problems on time varying port controlled hamiltonian systems geometric structure and dissipative realization to apply time varying port controlled hamiltonian pch systems to practical control designs two basic problems should be dealt with one is how to provide such time varying systems a geometric structure to guarantee the completeness of representations in mathematics and the other is how to express the practical system under consideration as a time varying pch system which is called the dissipative hamiltonian realization problem the paper investigates the two basic problems a suitable geometric structure for time varying pch systems is proposed first then the dissipative realization problem of time varying nonlinear systems is investigated and serval new methods and sufficient conditions are presented for the realization

x simple image eigencones of tropical matrices abstract we investigate max algebraic tropical one sided systems a x b where b is an eigenvector and x lies in an interval x a matrix a is said to have x simple image eigencone associated with an eigenvalue if any eigenvector x associated with and belonging to the interval x is the unique solution of the system a y x in x we characterize matrices with x simple image eigencone geometrically and combinatorially and for some special cases derive criteria that can be efficiently checked in practice

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

solving systems of linear fuzzy equations by parametric functions an improved algorithm buckley and qu proposed a method to solve systems of linear fuzzy equations basically in their method the solutions of all systems of linear crisp equations formed by the a levels are calculated we propose a new method for solving systems of linear fuzzy equations based on a practical algorithm using parametric functions in which the variables are given by the fuzzy coefficients of the system by observing the monotonicity of the parametric functions in each variable i e each fuzzy coefficient in the system we improve the algorithm by calculating less parametric functions and less evaluations of these parametric functions we show that our algorithm is much more efficient than the method of buckley and qu

stabilization of hamiltonian systems with nonholonomic constraints based on time varying generalized canonical transformations this paper is concerned with the stabilization of nonholonomic systems in port controlled hamiltonian formulae based on time varying generalized canonical transformations a special class of time varying generalized canonical transformations are introduced which modify the kinetic energy of the original system without changing the generalized hamiltonian structure with passivity utilizing these transformations time varying asymptotically stabilizing controllers for the nonholonomic hamiltonian systems are derived since the proposed method is a natural generalization of passivity based control for conventional holonomic systems it is expected that the tools developed for conventional systems will be applicable to nonholonomic systems based on the proposed method

using mixture models to detect sex bias in health outcomes in bangladesh abstract many interesting economic hypotheses entail differences in behaviors of groups within a population but analyses of pooled samples shed only partial light on underlying segmentations finite mixture models are considered as an alternative to methods based on pooling robustness checks using t regressions and a bayesian analogue to the likelihood ratio test for model evaluation are developed the methodology is used to investigate pro son bias in child health outcomes in bangladesh while regression analysis on the entire sample appears to wash out evidence of bias the mixture models reveal systematic girl boy differences in health outcomes

brief paper canonical transformations used to derive robot control laws from a port controlled hamiltonian system perspective this paper addresses the problem of deriving control laws for robot manipulators in the framework of port controlled hamiltonian systems via canonical transformations and passivity based control the control design is focused on the presentation of a new energy shaping methodology for tracking control based on the introduction of virtual non homogeneous fields where a desired energy is defined to compensate for the actual energy of the robot manipulator while a virtual field forces the system to track a general reference trajectory this requires use of the legendre fenchel transformation and allows for the derivation standard control laws in the robotics field such as pd control with gravity compensation or pd with precompensation finally the passivity of the input output mapping of the non autonomous hamiltonian system is analyzed in detail resulting in new lyapunov candidate functions having their roots in physics

iterative learning control of hamiltonian systems i o based optimal control approach in this note a novel iterative learning control scheme for a class of hamiltonian control systems is proposed which is applicable to electromechanical systems the proposed method has the following distinguished features this method does not require either the precise knowledge of the model of the target system or the time derivatives of the output signals despite the lack of information the tracking error monotonously decreases in l sub 2 sense and further perfect tracking is achieved when it is applied to mechanical systems the self adjoint related properties of hamiltonian systems proven in this note play the key role in this learning control those properties are also useful for general optimal control furthermore experiments of a robot manipulator demonstrate the effectiveness of the proposed method

