learning gaussian mixture models with entropy based criteria in this paper we address the problem of estimating the parameters of gaussian mixture models although the expectation maximization em algorithm yields the maximum likelihood ml solution its sensitivity to the selection of the starting parameters is well known and it may converge to the boundary of the parameter space furthermore the resulting mixture depends on the number of selected components but the optimal number of kernels may be unknown beforehand we introduce the use of the entropy of the probability density function pdf associated to each kernel to measure the quality of a given mixture model with a fixed number of kernels we propose two methods to approximate the entropy of each kernel and a modification of the classical em algorithm in order to find the optimum number of components of the mixture moreover we use two stopping criteria a novel global mixture entropy based criterion called gaussianity deficiency gd and a minimum description length mdl principle based one our algorithm called entropy based em ebem starts with a unique kernel and performs only splitting by selecting the worst kernel attending to gd we have successfully tested it in probability density estimation pattern classification and color image segmentation experimental results improve the ones of other state of the art model order selection methods

stochastic convexity on general space this paper presents a general theory of stochastic convexity the notions of stochastic convexity formulated by shaked and shanthikumar 1988a 1988b 1990 are defined for general partially ordered spaces all of the closure properties of the one dimensional real theory are proved to be true in this general framework as well and results concerning the temporal convexity of markov chains are sharpened many proofs are based on new ideas some of which also provide insightful alternatives for proofs in shaked and shanthikumar 1990 the general theory encompasses the largely one dimensional stochastic convexity theory as known from these papers and at the same time permits treatment of multivariate multiparameter families as well as more general random objects among others it applies to real vector spaces and yields a theory of stochastic convexity for random vectors and stochastic processes we illustrate this new scope with examples and applications from queueing theory coverage processes reliability and branching processes we show that the virtual waiting time process of an nhpp driven i g 1 queue is stochastically convex in the arrival intensity function which explains the known adverse effect of fluctuating arrival rates that the expected size of an i i d union of random sets grows concavely that the expected utility of repairable items under imperfect repair policies is increasing and convex in the probabilities of successful repair

the application of generalized diagonal dominance to linear system stability theory abstract this paper shows that the well known diagonal dominance condition associated with rosenbrock s stability theorems is unnecessary and can be replaced by a less restrictive generalized diagonal dominance condition similar results are derived for generalized block diagonally dominant systems whenever possible graphical interpretations are given to facilitate the implementation of these ideas in computer aided design packages

perfect and subperfect regulation in linear multivariable control systems this paper is concerned with the synthesis of a high gain feedback control called perfect regulation p r for linear multivariable systems with external signals the existence condition for p r is derived in which the minimum phase property plays an essential role the use of an observer is discussed for achieving p r under restricted state observation some asymptotically ideal feedback properties are demonstrated such as the complete desensitization the complete servo performance with decoupling and the complete disturbance rejection which formulate the loop tightness for multivariable systems a design method for applying p r to non minimum phase systems called subperfect regulation s p r is proposed based on the factorization of the plant transfer function matrix into the minimum phase part and the totally non minimum phase part it is a multivariable extension of a well known design technique for scalar systems to overcome the difficulty of phase non minimality computational procedures for p r and s p r are discussed an illustrative example is shown

invited paper survey of quantitative feedback theory qft abstract qft is an engineering design theory devoted to the practical design of feedback control systems the foundation of qft is that feedback is needed in control only when plant p parameter and or disturbance d uncertainties sets p p d d exceed the acceptable a system performance uncertainty set a a the principal properties of qft are as follows 1 the amount of feedback needed is tuned to the p d a sets if a exceeds p d feedback is not needed at all 2 the simplest modelling is used a command disturbance and sensor noise inputs and b the available sensing points and the defined outputs no special controllability test is needed in either linear or non linear plants it is inherent in the design procedure there is no observability problem because uncertainty is included the number of independent sensors determines the number of independent loop transmissions li the functions which provide the benefits of feedback 3 the simplest mathematical tools h

