stability analysis for continuous time positive systems with time varying delays this note addresses the stability problem of continuous time positive systems with time varying delays it is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a hurwitz matrix the result is a time varying version of the widely known asymptotic stability criterion for constant delay positive systems a numerical example illustrates the correctness of our result

frequency limited h controller order reduction for linear parameter varying systems abstractin this paper a controller order reduction method for linear parameter varying systems is presented the proposed method is based on the frequency weighted balanced truncation technique which has the advantage to reduce the order in a specific frequency range the approach is discussed and is proved to preserve the closed loop stability with a guaranteed upper error bound effectiveness and performance of the obtained reduced order controller are investigated by applying it to an automotive semi active suspension control the obtained simulation results show that objectives such as the road handling and the passenger comfort realised with the reduced order controller are kept in the same performance level as with the full order controller moreover a comparison with an other order reduction method is shown and confirms the advantage of the developed method

on a new non isospectral variant of the boussinesq hierarchy we give a new non isospectral extension to 2 1 dimensions of the boussinesq hierarchy such a non isospectral extension of the third order scattering problem xxx u x v 0 has not been considered previously this extends our previous results on one component hierarchies in 2 1 dimensions associated to third order non isospectral scattering problems we characterize our entire 2 1 dimensional hierarchy and its linear problem using a single partial differential equation and its corresponding non isospectral scattering problem this then allows an alternative approach to the construction of linear problems for the entire 2 1 dimensional hierarchy reductions of this hierarchy yield new integrable hierarchies of systems of ordinary differential equations together with their underlying linear problems in particular we obtain a fourth painleve hierarchy i e a hierarchy of ordinary differential equations having the fourth painleveequation as its first member we also obtain a hierarchy having as its first member a generalization of an equation defining a new transcendent due to cosgrove

passivity preserving model reduction with finite frequency h approximation performance this paper is concerned with model reduction for passive systems for a given linear time invariant system that is stable and positive real pr our goal is to find a pr reduced order model to approximate it and our attention is focused on reducing the error with respect to a finite frequency h performance which is the most remarkable difference between the proposed approach and the existing ones first by applying multiplier expansion new conditions in terms of linear matrix inequalities are derived for characterizing the positive realness of the reduced order model and the finite frequency h performance of the error system a necessary and sufficient condition is then established for parameterizing a pr reduced order model with finite frequency h approximation performance based on which an iterative algorithm is constructed for numerically exploring such a reduced order model particularly a partial multiplier expansion treatment is introduced which greatly reduces the decision variables but does not cause conservatism to the derived conditions the proposed method is also extended to robust passivity reserving model reduction with polytopic uncertainty finally we provide two numerical examples about rlc circuits to show the effectiveness and advantages of the proposed model reduction method

l1 induced norm and controller synthesis of positive systems in this paper the problem of 1 1 induced controller design for discrete time positive systems is investigated with the use of linear lyapunov function an analytical method to compute the exact value of 1 1 induced norm is first presented then a novel characterization for stability and 1 1 induced performance is proposed based on the characterization a necessary and sufficient condition for the existence of desired controllers is derived and an iterative convex optimization approach is developed to solve the condition in addition the synthesis of the state feedback controller for single input multiple output simo positive systems is investigated for this special case an analytic solution is established to show how the optimal 1 1 induced controller can be designed and some links to the spectral radius of the closed loop systems are provided finally the theoretical results are illustrated through a numerical example

shape analysis via oriented distance functions the object of this paper is twofold we first present constructions which induce topologies on subsets of a fixed domain or hold all d in rn by using set parameterized functions in an appropriate function space second we study the role of the family of oriented distance functions also known as algebraic or signed distance functions in the analysis of shape optimization problems they play an important role in the introduction of topologies which retain the classical geometric properties associated with sets convexity exterior normals mean curvature ck boundaries etc

stability and l1 gain analysis of linear periodic piecewise positive systems this paper investigates the stability stabilization and l1 gain of linear periodic piecewise positive systems the monotonicity of linear periodic piecewise positive systems is first studied then a time varying co positive lyapunov function for periodic piecewise positive systems is employed and a sufficient condition for the asymptotic stability of the system is established based on the provided co positive lyapunov function and the sufficient stability condition a state feedback periodic piecewise controller to stabilize the system is formed and an upper bound of l1 gain of the system is given finally numerical examples are given to illustrate the theoretical results

positive output state maps and quasi positive realization of mimo discrete systems the positive realization of externally positive systems described by their transfer matrix g z is a complex problem whose analysis has been completed only recently for the siso case on the basis of algebraic and geometric approaches that underline the many constraints that condition its solution these constraints concern the minimal order of the obtained models the minimality of their parameterizations and even their existence this paper considers the new category of quasi positive state space models introduced in guidorzi 2014 that limit the assumptions on the nonnegativeness of the state space trajectories to the only trajectories that can be actually generated by the system under nonnegative controls it is shown that all externally positive systems admit a quasi positive minimally parameterized state space realization whose existence is not conditioned by restrictions on the signs of the parameters of the polynomials in g z