max algebraic attraction cones of nonnegative irreducible matrices abstract it is known that the max algebraic powers ar of a nonnegative irreducible matrix are ultimately periodic this leads to the concept of attraction cone attr a t by which we mean the solution set of a two sided system t a ar x ar t x where r is any integer after the periodicity transient t a and a is the maximum cycle geometric mean of a a question which this paper answers is how to describe attr a t by a concise system of equations without knowing t a this study requires knowledge of certain structures and symmetries of periodic max algebraic powers which are also described we also consider extremals of attraction cones in a special case and address the complexity of computing the coefficients of the system which describes attraction cone

interval systems of max separable linear equations for a given matrix interval a a a and a given vector interval b b b the notation a x b if max represents an interval system of linear max separable equations we define and characterize several types of solutions and solvability of interval systems of max separable linear equations

reachability of eigenspaces for interval circulant matrices in max algebra abstract a nonnegative matrix a is said to be strongly robust if its max algebraic eigencone is universally reachable i e if the orbit of any initial vector ends up with a max algebraic eigenvector of a consider the case when the initial vector is restricted to an interval and a can be any matrix from a given interval of nonnegative circulant matrices the main aim of this paper is to classify and characterize the six types of interval robustness in this situation this naturally leads us also to study the max algebraic spectral theory of circulant matrices and the relation of inclusion between attraction cones of circulant matrices in max algebra

relaxing the conditions for parameter estimation based observers of nonlinear systems via signal injection parameter estimation based observers are a new kind of state reconstruction methods where the state observation task is translated into an on line parameter estimation problem a key step for its application is the transformation of the system dynamics into a particular cascade form which involves the solution of a partial differential equation that moreover should satisfy some injective requirement in this note we use a recently proposed technique of signal injection to generate new outputs and simplify these tasks in this way we make this observer applicable to a wider class of nonlinear systems even with indistinguishable states the application of the proposed approach is illustrated with the design of a novel sensorless controller for magnetic levitation systems

smoothly mixing regressions this paper extends the conventional bayesian mixture of normals model by permitting state probabilities to depend on observed covariates the dependence is captured by a simple multinomial probit model a conventional and rapidly mixing mcmc algorithm provides access to the posterior distribution at modest computational cost this model is competitive with existing econometric models as documented in the paper s illustrations the first illustration studies quantiles of the distribution of earnings of men conditional on age and education and shows that smoothly mixing regressions are an attractive alternative to nonbayesian quantile regression the second illustration models serial dependence in the s p 500 return and shows that the model compares favorably with arch models using out of sample likelihood criteria

control solvability of interval systems of max separable linear equations abstract for a given matrix interval a a a and a given vector interval b b b the notation a x b if max represents an interval system of linear max separable equations several types of solvability of interval systems are known we define control solvability weak control solvability and weak universal solvability and give necessary and sufficient condition for an interval system to be solvable according to each definition

approximate dissipative hamiltonian realization and construction of local lyapunov functions the key in applying energy based control approach is to be able to express the system under consideration as a dissipative hamiltonian system i e to obtain dissipative hamiltonian realization dhr for the system in general the precise dhr form is hard to obtain for nonlinear dynamic systems when a precise dhr does not exist for a dynamic system or such a precise realization is difficulty to obtain it is necessary to consider its approximate realization this paper investigates approximate dhr and construction of local lyapunov functions for time invariant nonlinear systems it is shown that every nonlinear affine system has an approximate dhr if linearization of the system is controllable based on the diagonal normal form of nonlinear dynamic systems a new algorithm is established for the approximate dhr finally we present the concept of kth degree approximate lyapunov function and provide a method to construct such a lyapunov function example studies show that the methodology presented in this paper is very effective

passivity based control of a class of hamiltonian systems with nonholonomic constraints this paper is concerned with state and output feedback stabilization of a class of port hamiltonian systems with nonholonomic constraints first we study canonical forms for port hamiltonian systems with nonholonomic constraints second we give a new state feedback stabilization method by using non smooth hamiltonian functions via generalized canonical transformations third we propose a dynamic output feedback stabilization method without measuring the velocity based on the corresponding state feedback result numerical examples demonstrate the effectiveness of the proposed method

on an intrinsic formulation of time variant port hamiltonian systems in this contribution we present an intrinsic description of time variant port hamiltonian systems as they appear in modeling and control theory this formulation is based on the splitting of the state bundle and the use of appropriate covariant derivatives which guarantees that the structure of the equations is invariant with respect to time variant coordinate transformations in particular we will interpret our covariant system representation in the context of control theoretic problems typical examples are time variant error systems related to trajectory tracking problems which allow for a hamiltonian formulation furthermore we will analyze the concept of collocation and the balancing interaction of power flows in an intrinsic fashion