a condition for robust stabilizability a family of linear time invariant finite dimensional plants is called robustly stabilizable if there exists a single controller that stabilizes each plant in the family a condition for robust stabilizability is given that requires the plant transmission zeros to remain in the left half complex plane and moreover imposes a restriction on the high frequency behavior of the plant transfer matrix

robustness analysis a case study the stability test of polynomials whose coefficients depend multilinearly on interval parameters is considered the authors describe and compare four brute force solution approaches these are eigenvalue calculation zero exclusion from a specified value set algebraic tests of real and complex hurwitz roots and the parameter space method they are applied to a simple example with two parameters and third order polynomial an interesting feature of the example is that it can have an isolated unstable point the example may be useful as a benchmark for future approaches to the multilinear problem all four methods are shown to be feasible for the simple example but they require effort

an iterative design procedure for simultaneous stabilization of mimo systems this paper considers the problem of finding one compensator which simultaneously stabilizes a family of mimo plants the family of plants bdp s q q q represented by their transfer function matrices may be uncountable thus allowing for the possibility of a continuum of variations in plant parameters a hermite invariant factorization of the plant is introduced and shown to be quite useful as far as stabilization is concerned to obtain the desired results a number of assumptions describing the set of allowable plants are imposed these assumptions include some regularity conditions on the plant and mimo versions of minimum phase and one sign high frequency gain requirements the satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator c s guaranteeing simultaneous stabilization the algorithm used for controller design has one most attractive feature namely it is recursive in nature and allows the designer to select one compensator coefficient at a time

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

a recurrent probabilistic neural network with dimensionality reduction based on time series discriminant component analysis this paper proposes a probabilistic neural network nn developed on the basis of time series discriminant component analysis tsdca that can be used to classify high dimensional time series patterns tsdca involves the compression of high dimensional time series into a lower dimensional space using a set of orthogonal transformations and the calculation of posterior probabilities based on a continuous density hidden markov model with a gaussian mixture model expressed in the reduced dimensional space the analysis can be incorporated into an nn which is named a time series discriminant component network tsdcn so that parameters of dimensionality reduction and classification can be obtained simultaneously as network coefficients according to a backpropagation through time based learning algorithm with the lagrange multiplier method the tsdcn is considered to enable high accuracy classification of high dimensional time series patterns and to reduce the computation time taken for network training the validity of the tsdcn is demonstrated for high dimensional artificial data and electroencephalogram signals in the experiments conducted during the study

rbfn restoration of nonlinearly degraded images we investigate a technique for image restoration using nonlinear networks based on radial basis functions the technique is also based on the concept of training or learning by examples when trained properly these networks are used as spatially invariant feedforward nonlinear filters that can perform restoration of images degraded by nonlinear degradation mechanisms we examine a number of network structures including the gaussian radial basis function network rbfn and some extensions of it as well as a number of training algorithms including the stochastic gradient sg algorithm that we have proposed earlier we also propose a modified structure based on the gaussian mixture model and a learning algorithm for the modified network experimental results indicate that the radial basis function network and its extensions can be very useful in restoring images degraded by nonlinear distortion and noise

a multiloop generalization of the circle criterion for stability margin analysis in order to provide a theoretical tool well suited for use in characterizing the stability margins e g gain and phase margins of multiloop feedback systems multiloop input output stability results generalizing the circle stability criterion are considered generalized conic sectors with centers and radii determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency dependent convex set of modeling errors including nonlinearities gain variations and phase variations which the system must be able to tolerate in each feedback loop without instability the resulting stability criterion gives sufficient conditions for closed loop stability in the presence of such frequency dependent modeling errors even when the modeling errors occur simultaneously in all loops so for example stability is assured as loop gains and phases vary throughout a set of nonzero measure whose boundaries are frequency dependent the stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds or falls short of its stability margin specifications