improved results on h model reduction for markovian jump systems with partly known transition probabilities abstract this paper is concerned with the model reduction problem for markovian jump systems with partly known transition probabilities by making use of an existing result on the convex properties of the transition probabilities an improved condition is first derived for the h performance analysis of the error system two different approaches one in terms of linear matrix inequalities lmis and another in the form of an iterative algorithm subject to lmi constraints are then proposed to find a reduced order model such that the h performance of the error system is bounded by a specified level the first approach is obtained using finsler s lemma and involves fewer decision variables than the existing method it is shown that the proposed methods cover some existing results as special cases finally the advantages of our results are clearly illustrated by a numerical example

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

brief paper positivity preserving h model reduction for positive systems this paper is concerned with the model reduction of positive systems for a given stable positive system our attention is focused on the construction of a reduced order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed h performance based upon a system augmentation approach a novel characterization on the stability with h performance of the error system is first obtained in terms of linear matrix inequality lmi then a necessary and sufficient condition for the existence of a desired reduced order model is derived accordingly furthermore iterative lmi approaches with primal and dual forms are developed to solve the positivity preserving h model reduction problem finally a compartmental network is provided to show the effectiveness of the proposed techniques

brief paper stability of switched positive linear systems with average dwell time switching in this paper the stability analysis problem for a class of switched positive linear systems splss with average dwell time switching is investigated a multiple linear copositive lyapunov function mlclf is first introduced by which the sufficient stability criteria in terms of a set of linear matrix inequalities are given for the underlying systems in both continuous time and discrete time contexts the stability results for the splss under arbitrary switching which have been previously studied in the literature can be easily obtained by reducing mlclf to the common linear copositive lyapunov function used for the system under arbitrary switching those systems finally a numerical example is given to show the effectiveness and advantages of the proposed techniques

finite time balanced truncation for linear systems via shifted legendre polynomials abstract in this paper we present a finite time model order reduction method for linear systems via shifted legendre polynomials the main idea of the approach is to use finite time empirical gramians which are constructed from impulse responses by solving block tridiagonal linear systems to generate approximate balanced system for the large scale system the balancing transformation is directly computed from the expansion coefficients of impulse responses in the space spanned by shifted legendre polynomials without individual reduction of the gramians and a separate eigenvector solve then the reduced order model is constructed by truncating the states corresponding to the small approximate hankel singular values hsvs the stability preservation of the reduced model is briefly discussed and in combination with the dominant subspace projection method we modify the reduction procedure to alleviate the shortcomings of the above method which may unexpectedly lead to unstable systems even though the original one is stable furthermore the properties of the resulting reduced models are considered finally numerical experiments are given to demonstrate the effectiveness of the proposed methods

a boundary differential equation for thin shells abstract we present a mathematical construction of boundary equations for thin shells from classical elasticity by using the differential boundary calculus and the oriented distance function this model extends to thin shells the natural theory and the theory of love kirchhoff as given by germain for plates we specify the appropriate function spaces and give existence and uniqueness theorems we conjecture that our second order model is related to the one of naghdi and that the fourth order model is related to the one of koiter

the optimum finger spacing in human swimming competitive swimmers spread fingers during the propulsive stroke due to the inherent inefficiency of human swimming the question is does this strategy enhance performance or is it just a more comfortable hand posture here we show through computational fluid dynamics cfd of a 3d model of the hand that an optimal finger spacing 12 degrees roughly corresponding to the resting hand posture increases the drag coefficient 8 8 which is functionally equivalent to a greater hand palm area thus a lower stroke frequency can produce the same thrust with benefits to muscle hydraulic and propulsive efficiencies cfd through flow visualization provides an explanation for the increased drag associated with the optimum finger spacing

generalized kyp lemma with real data a recent generalization of the kalman yakubovich popov kyp lemma establishes the equivalence between a semi infinite inequality on a segment of a line or circle in the complex plane and a linear matrix inequality lmi in this technical note we show that when the data are real the matrix variables in the lmi can be restricted to be real even when the frequency range is asymmetric with respect to the real axis