simultaneous stabilization of a set of nonlinear port controlled hamiltonian systems this paper investigates simultaneous stabilization of a set of nonlinear port controlled hamiltonian pch systems and proposes a number of results on the design of simultaneous stabilization controllers for the pch systems firstly the case of two pch systems is studied using the dissipative hamiltonian structural properties the two systems are combined to generate an augmented pch system with which some results on the control design are then obtained for the case that there exist parametric uncertainties in the two systems hamiltonian structures an adaptive simultaneous stabilization controller is proposed when there are external disturbances and parametric uncertainties in the two systems two simultaneous stabilization controllers are designed for the systems one is a robust controller and the other is a robust adaptive one secondly the case of more than two pch systems is investigated and a new result is proposed for the simultaneous stabilization of the systems finally two illustrative examples are studied by using the results proposed in this paper simulations show that the simultaneous stabilization controllers obtained in this paper work very well

dynamic extension is unnecessary for stabilization via interconnection and damping assignment passivity based control interconnection and damping assignment passivity based control ida pbc is a technique that regulates the behavior of nonlinear systems assigning a desired port hamiltonian structure to the closed loop this basic idea introduced seven years ago has turned out to be very successful and has provided solutions to a wide variety of physical problems although ida pbc is originally formulated as a static state feedback technique a natural question that arises is whether it is possible to extend the realm of applicability of the method by considering dynamic controllers more precisely is the set of plants that is stabilizable with static state feedback ida pbc smaller than the one stabilizable with dynamic ida pbc the main contribution of this paper is to prove that the answer to this question is unfortunately negative

x robustness of interval circulant matrices in fuzzy algebra abstract fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by and where a b max a b a b min a b a matrix is x robust if its eigenspace is achieved starting at each vector from a given interval vector x the possible and universal x robustness of interval matrices over fuzzy algebra are defined polynomial algorithms for checking the possible and universal x robustness of interval circulant matrices are described

exponential stabilization of port hamiltonian boundary control systems via energy shaping this article is concerned with the exponential stabilization of a class of linear boundary control systems bcss in port hamiltonian form through energy shaping starting from a first feedback loop that is in charge of modifying the hamiltonian function of the plant a second control loop that guarantees exponential convergence to the equilibrium is designed in this way a major limitation of standard energy shaping plus damping injection control laws applied to linear port hamiltonian bcss namely the fact that only asymptotic convergence is assured has been removed

on matrix powers in max algebra abstract let a a ij r n n n 1 n and da be the digraph n i j a ij the matrix a is called irreducible if da is strongly connected and strongly irreducible if every max algebraic power of a is irreducible a is called robust if for every x with at least one finite component a k x is an eigenvector of a for some natural number k we study the eigenvalue eigenvector problem for powers of irreducible matrices this enables us to characterise robust irreducible matrices in particular robust strongly irreducible matrices are described in terms of eigenspaces of matrix powers

systems of linear interval equations this paper presents theory and methods for computing the exact bounds on the solution of a system of n linear equations in n variables whose coefficients and right hand sides vary in some real intervals finite and iterative methods are given based on results from linear complementarity theory also regularity conditions regularity testing and computing the exact inverse of an interval matrix are dealt with

new techniques for the analysis of linear interval equations abstract the basic properties of interval matrix multiplication and several well known solution algorithms for linear interval equations are abstracted by the concept of a sublinear map the new concept coupled with a systematic use of ostrowski s comparison operator in a form generalized to interval matrices is used to derive quantitative information about the result of interval gauss elimination andthe limit of various iterative schemes for the solution of linear interval equations moreover optimality results are prove for 1 the use of the midpoint inverse as a preconditioning matrix and 2 gauss seidel iteration with componentwise intersection this extends and improves results by scheu krawczyk and alefeld and herzberger

trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations this paper addresses trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations and passivity based control the main strategy adopted in this paper is to construct an error system which describes the dynamics of the tracking error by a passive port controlled hamiltonian system after obtaining the error system tracking control of the original system can be achieved by stabilizing the error system via passivity based approach first a fundamental framework is provided for constructing the error system via generalized canonical transformations then a concrete design procedure is derived for a class of electro mechanical systems furthermore the proposed method is applied to a magnetic levitation system and laboratory experiments demonstrate its effectiveness