simultaneous stabilization of single input single output discrete time systems the problem of finding one compensator which simultaneously stabilizes a family of single input single output siso discrete time plants is considered the family of plants is described by the transfer functions pz q q in q which are generated via a z transformation a number of assumptions describing the set of allowable plants are then given these assumptions include some regularity conditions on the plants and a minimum phase requirement the satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator c z for simultaneous stabilization an iterative computation method is provided for control design

maximum likelihood estimation for multivariate observations of markov sources parameter estimation for multivariate functions of markov chains a class of versatile statistical models for vector random processes is discussed the model regards an ordered sequence of vectors as noisy multivariate observations of a markov chain mixture distributions are a special case the foundations of the theory presented here were established by baum petrie soules and weiss a powerful representation theorem by fan is employed to generalize the analysis of baum em et al to a larger class of distributions

almost decoupling of uncertain multivariable systems an effective almost decoupling theory using an internal model reference loop is developed for linear uncertain multivariable systems based on non negative matrix theory a useful design guide is derived to achieve the generalized diagonal dominance condition for the internal model reference loop using a perron root a sufficient condition is given to guarantee the inverse transfer matrix to be generalized diagonally dominant for all plants in a given family one of the main features of the proposed scheme is the reduction of uncertainty in the resultant compensated internal loop system which makes the subsequent design process of the individual channels using standard siso techniques much simpler

stability and performance robustness analysis with highly structured uncertainties necessary and sufficient test the author presents an extension of a technique of analyzing the stability of linear time invariant interconnected systems with uncertainties each element of the frequency response matrix is assumed to lie inside a polygon at each frequency it is shown that the exterior boundary of the image of the cartesian product of these polygons under the map det i m delta is contained in the boundary of the image of the cartesian product of the boundaries of these polygons under the same map thus the image can be constructed from the images of the edges the computational technique of r r e de gaston and m g safonov 1988 can then be applied to perform a nonconservative robustness analysis of the feedback system

unsupervised learning of finite mixture models this paper proposes an unsupervised algorithm for learning a finite mixture model from multivariate data the adjective unsupervised is justified by two properties of the algorithm 1 it is capable of selecting the number of components and 2 unlike the standard expectation maximization em algorithm it does not require careful initialization the proposed method also avoids another drawback of em for mixture fitting the possibility of convergence toward a singular estimate at the boundary of the parameter space the novelty of our approach is that we do not use a model selection criterion to choose one among a set of preestimated candidate models instead we seamlessly integrate estimation and model selection in a single algorithm our technique can be applied to any type of parametric mixture model for which it is possible to write an em algorithm in this paper we illustrate it with experiments involving gaussian mixtures these experiments testify for the good performance of our approach

stabilization of a linear plant via a stable compensator having no real unstable zeros abstract this paper studies the following problem under what conditions can a linear plant be stabilized by a stable compensator having no real zeros in the closed right half plane solving this problem is an important step towards to solving the problems of stabilization of linear systems via stable minimum phase compensation and simultaneous stabilization of n n 2 plants in the paper necessary and sufficient conditions are derived these conditions are completely general and therefore encompass unstable nonminimum phase plants as well it is shown that the stabilizability solely depends on the locations of real zeros and real poles of a given plant for a plant satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is also provided and illustrated via an example

a generalization of the routh hurwitz stability criteria and an application to a problem in robust controller design the classical results of routh and hurwitz on the stability of polynomials are generalized from the open left half plane to certain other subregions g of the complex plane by our method arbitrary conic sections can be handled the results are interpreted as criteria for g stability of linear systems a numerical algorithm to compute the criteria is given an application to a problem in robust controller design is outlined