blind separation of instantaneous mixtures of nonstationary sources most source separation algorithms are based on a model of stationary sources however it is a simple matter to take advantage of possible nonstationarities of the sources to achieve separation this paper develops novel approaches in this direction based on the principles of maximum likelihood and minimum mutual information these principles are exploited by efficient algorithms in both the off line case via a new joint diagonalization procedure and in the on line case via a newton like procedure some experiments showing the good performance of our algorithms and evidencing an interesting feature of our methods are presented their ability to achieve a kind of super efficiency the paper concludes with a discussion contrasting separating methods for non gaussian and nonstationary models and emphasizing that as a matter of fact what makes the algorithms work is strictly speaking not the nonstationarity itself but rather the property that each realization of the source signals has a time varying envelope

an existence result for a class of shape optimization problems given a bounded open subset of rn we prove the existence of a minimum point for a functional f defined on the family a of all quasiopen subsets of under the assumption that f is decreasing with respect to set inclusion and that f is lower semicontinuous on a with respect to a suitable topology related to the resolvents of the laplace operator with dirichlet boundary condition applications are given to the existence of sets of prescribed volume with minimal kth eigenvalue or with minimal capacity with respect to a given elliptic operator

structure of shape derivatives for nonsmooth domains abstract the object of this paper is to study the shape gradient and the shape hessian by the velocity speed method for arbitrary domains with or without constraints it makes the connection between methods using a family of transformations such as first or second order perturbations of the identity operator new definitions for shape derivatives are given they naturally extend existing theories for ck or lipchitzian domains to arbitrary domains without any smoothness conditions on their geometric boundary in this new framework extensions of the classical structure theorems are given for the shape gradient and the shape hessian

design of positive linear observers for positive linear systems via coordinate transformations and positive realizations two new approaches to designing positive linear observers for positive linear systems are proposed the first one employs a coordinates transformation and the second relies on the theory of positive realization these approaches allow one to enlarge the class of positive systems that admit positive linear observers new results on compartmental systems are also presented

a survey of model reduction by balanced truncation and some new results balanced truncation is one of the most common model reduction schemes in this note we present a survey of balancing related model reduction methods and their corresponding error norms and also introduce some new results five balancing methods are studied 1 lyapunov balancing 2 stochastic balancing 3 bounded real balancing 4 positive real balancing and 5 frequency weighted balancing for positive real balancing we introduce a multiplicative type error bound moreover for a certain subclass of positive real systems a modified positive real balancing scheme with an absolute error bound is proposed we also develop a new frequency weighted balanced reduction method with a simple bound on the error system based on the frequency domain representations of the system gramians two numerical examples are illustrated to verify the efficiency of the proposed methods

manifold derivative in the laplace beltrami equation abstract this paper is concerned with the derivative of the solution with respect to the manifold more precisely with theshape tangentialsensitivity analysis of the solution to the laplace beltrami boundary value problem with homogeneous dirichlet boundary conditions the domain is an open subset of a smooth compact manifold of r n the flow of a vector fieldv t changes in t and in t the relative boundary tof tin tis smooth enough andy t is the solution in tof the laplace dirichlet problem with zero boundary value on t the shape tangential derivative is characterized as being the solution of a similar non homogeneous boundary value problem that elementy v can be simply defined by the restriction to ofy y vwhereyis the material derivative ofyand yis the tangential gradient ofy the study splits in two parts whether the relative boundary of is empty or not in both cases the shape derivative depends on the deviatoric part of the second fundamental form of the surface on the fieldv 0 through its normal component on and on the tangential fieldv 0 through its normal component on the relative boundary we extend the structure results for theshape tangentialderivative making use ofintrinsic geometryapproach and intensive use of extension operators

domain perturbation for linear and nonlinear parabolic equations abstract we shall develop a general theory for domain perturbation for linear and nonlinear parabolic equations with measurable coefficients subject to dirichlet boundary conditions we show how solutions of linear and nonlinear parabolic equations behave as a sequence of domains approaches an open set convergence of domains is understood in a very general sense which allows that certain parts of the domains degenerate and are deleted in the limit or that small sets are removed we also consider the periodic problem and establish existence and uniqueness results for periodic solutions for the perturbed problem in a neighborhood of a periodic solution of the original equation the theory can be used for instance to construct domains where a given nonlinear periodic parabolic equation has many periodic solutions

stabilization of positive linear systems we consider stabilization of equilibrium points of positive linear systems which are in the interior of the first orthant the existence of an interior equilibrium point implies that the system matrix does not possess eigenvalues in the open right half plane this allows to transform the problem to the stabilization problem of compartmental systems which is known and for which a solution has been proposed already we provide necessary and sufficient conditions to solve the stabilization problem by means of affine state feedback a class of stabilizing feedbacks is given explicitly

