conditions for the 2 d characteristic polynomial of a matrix to be very strict hurwitz conditions for the bivariate characteristic polynomial of a matrix to be very strict hurwitz are presented these conditions are based on the necessary and sufficient conditions for the existence of positive definite solutions to the 2 d continuous lyapunov equation it is shown that such an existence is only sufficient but not necessary for the characteristic polynomial to be very strict hurwitz further the testing of zeros at infinite distant points requires the use of a class of very strict positive real functions

eigenvalue based characterization and test for positive realness of scalar transfer functions an eigenvalue based characterization of positive realness of transfer functions of a single input single output time invariant linear system is derived based on this characterization we propose an efficient computational procedure to determine if a given transfer function is positive real the input for this eigenvalue based test is any given not necessarily minimal state space representation of the linear system the test only involves standard matrix computations such as computing eigenvalues of a matrix or a matrix pencil results of numerical experiments are reported

robust h 2 and h control of discrete time systems with polytopic uncertainties via dynamic output feedback this paper addresses the problem of robust h 2 and h control of discrete linear time invariant lti systems with polytopic uncertainties via dynamic output feedback the problem has been known to be difficult when a parameter dependent lyapunov function is to be applied for a less conservative design due to non convexity our approach is based on a novel bounding technique that converts the non convex optimization into a convex one together with a line search which is simple but may be conservative to further reduce the design conservatism an algorithm based on the sequentially linear programming method slpmm is proposed a numerical example is given which demonstrates the feasibility of the proposed design methods

positive real control of two dimensional systems roesser models and linear repetitive processes this paper considers the problem of positive real control for two dimensional 2 d discrete systems described by the roesser model and also discrete linear repetitive processes which are another distinct sub class of 2 d linear systems of both systems theoretic and applications interest the purpose of this paper is to design a dynamic output feedback controller such that the resulting closed loop system is asymptotically stable and the closed loop system transfer function from the disturbance to the controlled output is extended strictly positive real we first establish a version of positive realness for 2 d discrete systems described by the roesser state space model then a sufficient condition for the existence of the desired output feedback controllers is obtained in terms of four lmis when these lmis are feasible an explicit parameterization of the desired output feedback controllers is given we then apply a similar approach to discrete linear repetitive processes represented in their equivalent 1 d state space form finally we provide numerical examples to demonstrate the applicability of the approach

symmetrically trimmed least squares estimation for tobit models this paper proposes alternatives to maximum likelihood estimation of the censored and truncated regression models known to economists as tobit models the proposed estimators are based upon symmetric censoring or truncation of the upper tail of the distribution of the dependent variable unlike methods based on the assumption of identically distributed gaussian errors the estimators are semiparametric in the sense that they are consistent and asymptotically normal for a wide class of symmetric error distributions with heteroskedasticity of unknown form the paper gives the regularity conditions and proofs of these large sample properties demonstrates how to construct consistent estimators of the asymptotic covariance matrices and presents the results of a simulation study for the censored case extensions and limitations of the approach are also considered

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 stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

frequency domain controller design for switched systems automatic control laboratory ecole polytechnique f ed erale de lausanne epfl 1015 lausanne switzerlandabstractin a recent work a new framework to design controllers using frequency domain data is proposed the method is basedon the shaping of the open loop transfer function in the nyquist diagram with constraints on the robustness margins andperformance in terms of the crossover frequency by solving a linear programming problem it is possible to design xed orderlinearly parameterized controllers for stable siso lti multi model systems in this paper it is proposed to extend this designframework to guarantee quadratic stability of certain classes of switched systems by adding new linear constraints based onthe phase di erence of the characteristic polynomials of the closed loop subsystems these new linear constraints can also beused to guarantee quadratic stability of certain classes of lpv systems some simulation examples are provided to illustratethe proposed approach key words switched systems nyquist diagram linear programming quadratic stability lpv systems