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

continuity properties of the real complex structured singular value the structured singular value function mu is defined with respect to a given uncertainty set this function is continuous if the uncertainties are allowed to be complex however if some uncertainties are required to be real then it can be discontinuous it is shown that mu is always upper semi continuous and conditions are derived under which it is also lower semi continuous with these results the real parameter robustness problem is reexamined a related although not equivalent problem is formulated which is always continuous and the relationship between the new problem and the original real mu m problem is made explicit a numerical example and results obtained via this related problem are presented

robust stability of systems with integral control a number of necessary and sufficient conditions are derived which must be satisfied by the plant d c gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is stable based on these results the robustness of integral control systems is analyzed i e the family of plants is defined which are stable when controlled with the same integral controller conditions for actuator sensor failure tolerance of systems with integral control are also given finally parallels are drawn between the results of this paper and the bifurcation theory of nonlinear systems

robust stabilizability verification of polynomially uncertain lti systems this paper investigates the stabilizability of uncertain linear time invariant lti systems via structurally constrained controllers first an lti uncertain system is considered whose state space matrices depend polynomially on the uncertainty vector defined over some region it is shown that if the system is stabilizable by a structurally constrained controller in one point belonging to the region then it is stabilizable by a controller with the same structure in all points belonging to the region except for those located on an algebraic variety thus if a system is stabilizable via a constrained controller at the nominal point then it is almost always stabilizable at any operating point around the nominal model it is also shown how this algebraic variety or the dominant subvariety of it can be computed efficiently the results obtained in this paper encompass a broad range of the existing results in the literature on robust stability of the lti systems in addition to new ones

on the order of simultaneously stabilizing compensators in this paper simultaneous strong stabilization problem is considered and it is shown that there is no upper bound for the minimal order of a simultaneously strongly stabilizing compensator in terms of the plant orders a similar problem was also considered by smith et al 1986 where it was shown that such a bound does not exist for the strong stabilization problem of a single plant but the examples given in the article were forcing an approximate unstable pole zero cancellation or forcing the distance between two distinct unstable zeros to go to zero in this paper it is shown that 1 if approximate unstable pole zero cancellation does not occur and the distances between distinct unstable zeros are bounded below by a positive constant then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator and 2 for the simultaneous strong stabilization problem even for the two plant case such a bound cannot be found

robust controllers for uncertain linear multivariable systems abstract this paper is addressed to three distinct yet related topics in the design of controllers for imprecisely known linear multivariable systems in the first part it is supposed that the plant to be stabilized is subject to additive or multiplicative uncertainties and necessary and sufficient conditions are derived for the existence of a controller that stabilizes all plants within this band of uncertainty in the second part in contrast with the first part it is supposed that the number of unstable poles of the plant to be stabilized is not precisely known the type of plant uncertainty is the so called stable factor uncertainty and necessary and sufficient conditions are given for robust stabilization in the third part the model of uncertainty is a ball in the space of rational matrices metrized by the so called graph metric and sufficient conditions for robust stabilization are derived

mapping non linear integro differential equations into the frequency domain a recursive algorithm is derived to compute the generalized frequency response functions for a large class of non linear integro differential equations applications to duffing s equation and a modified van der pol model are discussed

reduction of robust stabilization problems to standard h problems for classes of systems with structured uncertainty we consider the problem of robustly stabilizing a family of linear time invariant systems with a linear time invariant controller for classes of robust stabilization problems with unmodelled dynamics recent breakthroughs in h theory lead to solution via two riccati equations for systems with structured real uncertainty however a similar comprehensive theory does not exist the objective of this paper is to delineate classes of linear time invariant systems with structured uncertainty either real or complex for which a similar solution to the robust stabilization problem is possible the theory has the following salient features first for classes of uncertainty structures no conservatism is introduced for structured real parametric uncertainty we make a connection with h theory that does not amount to any crude overbounding via complex discs the stabilizability conditions we obtain are not only sufficient but also necessary the second salient feature in the theory is a special weighting function which we construct for example for the case when the structured uncertainty enters only in the denominator the robust stabilization problem is replaced by a standard h sensitivity minimization problem with our special weighting function a similar h complementary sensitivity problem is associated with numerator uncertainty