repetitive control of hamiltonian systems based on variational symmetry this paper is concerned with repetitive control of hamiltonian systems which is based on iterative learning control utilizing the variational symmetry of those systems variational symmetry allows us to obtain an algorithm to solve a certain class of optimal control problems in a repetitive control framework therefore the proposed method can deal with not only trajectory tracking control problems but also optimal trajectory generation problems never before considered in a repetitive control framework a convergence analysis of this algorithm is also discussed furthermore some numerical simulations demonstrate the effectiveness of the proposed method

bounded stabilisation of stochastic port hamiltonian systems this paper proposes a stochastic bounded stabilisation method for a class of stochastic port hamiltonian systems both full actuated and underactuated mechanical systems in the presence of noise are considered in this class the proposed method gives conditions for the controller gain and design parameters under which the state remains bounded in probability the bounded region and achieving probability are both assignable and a stochastic lyapunov function is explicitly provided based on a hamiltonian structure although many conventional stabilisation methods assume that the noise vanishes at the origin the proposed method is applicable to systems under persistent disturbances

shaping the energy of mechanical systems without solving partial differential equations control of underactuated mechanical systems via energy shaping is a well established robust design technique unfortunately its application is often stymied by the need to solve partial differential equations pdes in this technical note a new fully constructive procedure to shape the energy for a class of mechanical systems that obviates the solution of pdes is proposed the control law consists of a first stage of partial feedback linearization followed by a simple proportional plus integral controller acting on two new passive outputs the class of systems for which the procedure is applicable is identified imposing some directly verifiable conditions on the systems inertia matrix and its potential energy function it is shown that these conditions are satisfied by three benchmark examples

linear matrix period in max plus algebra abstract linear periodicity of matrices in max plus algebra is studied it is proved that the linear period of a matrix can be computed in o n 3 time if the digraph of the matrix is strongly connected the general problem of deciding whether a given matrix is almost linear periodic is shown to be np complete

control by interconnection and standard passivity based control of port hamiltonian systems the dynamics of many physical processes can be suitably described by port hamiltonian ph models where the importance of the energy function the interconnection pattern and the dissipation of the system is underscored to regulate the behavior of ph systems it is natural to adopt a passivity based control pbc perspective where the control objectives are achieved shaping the energy function and adding dissipation in this paper we consider the pbc techniques of control by interconnection cbi and standard pbc in cbi the controller is another ph system connected to the plant through a power preserving interconnection to add up their energy functions while in standard pbc energy shaping is achieved via static state feedback in spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems the current version of cbi imposes a severe restriction on the plant dissipation structure that stymies its practical application on the other hand standard pbc which is usually derived from a uninspiring and non intuitive ldquopassive output generationrdquo viewpoint is one of the most successful controller design techniques the main objectives of this paper are 1 to extend the cbi method to make it more widely applicable in particular to overcome the aforementioned dissipation obstacle 2 to show that various popular variants of standard pbc can be derived proceeding from a unified perspective 3 to establish the connections between cbi and standard pbc proving that the latter is obtained restricting the former to a suitable subset providing a nice geometric interpretation to standard pbc and comparing the size of the set of ph plants for which they are applicable

power based control canonical coordinate transformations integral and adaptive control power based modeling was originally developed in the early sixties to describe a large class of nonlinear electrical rlc networks in a special gradient form recently this idea has been extended for modeling and control of a larger class of physical systems in this paper first coordinate transformations are introduced for systems described in this framework such that the physical structure is preserved such a transformation can provide new insights for both analysis and control design second power based integral and adaptive control schemes are presented advantages of these schemes are shown by their application on standard mechanical systems

robust integral control of port hamiltonian systems the case of non passive outputs with unmatched disturbances regulation of passive outputs of nonlinear systems can be easily achieved with an integral control ic in many applications however the signal of interest is not a passive output and ensuring its regulation remains an open problem also ic of passive systems rejects constant input disturbances but no similar property can be ensured if the disturbance is not matched in this paper we address the aforementioned problems and propose a procedure to design robust ics for port hamiltonian models that characterize the behavior of a large class of physical systems necessary and sufficient conditions for the solvability of the problem in terms of some rank and controllability properties of the linearized system are provided for a class of fully actuated mechanical systems a globally asymptotically stabilizing solution is given simulations of the classical pendulum system illustrate the good performance of the scheme