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

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

non fragile positive real control for uncertain linear neutral delay systems this paper is concerned with the problem of non fragile positive real control for uncertain neutral delay systems with time invariant norm bounded parameter uncertainty time delays are assumed to appear in both the state and the controlled output equations the state feedback gains are with norm bounded controller uncertainties for both the cases with additive and multiplicative controller uncertainties we address the problem of designing memoryless state feedback controllers such that for all admissible uncertainties the resulting closed loop system is stable and the closed loop transfer function is extended strictly positive real sufficient conditions for the existence of desired controllers are given in terms of linear matrix inequalities lmis when these lmis are feasible the expected memoryless state feedback controller can be easily constructed via convex optimization an illustrative example is given to demonstrate the validity and applicability of the proposed approach

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

spectral conditions for positive realness of single input single output systems in this note we derive necessary and sufficient conditions for a single input single output system to be strictly positive real these conditions take the form of a spectral condition on a matrix product constructed from the state space representation of the linear time invariant system a b c d numerical examples are given to illustrate the usefulness of our conditions

division algebras over henselian fields in this chapter we focus on the tame division algebras d with center a field f with henselian valuation v as usual we approach this by first obtaining results for graded division algebras then lifting back from operatorname mathsf gr d to d this is facilitated by results in 8 1 on existence and uniqueness of lifts of tame subalgebras from operatorname mathsf gr d to d in 8 2 we describe four fundamental canonical up to conjugacy subalgebras of d that reflect its valuative structure the rest of the chapter is devoted to brauer group factorizations of d corresponding to the noncanonical direct product decomposition of operatorname mathit br t f given in cor 7 85 the factor operatorname mathit hom c operatorname mathcal g overline f mathbb t gamma f is represented by a type of division algebra n called decomposably semiramified defined in 8 3 and characterized by the property that n contains a maximal subfield inertial over f and another totally ramified over f we show in 8 4 that every tame division algebra d is brauer equivalent to some s f t where s is inertially split and t is tame and totally ramified over f we show further that every inertially split division algebra s is brauer equivalent to some i f n where i is inertial over f and n is decomposably semiramified the classes overline i for the i appearing in the i f n decompositions of s are shown to range over a single coset of mathit dec z overline s overline f in operatorname mathit br overline f called the specialization coset of s in the final subsection 8 4 6 we summarize what happens in the special case that v is discrete of rank 1 where substantial simplifications occur

truncated logistic regression truncated binary data occurs when a group of individuals who each have a binary response are observed only if one or more of the individuals has a positive response in this paper the group will be taken to be a motor vehicle accident and the binary response taken to be survival or death we compare two regression techniques that can be used for truncated binary data the first procedure conditional logistic regression breslow and day 1980 statistical methods in cancer research 1 the analysis of case control studies no 32 lyon iarc conditions on the actual number of deaths and has been previously used for this type of data the second procedure truncated logistic regression conditions on there being at least one death it is computationally simpler than conditional logistic for groups of size greater than two and can be considerably more efficient a major difference between the two methods is that only truncated logistic regression requires a knowledge of group level covariates and allows estimation of group level effects language en

the effect of truncation on the identifiability of regression coefficients abstract when data are truncated and hence partly unobservable parameters identifiable under the complete observation may not be identifiable a class of distributions is characterized under which regression coefficients are unidentifiable by truncation of a dependent variable in the regression model in a class of strongly unimodal densities regression coefficients are shown to be unidentifiable only when the underlying distribution is proportional to the exponential distribution in support of the truncated observation the exponential double exponential and huber s least informative distribution for a location parameter are apparent examples of the distributions under which the unidentifiability can occur in a more restrictive class of symmetric and strongly unimodal densities the unidentifiability arises only when the error distribution has exponential tails and the degree of truncation is at least 50 the likelihood function becomes completely flat with respect to the regression coefficients and

technical communique observer based positive real control of uncertain linear systems this paper is concerned with the positive control problem for a class of linear systems with norm bounded uncertainties we address the problem of designing observer based dynamic output feedback controllers that robustly stabilize the uncertain system and achieve the extended strict positive realness for a given closed loop transfer function by casting the problem at hand into a class of strict positive real control problems with scaling parameters an uncertainty independent solution is then establised and expressed in linear matrix inequalities format