algebraic and topological aspects of quantitative feedback theory the current interest in robust control has called into question the applicability of the quantitative feedback theory qft robust design method introduced by horowitz a number of issues have been raised regarding inherent restrictions of both the design method and the uncertain plant set using a multivariable root locus technique extended to uncertain systems this paper shows that the qft assumptions are indeed not restrictive and are in fact equivalent to other well known conditions for robust stabilizability because qft is one of the very few methods to specifically address the quantitative robust performance issue these results should lead to better methods of developing new qft design software as well as improved robust control methods to satisfy a priori quantitative performance bounds

on multivariable stability in the gain space abstract general existence conditions under which the stability of the individual loops of a multivariable system in a given compact and bounded gain space imply the global asymptotic stability of the multivariable system in the same space are very useful in practice and essentially indicate when in principle it is possible to obtain stable closed loop performance of a multivariable system by tuning every loop separately such conditions are particularly useful for fault tolerant control of multivariable systems this paper gives the required necessary and sufficient conditions and effectively unifies all previous work on diagonal stabilizability which includes as special cases the diagonal dominance the h matrix the gkk matrix and the decentralized integral controllability dic conditions reported previously in the literature some application examples are included

a multiple hyper ellipsoidal subclass model for an evolutionary classifier abstract a pattern classification scheme in which the classifier is able to grow and evolve during the operation process is presented the evolutionary property of the classifier is made possible by modeling the pattern vectors in multiple hyper ellipsoidal subclass distributions learning of the classifier takes place at the subclass levels only this property allows the classifier to retain its previously learned patterns while accepting and learning new pattern classes the classifier is suitable to operate in dynamical environments where continuous updating of the pattern class distributions is needed

maximum likelihood training of probabilistic neural networks a maximum likelihood method is presented for training probabilistic neural networks pnn s using a gaussian kernel or parzen window the proposed training algorithm enables general nonlinear discrimination and is a generalization of fisher s method for linear discrimination important features of maximum likelihood training for pnn s are 1 it economizes the well known parzen window estimator while preserving feedforward nn architecture 2 it utilizes class pooling to generalize classes represented by small training sets 3 it gives smooth discriminant boundaries that often are piece wise flat for statistical robustness 4 it is very fast computationally compared to backpropagation and 5 it is numerically stable the effectiveness of the proposed maximum likelihood training algorithm is assessed using nonparametric statistical methods to define tolerance intervals on pnn classification performance

robustness analysis of feedback systems with block diagonal structured uncertainties the results for magnitude bounded diagonal perturbation are extended to norm bounded block diagonal perturbation a useful consequence to this extension is that an easily computable upper bound for the structured singular value via suboptimal diagonal similarity scaling is obtained it is concluded that the results are applicable to a wider class of perturbations i e the norm which bounds the perturbation p in this study need not be the 2 norm maximum singular value in the scalar case this does not give much advantage as all pth norms reduce to the magnitude of the element however in the matrix case different norms would characterize different types of perturbations

simultaneous stabilization with almost disturbance decoupling uniform rank system abstract in this paper we study the problem of stabilization with almost disturbance decoupling for a family of linear time invariant finite dimensional uniform rank plants with a fixed controller it is shown that for a family of minimum phase plants which have the same order of infinite zeros and have high frequency gain matrices satisfying a certain condition such a fixed controller exists the restriction on the high frequency gain matrices is equivalent to requiring that the sign of high frequency gain for siso plants be known

the graph metric for unstable plants and robustness estimates for feedback stability in this paper a graph metric is defined that provides a measure of the distance between unstable multivariable plants the graph metric induces a graph topology on unstable plants which is the weakest possible topology in which feedback stability is robust using the graph metric it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of rhp poles if the perturbed and unperturbed systems have the same rhp poles then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations as an application of these results the design of stabilizing controllers for unstable singularly perturbed systems is studied finally the relationship of the graph metric to the gap metric introduced by zames and el sakkary is studied in detail in particular it is shown that the robustness results of zames and el sakkary do not enable one to conclude the causality of the perturbed system whereas the present results do