total energy shaping control of mechanical systems simplifying the matching equations via coordinate changes total energy shaping is a controller design methodology that achieves asymptotic stabilization of mechanical systems endowing the closed loop system with a lagrangian or hamiltonian structure with a desired energy function that qualifies as lyapunov function for the desired equilibrium the success of the method relies on the possibility of solving two pdes which identify the kinetic and potential energy functions that can be assigned to the closed loop particularly troublesome is the partial differential equation pde associated to the kinetic energy which is nonlinear and inhomogeneous and the solution that defines the desired inertia matrix must be positive definite in this note we prove that we can eliminate or simplify the forcing term in this pde by modifying the target dynamics and introducing a change of coordinates in the original system furthermore it is shown that in the particular case of transformation to the lagrangian coordinates the possibility of simplifying the pdes is determined by the interaction between the coriolis and centrifugal forces and the actuation structure the examples of pendulum on a cart and furuta s pendulum are used to illustrate the results

nonsingularity under data rounding abstract for a square floating point matrix a we give a test for the existence of a singular real matrix which rounds to a

structure preserving adaptive control of port hamiltonian systems in this technical note an adaptive control scheme is presented for general port hamiltonian systems adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system the adaptive control is also combined with canonical transformation theory for port hamiltonian systems this allows for the adaptive control to be applied on a large class of systems and for being included in the port hamiltonian framework

on the spectrum of convex sets of matrices let k be an arbitrary compact convex set of square matrices this paper presents necessary and sufficient conditions for the spectrum of k to have no eigenvalues in a prespecified closed convex subset of the complex plane the obtained result implies different criteria for analysis of the spectral set of k in particular we have formulated criteria for nonsingularity inertia and hurwitz stability of k which can be used in the robustness analysis of linear control systems with uncertain parameters

the robustness of interval fuzzy matrices abstract robust interval matrices over max min algebra fuzzy matrices are studied and equivalent conditions for interval fuzzy matrices to be robust are presented polynomial algorithms for checking the necessary and sufficient conditions for robustness of interval fuzzy matrices are introduced in addition more efficient algorithms for verifying the robustness of interval circulant matrices are described

asymptotic stabilization via control by interconnection of port hamiltonian systems we study the asymptotic properties of control by interconnection a passivity based controller design methodology for stabilization of port hamiltonian systems it is well known that the method in its basic form imposes some unnatural controller initialization to yield asymptotic stability of the desired equilibrium we propose two different ways to overcome this restriction one based on adaptation ideas and the other one adding an extra damping injection to the controller the analysis and design principles are illustrated through an academic example

using em to obtain asymptotic variance covariance matrices the sem algorithm abstract the expectation maximization em algorithm is a popular and often remarkably simple method for maximum likelihood estimation in incomplete data problems one criticism of em in practice is that asymptotic variance covariance matrices for parameters e g standard errors are not automatic byproducts as they are when using some other methods such as newton raphson in this article we define and illustrate a procedure that obtains numerically stable asymptotic variance covariance matrices using only the code for computing the complete data variance covariance matrix the code for em itself and code for standard matrix operations the basic idea is to use the fact that the rate of convergence of em is governed by the fractions of missing information to find the increased variability due to missing information to add to the complete data variance covariance matrix we call this supplemented em algorithm the sem algorithm theory and particular examples reinforce the conclusion that the sem alg

exact bounds for the static response set of structures with uncertain but bounded parameters abstract the numerical estimation of the static displacement bounds of structures with uncertain but bounded parameters is considered in this paper by representing each uncertain but bounded parameter as an interval number or vector a static response analysis problem for the structure can be expressed in the form of a system of linear interval equations in which the coefficient matrix and the right hand side term are respectively the interval matrix and the interval vector in this study we present two new simple mathematical proofs of the vertex solution theorem using cramer s rule for solving linear interval equations different from the other proof methods to find the upper and lower bounds on the set of solutions the first takes advantage of optimization theory while the second is based on interval extension by means of a typical example considered first by hansen it can be seen that the result calculated by the vertex solution theorem is the same as one predicted by the oettli prager criterion examples of a three stepped beam and a 10 bar truss are presented to illustrate the computational aspects of the vertex solution theorem in comparison with the interval perturbation method