on the characterization of strict positive realness for general matrix transfer functions we present conditions which are necessary and sufficient for a transfer function or transfer function matrix to be strictly positive real a counter example is given to illustrate that the conditions presented here differ from those previously presented in the literature the proof of our results differs from previous related proofs in that it only uses properties of analytic functions and matrices and does not require state space realizations also the results are not restricted to rational transfer functions with real coefficients

synthesis of positive real multivariable feedback systems this is a tutorial paper describing the application of infinity norm optimal control theory to the synthesis of sector bounded and positive real multivariable feedback systems the paper gives a concise treatment of the practical aspects of the theory describing how it has been implemented via state space oriented computer algorithms included is a concise summary of the state space approach to infinity norm control developed by doyle and by safonov and verma based on the hankel model reduction theory and incorporating the multivariable hankel results of glover

positive real control problem for uncertain linear time invariant systems abstract this paper focuses on positive real control of linear time invariant systems which are subjected to norm bounded uncertainties in the state equation we address the problem of designing a linear dynamic output feedback controller that robustly stabilizes the uncertain system and achieves the extended strict positive realness property for a given closed loop transfer function it is shown that a solution to the above problem can be obtained by solving a scaled strict positive real control problem for which no parameter uncertainty occurs

nonparametric estimation of the slope of a truncated regression a nonparametric estimate b is presented for the slope of a regression line y 83ox v subject to the truncation y c yo this model is relevant to a cosmological controversy which concerns hubble s law in astronomy the estimate 3 corresponds to the zero crossing of a random function s 3 which for each 8 is a mann whitney type of statistic designed to measure heterogeneity among the calculated residuals y 3x the asymptotic distribution of p is derived making extensive use of u statistics to show that sn 3o is asymptotically normal and then showing that s 3 behaves like sn 3o plus a deterministic term which is locally linear results on asymptotic efficiency are compared with finite sample size results by simulation

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

robust strict positive real stabilization and asymptotic hyperstability robustness abstract this paper is devoted to the study of robust strict positive real stabilization of siso uncertain systems i e finding a single controller that not only robustly stabilizes a plant with uncertainties under unity feedback but also makes the closed loop system robustly strictly positive real it is proved that there must exist a stable controller achieving robust strict positive real stabilization of uncertain systems with both parameter variations and unstructured uncertainties under some reasonable assumptions the propemess of the controller is guaranteed when the largest relative degree of an uncertain system is retricted by applying these results to nonlinear systems some significant conclusions on asymptotic hyperstability robustness are given

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

preservation of spr functions and stabilization by substitutions in siso plants in this paper we present sufficient conditions to preserve stability by rational function substitutions it is proved that by making substitutions with strictly positive real spr zero relative degree functions it is possible to preserve the stability and coprime factorization of transfer functions it is also proved that these functions are closed under function composition finally we prove some results about robust stabilization using constant compensators spr robust functions and robust stability based on the result over closure of spr functions

robust strict positive real stabilization criteria for siso uncertain systems abstract this paper is devoted to the study of robust strict positive real stabilization criteria for siso uncertain systems i e considering the problem of when a single controller not only robustly stabilizes a plant with uncertainty under unity feedback but also enables the closed loop system to be robustly strictly positive real the uncertain system models with both parameter variation and unstructured perturbation are considered and some necessary and sufficient conditions for the problem are derived

positive real control for 2 d discrete delayed systems via output feedback controllers this paper considers the problem of positive real control for two dimensional 2 d discrete delayed systems in the fornasini marchesini second local state space model attention is focused on the design of dynamic output feedback controllers which guarantee that the closed loop system is asymptotically stable and the closed loop transfer function is extended strictly positive real we first present a sufficient condition for extended strictly positive realness of 2 d discrete delayed systems based on this a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality lmi when the lmi is feasible an explicit parametrization of a desired output feedback controller is presented finally we provide a numerical example to demonstrate the application of the proposed method