adaptive decoupling of multivariable systems for many industrial processes it is of interest to design a decoupling precompensator the precompensator makes it possible to design controllers based on single input single output models of the process a model of the process must be known to design the precompensator this paper shows how the precompensator can be designed adaptively using input output measurements the precompensator is first designed for the case when the process is known the adaptive precompensator is then constructed using the certainty equivalence principle the convergence properties and the implementation of the adaptive decoupler are discussed it is shown that the adaptive scheme will converge provided the system is persistently excited and that a suitable model structure is used in the estimation

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

stochastic comparisons for non markov processes a technique is developed for comparing a non markov process to a markov process on a general state space with many possible stochastic orderings two such comparisons with a common markov process yield a comparison between two non markov processes the technique which is based on stochastic monotonicity of the markov process yields stochastic comparisons of the limiting distributions and the marginal distributions at single time points but not the joint distributions these stochastic comparisons are obtained under the condition that the one step transition probabilities in discrete time or infinitesimal transition rates in continuous time are appropriately ordered uniformly in the extra information needed to add to the state to make the non markov process markov the technique is illustrated by establishing an inequality in traffic theory concerning the blocking in multi server service facilities when each customer requires service from several facilities simultaneously

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

technical communique on minimal order stabilization of minimum phase plants in this note the problem of minimal order stabilization in the case where the plant is minimum phase is studied a low bound on the order of stabilizers is derived and a set of minimal order stabilizers are characterized the low bound is related to the number and location of the plant s unstable and lightly damped poles and the number of zeros how to construct a minimal order or low order stabilizer for a general case is also discussed and the algorithm is provided numerical examples are given to illustrate the proposed method

stochastic convexity and concavity of markov processes in this paper we consider the temporal stochastic convexity and concavity properties of markov processes x t t s in discrete time then s n 0 1 2 or in continuous time then s 0 that is we obtain conditions on the process x t t s which imply that the expectation ef x t is a monotone convex concave function of t whenever f is a monotone convex concave function the theory is illustrated through some examples after giving some background we define monotonicity and then obtain some general results concerning stochastic convexity and concavity of markov processes by using the notion of monotone operators we then introduce a method for identifying monotone operators and we discuss the relationship between our results concerning temporal convexity and other results in the literature in particular we center our attention on a notion of stochastic concavity in this respect we show that a result of shaked and shanthikumar is incorrect and we prove two alternativ

explicit solution to the unstable stationary filtering problem an expression in closed form for the constant kalman gain in stationary filtered estimation of linear unstable processes is obtained and bounds on the achievable accuracy of the estimate are derived this expression is used to find lower and upper bounds for the singular values of the solution of the algebraic matrix riccati equation and to derive the minimum phase image of linear systems that possess zeros in the right half plane

a survey of extreme point results for robustness of control systems abstract this paper surveys a subset of the body of research which was sparked by kharitonov s theorem the focal point is extreme point results for robust stability and robust performance that is we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family the results which are surveyed apply mainly to systems with structured real parametric uncertainty in addition a number of counterexamples are given to illustrate cases for which an extreme point result does not hold for such cases a solution via the so called edge theorem is often possible

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

stochastic orderings for markov processes on partially ordered spaces the purpose of this paper is to develop a unified theory of stochastic ordering for markov processes on countable partially ordered state spaces when such a space is not totally ordered it can induce a wide range of stochastic orderings none of which are equivalent to sample path comparisons similar comparison theorems are also developed for non markov processes that are functions of markov processes and for time inhomogeneous markov processes such alternative orderings can be quite useful when analyzing multi dimensional stochastic models such as queueing networks