stabilization of oscillations through backstepping in high dimensional systems this note introduces a method for obtaining stable and robust self sustained oscillations in a class of single input nonlinear systems of dimension n spl ges 2 the oscillations are associated to a limit cycle that is produced in a second order subsystem by means of an appropriate feedback law then the controller is extended to the full system by a backstepping procedure it is shown that the closed loop system turns out to be generalized hamiltonian and that the limit cycle can be thought as born in a hopf bifurcation after moving a parameter

canonical transformation and stabilization of generalized hamiltonian systems abstract this paper introduces generalized canonical transformations for generalized hamiltonian systems which convert a generalized hamiltonian system into another one and preserve the generalized hamiltonian structure of the original as in classical mechanics it is expected that canonical transformations will provide new insights and fundamental tools for both analysis and synthesis of those systems firstly the class of generalized canonical transformations and some of their properties are indicated secondly it is shown how to stabilize the generalized hamiltonian systems using canonical transformations in addition some examples illustrate how such transformations are utilized for control systems design

solution of the fully fuzzy linear systems using the decomposition procedure abstract this paper tries to extend the adomian decomposition method for solving fully fuzzy linear systems shown as ffls for finding a positive fuzzy vector x that satisfies a x b where a and b are respectively a fuzzy matrix and a fuzzy vector we employ dubois and prade s approximate arithmetic operators on lr fuzzy numbers we also transform the ffls and use the adomian decomposition method for solving an ffls then we compare this method with the jacobi iterative technique additionally we give some numerical examples

brief generalized hamiltonian realization of time invariant nonlinear systems a key step in applying the hamiltonian function method is to express the system under consideration into a generalized hamiltonian system with dissipation which yields the so called generalized hamiltonian realization ghr in this paper we investigate the problem of ghr several new methods and the corresponding sufficient conditions are presented a major result is that if the jacobian matrix of a time invariant nonlinear system is nonsingular the system has a ghr whose structure matrix and hamiltonian function are given in simple forms then the orthogonal decomposition method and a sufficient condition for the feedback dissipative realization are proposed

on the matching equations of energy shaping controllers for mechanical systems total energy shaping is a controller design methodology that achieves asymptotic stabilisation of mechanical systems endowing the closed loop system with a lagrangian or hamiltonian structure with a desired energy function the success of the method relies on the possibility of solving two partial differential equations pdes which identify the kinetic and potential energy functions that can be assigned to the closed loop particularly troublesome is the pde associated to the kinetic energy ke which is quasi linear and non homogeneous and the solution that defines the desired inertia matrix must be positive definite this task is simplified by the inclusion of gyroscopic forces in the target dynamics which translates into the presence of a free skew symmetric matrix in the ke matching equation that reduces the number of pdes to be solved recently it has been claimed that considering a more general form for the target dynamic forces that relax the skew symmetry condition further reduces the number

on feedback equivalence to port controlled hamiltonian systems in the last few years port controlled hamiltonian pch systems have emerged as an interesting class of nonlinear models suitable for a large number of physical applications in this paper we study the question of feedback equivalence of nonlinear systems to pch systems more precisely we give conditions under which a general nonlinear system can be transformed into a pch system via static state feedback we consider the two extreme cases where the target pch system is completely a priori fixed or completely free as well as the case where it is only partially predetermined when the energy function is free a set of partial differential equations needs to be solved on the other hand if it is fixed we have to deal with a set of algebraic equations in the former case we give some verifiable necessary and sufficient conditions for solvability as a by product of our analysis we obtain some stabilization results for nonlinear systems

transient stabilization of multimachine power systems with nontrivial transfer conductances we provide a solution to the long standing problem of transient stabilization of multimachine power systems with nonnegligible transfer conductances more specifically we consider the full 3n dimensional model of the n generator system with lossy transmission lines and loads and prove the existence of a nonlinear static state feedback law for the generator excitation field that ensures asymptotic stability of the operating point with a well defined estimate of the domain of attraction provided by a bona fide lyapunov function to design the control law we apply the recently introduced interconnection and damping assignment passivity based control methodology that endows the closed loop system with a port controlled hamiltonian structure with desired total energy function the latter consists of terms akin to kinetic and potential energies thus has a clear physical interpretation our derivations underscore the deleterious effects of resistive elements which as is well known hamper the assignment of simple gradient energy functions and compel us to include nonstandard cross terms a key step in the construction is the modification of the energy transfer between the electrical and the mechanical parts of the system which is obtained via the introduction of state modulated interconnections that play the role of multipliers in classical passivity theory