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

on the relationship between the model order reduction problem and the simultaneous stabilization problem this note points out the fact that under certain conditions the model order reduction problem is very closely tied to the simultaneous stabilization problem these conditions occur when the reduced order model is to be used to design a suboptimal controller for a high order plant under these conditions the controller must not only stabilize the low order model but must also stabilize the high order plant the result concerning the existence of a controller that will simultaneously stabilize two plants is used to conclude that the approximate inclusion of any unstable real modes of the high order plant in the low order model will guarantee the existence of such a controller

strict positive realness of descriptor systems in state space in this article we give necessary and sufficient spectral conditions for various notions of strict positive realness for single input single output descriptor systems these conditions only require calculation of eigenvalues of a single matrix a characterisation of a kalman yacubovich popov like lemma for descriptor systems is also derived and its implications for the stability of a class of switched descriptor systems are briefly discussed

concepts of strict positive realness and the absolute stability problem of continuous time systems after the conditions for absolute stability and positive realness are reviewed it is shown that the current definition of positive realness is inadequate to establish less conservative criteria for absolute stability in this paper the concepts of wide positive realness wpr and wide strict positive realness wspr are proposed both wpr and wspr functions may have poles in the open left and right half planes and wpr functions may have single poles on the imaginary axis including j using the concepts of wpr and wspr less conservative criteria including algebraic and frequency domain criteria are presented for absolute stability of slope restricted multiple nonlinearity feedback systems refined results for non slope restricted nonlinearity feedback systems are also proposed it is pointed out that there is no spectral factorization for wpr and wspr functions if they have poles at both j and j this can be used to explain the deficiencies of algebraic criteria presented in previous publications

comments on a note on spectral conditions for positive realness of single input single output systems with strictly proper transfer functions the necessary and sufficient conditions for strict positive realness of strictly proper transfer functions are derived in the above mentioned paper 1 presenting a counter example we show that there are inconsistencies between definitions stated in section ii and main results proved in section iii of 1 also the required corrections in the main results of 1 are presented note however that the results in 1 are correct for the definition of spr in the circuit theory sense

the asymptotic stability of nonlinear lur e systems with multiple slope restrictions the authors present the analysis of the asymptotic stability of multiple slope restricted nonlinear lur e systems by providing a lyapunov function they obtain a matrix language criterion in terms of algebraic riccati equations and linear matrix inequalities which are discussed at the point of computational issues additionally they consider the frequency domain interpretation of the result

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

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

an algorithm for interpolation with units in h with applications to feedback stabilization abstract the problem of finding a unit in h i e an h function the inverse of which is also h which interpolates to given points in the right half plane has important applications in a number of feedback stabilization problems i e strong stabilization and simultaneous stabilization an algorithm for computing such interpolating units is presented which requires a lower degree unit than other available algorithms

a sufficient condition for output feedback stabilization of uncertain dynamical systems a different proof than the one given by e zeheb ibid vol ac 31 p 1055 7 nov 1986 is given for the existence of an output feedback controller which stabilizes an uncertain single input single output dynamical system with a linear nominal part and matched uncertainties however there is no need to assume that the nominal system is stable a simple expression is obtained for the feedback gain which is necessary for the closed loop nominal system to become strictly positive real

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

stability and robustness properties of a simple adaptive controller a low order adaptive tracking controller is proposed for linear time invariant plants with a relative degree not exceeding two the order of the plant is not required to be known a priori the algorithm is robustly stable with respect to small linear time invariant plant perturbations and bounded disturbances the robustness is achieved by using a projection of the parameter estimates in the control law an additional a priori information needed to design the controller is bounds on the plant parameters in the absence of plant perturbations and disturbances perfect tracking is obtained

technical communique mitigation of symmetry condition in positive realness for adaptive control feasibility of nonlinear and adaptive control methodologies in multivariable linear time invariant systems with state space realization a b c is apparently limited by the standard strictly positive realness conditions that imply that the product cb must be positive definite symmetric this paper expands the applicability of the strictly positive realness conditions used for the proofs of stability of adaptive control or control with uncertainty by showing that the not necessarily symmetric cb is only required to have a diagonal jordan form and positive eigenvalues the paper also shows that under the new condition any minimum phase systems can be made strictly positive real via constant output feedback the paper illustrates the usefulness of these extended properties with an adaptive control example

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