system completes the extension of linear complementary filters to nonlinear lie group observers by allowing higher order filtering in practice the proposed method allows for greater design freedom and with the appropriate selection of the linear filter the ability to filter bias and noise over specific bandwidths a disturbance observer that accounts for constant and harmonic disturbances in group velocity measurements is also considered local asymptotic stability about the desired equilibrium point is demonstrated a numerical example that demonstrates the desirable properties of the observer is presented in the context of pose estimation

a second strain gradient elasticity theory with second velocity gradient inertia part ii dynamic behavior abstract this paper is the sequel of a companion part i paper devoted to the constitutive equations and to the quasi static behavior of a second strain gradient material model with second velocity gradient inertia in the present part ii paper a multi cell homogenization procedure developed in the part i paper is applied to a nonhomogeneous body modelled as a simple material cell system in conjunction with the principle of virtual work pvw for inertial actions i e momenta and inertia forces which at the macro scale level takes on the typical format as for a second velocity gradient inertia material model the latter macro scale pvw is used to determine the equilibrium equations relating the ordinary double and triple generalized momenta to the inertia forces as a consequence of the surface effects the latter inertia forces include ordinary inertia body forces within the bulk material as well as ordinary and double inertia surface tractions on the boundary layer and ordinary inertia line tractions on the edge line rod they all depend on the acceleration in a nonstandard way but the classical laws are recovered in the case of no higher order inertia the classical linear and angular momentum theorems are extended to the present context of second velocity gradient inertia showing that the extended theorems used in conjunction with the cauchy traction theorem lead to the local force and moment stress symmetry motion equations just like for a classical continuum a gradient elasticity theory is proposed whereby the dynamic evolution problem for assigned initial and boundary conditions is shown to admit a hamilton type variational principle the uniqueness of the solution is also discussed a few simple applications to wave propagation and dispersion problems are presented the paper indicates the correct way to describe the inertia forces in the presence of higher order inertia it extends and improves previous findings by the author polizzotto c 2012 a gradient elasticity theory for second grade materials and higher order inertia int j solids struct 49 2121 2137 overall conclusions are drawn at the end of the paper

a gradient elasticity theory for second grade materials and higher order inertia abstract second grade elastic materials featured by a free energy depending on the strain and the strain gradient and a kinetic energy depending on the velocity and the velocity gradient are addressed an inertial energy balance principle and a virtual work principle for inertial actions are envisioned to enrich the set of traditional theoretical tools of thermodynamics and continuum mechanics the state variables include the body momentum and the surface momentum related to the velocity in a nonstandard way as well as the concomitant mass accelerations and inertial forces which do intervene into the motion equations and into the force boundary conditions the boundary traction is the sum of two parts i e the cauchy traction and the gurtin murdoch traction whereas the traction boundary condition exhibits the typical format of the equilibrium equation of a material surface as known from the principles of surface mechanics whereby the gurtin murdoch traction incorporating the inertial surface force plays the role of applied surfacial force density the body s boundary surface constitutes a thin boundary layer which is in global equilibrium under all the external forces applied on it a feature that makes it possible to exploit the traction cauchy theorem within second grade materials this means that a second grade material is formed up by two sub systems that is the bulk material operating as a classical cauchy continuum and the thin boundary layer operating as a gurtin murdoch material surface the classical linear and angular momentum theorems are suitably extended for higher order inertia from which the local motion equations and the moment equilibrium equations stress symmetry can be derived for an isotropic material featured by four constants i e the lame constants and two length scale parameters aifantis model the dynamic evolution problem is characterized by a hamilton type variational principle and a solution uniqueness theorem closed form solutions of the wave dispersion analysis problem for beam models are presented and compared with known results from the literature the paper indicates a correct thermodynamically consistent way to take into account higher order inertia effects within continuum mechanics

strictly positive real matrices and the lefschetz kalman yakubovich lemma the authors give necessary and sufficient conditions in the frequency domain for rational matrices to be strictly positive real based on this result the matrix form of the lefschetz kalman yakubovich lemma is proved which gives necessary and sufficient conditions for strictly positive real transfer matrices in the state space realization form