a sharp version of bauer fike s theorem in this paper we present a sharp version of bauer fike s theorem we replace the matrix norm with its spectral radius or sign complex spectral radius for diagonalizable matrices 1 norm and norm for non diagonalizable matrices we also give the applications to the pole placement problem and the singular system

control via interconnection and damping assignment of linear time invariant systems a tutorial interconnection and damping assignment is a controller design methodology that regulates the behaviour of dynamical systems assigning a desired port hamiltonian structure to the closed loop a key step for the application of the method is the solution of the so called matching equation that in the case of nonlinear systems is a partial differential equation it has recently been shown that for linear systems the problem boils down to the solution of a linear matrix inequality that moreover is feasible if and only if the system is stabilisable making the method universally applicable it has also been shown that if we narrow the class of assignable structures e g to mechanical instead of the larger port hamiltonian the problem is still translated to a linear matrix inequality but now stabilisability is not sufficient to ensure its feasibility it is additionally required that the uncontrolled modes are simple and lie on the j axis which is consistent with the considered scenario of mechanical

universal grey system theory for analysis of uncertain structural systems the uncertainty present in many structural systems is commonly modeled using probabilistic fuzzy or interval approaches depending on the nature of uncertainty present the probabilistic approach

ae and ea robustness of interval circulant matrices in max min algebra abstract max min algebra is defined as a linearly ordered set with two binary operations classical addition and multiplication are replaced by maximum and minimum respectively a square matrix is robust if its eigenspace is achieved starting at arbitrary vector and it is x robust if its eigenspace is achieved starting at each vector from a given interval vector x the ea and ae robustness and x robustness of interval circulant matrices over max min algebra are defined polynomial algorithms for checking these types of robustness and x robustness are given

the robustness of interval matrices in max plus algebra abstract robust interval matrices in max plus algebra are studied and equivalent conditions for interval matrices to be robust are presented the necessary and sufficient conditions for robustness of interval matrices are introduced in addition efficient algorithms for verifying the robustness of interval circulant and interval zero one matrices are described

recognizing weakly stable matrices a max plus matrix a is called weakly stable if the sequence orbit x a otimes x a 2 otimes x ldots does not reach an eigenvector of a for any x unless x is an eigenvector this is in contrast to previously studied strongly stable robust matrices for which the orbit reaches an eigenvector with any nontrivial starting vector max plus matrices are used to describe multiprocessor interactive systems for which reachability of a steady regime is equivalent to reachability of an eigenvector by a matrix orbit we prove that an irreducible matrix is weakly stable if and only if its critical graph is a hamiltonian cycle in the associated graph we extend this condition to reducible matrices these criteria can be checked in polynomial time

theorems of perron frobenius type for matrices without sign restrictions abstract the paper attempts to solve a problem which was called a challenge for the future in linear algebra appl we define and investigate a new quantity for real matrices the sign real spectral radius and derive various characterizations bounds and properties of it in certain aspects our quantity shows similar behavior to the perron root of a nonnegative matrix it is shown that our quantity also has intimate connections to the componentwise distance to the nearest singular matrix relations to the perron root of the entrywise absolute value of the matrix and to the number are given as well

approximate linear algebra is intractable abstract it is shown that the problem of computing the optimal solutions of several versions of imprecise linear systems of equations is np hard an imprecise linear system is a linear system ax b where a a 0 p a b b 0 qv b v with unknown coefficients p qv constrained by one of the five relations p q p 2 q p q 2 p q 2 where p q is a vector formed by all values p and qv given such a system we would like to find its optimal solution i e the largest possible x j and the smallest possible x j values of xj our main result is that this problem is np hard in any of the five versions this holds even when the a b v 0 v 0 are restricted to have only a single nonzero entry each in disjoint positions and even if instead of the exact values x j x j we want to compute their approximations for a given accuracy 0 so unless np p algorithms that find the optimal solution of imprecise linear systems require in the worst case exponential time