frequency limited mmb h _ infty model reduction for positive systems in this paper the problem of frequency limited mmb h infty model reduction for positive linear time invariant systems is investigated specifically our goal is to find a stable positive reduced order model for a given positive system such that the mmb h infty norm of the error system is bounded over a frequency interval of interest a new condition in terms of matrix inequality is developed for characterizing the frequency limited mmb h infty performance then an equivalent parametrization of a positive reduced order model is derived based on which an iterative algorithm is constructed for optimizing the reduced order model the algorithm utilizes coarse reduced order models resulting from generalized balanced truncation as the initial value both continuous and discrete time systems are considered in the same framework numerical examples clearly show the effectiveness and advantages of the proposed model reduction method

internally positive representation of a class of continuous time systems the problem of realizing arbitrary transfer functions as combinations of positive filters or more in general of representing arbitrary systems by means of internally positive representations iprs has been widely investigated in the discrete time framework an ipr is a positive state space representation endowed with input state and output transformations that realizes arbitrary input state output dynamics this technical note investigates the problem of the ipr construction for continuous time systems and proposes a technique that provides stable iprs for a particular class of systems

minimal positive realizations of transfer functions with real poles a standard result of linear system theory states that a single input single output siso rational n th order transfer function always has a state space realization of the same order in some applications one is interested in having a realization with nonnegative entries i e a positive system and it is known that such constraints may lead to a minimal order positive realization of order much greater than the transfer function order n in this technical note necessary and sufficient conditions for a third order transfer function with distinct real poles to have a third order positive realization are given these conditions are expressed in terms of lower bounds for the first three samples of the impulse response and therefore are very easy to check this result is an extension of a previous result for transfer functions with distinct real positive poles

positivity preserving balanced truncation for descriptor systems we propose a model reduction method for positive systems that ensures the positivity of the reduced order model in the standard as well as in the descriptor case for continuous time and discrete time systems our approach is based on constructing diagonal solutions of lyapunov inequalities these are linear matrix inequalities lmis which are shown to be feasible positivity and stability are preserved and an error bound in the mathcal h infty norm is provided

generalized kyp lemma unified frequency domain inequalities with design applications the celebrated kalman yakubovic spl caron popov kyp lemma establishes the equivalence between a frequency domain inequality fdi and a linear matrix inequality and has played one of the most fundamental roles in systems and control theory this paper first develops a necessary and sufficient condition for an s procedure to be lossless and uses the result to generalize the kyp lemma in two aspects the frequency range and the class of systems and to unify various existing versions by a single theorem in particular our result covers fdis in finite frequency intervals for both continuous discrete time settings as opposed to the standard infinite frequency range the class of systems for which fdis are considered is no longer constrained to be proper and nonproper transfer functions including polynomials can also be treated we study implications of this generalization and develop a proper interface between the basic result and various engineering applications specifically it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain phase properties in several frequency ranges the method is illustrated by numerical design examples of digital filters and proportional integral derivative controllers

multiplicative approximation of transfer functions with frequency weighting abstract an algorithm for transfer function order reduction is presented which generalizes the balanced stochastic truncation algorithm to allow for input weighting an example illustrates use of the algorithm to secure smaller db error in selected frequency bands through the introduction of the weighting

a finite element boundary element method for three dimensional large displacement fluid structure interaction abstract this paper presents a hybrid finite element boundary element method for fluid structure interaction simulations of inflatable structures the flow model consists of the steady stokes equation which admits a boundary integral formulation the structure is represented by a kirchhoff love shell the boundary element approximation of the stokes equation reduces the flow problem to an integral equation on the actual structure configuration thus obviating the need for volumetric meshing of the strongly deforming fluid domain the stokes model moreover exhibits a lubrication effect that acts as an intrinsic mechanism to treat the ubiquitous self contact that occurs in inflation problems the aggregated fluid structure interaction problem composed of the boundary integral equation and the kirchhoff love shell connected by dynamic and kinematic interface conditions is approximated by means of isogeometric discretizations to accommodate the smoothness requirements on the approximation spaces imposed by the flexural rigidity in the kirchhoff love shell and to provide an accurate and smooth representation of the boundary for the boundary element method auxiliary results presented in this paper are 1 a parametrization free kirchhoff love formulation 2 establishment of a cubic relationship between distance and tractions due to the lubrication effect and 3 the interpretation of the lagrange multiplier pertaining to fluid incompressibility as the total excess pressure

induced l 2 norm model reduction of polytopic uncertain linear systems abstract in this paper we study an induced l 2 norm model reduction problem for polytopic uncertain linear systems the polytopic system has its state space data contained in a convex polytope a situation which often arises the problem we address is to approximate this type of system by a lower order polytopic uncertain linear system with a guaranteed induced l 2 norm error a sufficient solvability condition is provided in terms of lmis with one extra coupling rank constraint which generally leads to a nonconvex feasibility problem we use an improved computational scheme based on the alternating projection method to obtain solutions to the problem but only local convergence is guaranteed the reduced order uncertain system with its associated polytope is given explicitly by the solution of the feasibility problem