achieving diagonal dominance there are many occasions when one would like to see whether a transfer function can be made diagonally dominant there is the obvious and important case of system design using rosenbrock s methods but one also wants to use diagonal dominance in a different manner in robustness studies and in several nonlinear system analysis techniques commonly the compensators or similarity transforms used to achieve dominance are designed in an ad hoc way this paper shows how in the particular case of diagonal compensators or similarity transforms there is a very easy way based on perron frobenius theory of obtaining optimal reduction in the off diagonal elements

a simple solution to the singular linear minimum variance estimation problem a simple expression is obtained for the transfer function matrix of the minimum variance estimator for the states of a linear stationary continuous time right invertible system whose output is measured perfectly using the s domain approach it is shown that the optimal estimator first finds the driving noise input that achieves when applied on the minimum phase image model of the system an output spectrum which is identical to the measurement spectrum this input is then applied on a state space representation of the minimum phase image to produce the optimal estimate

a sufficient condition for simultaneous stabilization the condition under which it is possible to find a single controller that stabilizes k single input single output linear time invariant systems p sub i s i 1 k is investigated the concept of avoidance in the complex plane is introduced and used to derive a sufficient condition for k systems to be simultaneously stabilizable a method for constructing a simultaneous stabilizing controller is also provided and is illustrated by an example

robustness with simultaneous pole and zero movement across the jω axis in this paper we present some new tests for assessing the robustness of the stability property of a feedback design the tests offer a wider scope of application than those previously described in the literature the main result is a robustness test which can be used to assess closed loop stability when the nominal plant model and perturbed plant model representing uncertainty have different numbers of poles and zeros in the right half plane this test also indicates over which frequencies good sensitivity and robust stability are compatible objectives and over which frequencies a compromise has to be made contrary to popular belief if there are no uncertain zeros which can move across the imaginary axis then good sensitivity and robust stability are compatible objectives over the same frequencies

new dominance concepts for multivariable control systems design this paper sets out a revised view of the classical diagonal dominance method for multivariable feedback systems the various types of dominance measure are unified by using one fundamental dominance theorem fd l it is shown that the fundamental dominance condition yields the smallest dominance measure when compared with all the known classical diagonal dominance measures in addition it is shown that the dominance measures such as row column generalized dominance and a few new ones are special cases and can be derived from this same fd theorem this improved dominance criterion also provides the sufficient condition for a system to be approximated by a nominal one in the sense that the stabilization of this nominal system will assure the stability of the original one finally a new type of dominance measure named l dominance is presented it has been shown that this new approach yields an even smaller dominance measure and that when it is applied to matrices with non positive off diagonal elements

an m matrix and majorant approach to robust stability and performance analysis for systems with structured uncertainty uncertain multiinput multioutput systems described in the frequency domain are discussed the theory of nonnegative matrices and m matrices is used along with majorant bounding techniques to develop robust stability and performance results for two types of uncertainty the first type is uncertainty with norm bounded subblocks the second type is uncertainty that has subblocks with known patterns but unknown gains this latter uncertainty representation allows the elements of a given uncertainty block to be correlated for uncertainties of this type a recursive analysis methodology is developed which yields increasingly nonconservative results throughout this paper the performance analysis determines norm bounds on the deviations of the outputs from their nominal values the results are illustrated by a numerical example

describing functions volterra series and the analysis of non linear systems in the frequency domain a relationship between the higher order frequency response functions of the volterra series model and the well known describing function representation for non linear systems is derived it is shown that a large class of generalized describing functions can be derived from the volterra model and that this approach removes the restriction to specific inputs the concept of a worst case transfer function is introduced and examples are included to illustrate the results

dynamics of the maximum marginal likelihood hyperparameter estimation in image restoration gradient descent versus expectation and maximization algorithm dynamical properties of image restoration and hyperparameter estimation are investigated by means of statistical mechanics we introduce an exactly solvable model for image restoration and derive differential equations with respect to macroscopic quantities from these equations we evaluate relaxation processes of the system to the equilibrium state our statistical mechanical approach also enables us to investigate the hyperparameter estimation by means of maximization of the marginal likelihood by using gradient descent and the expectation and maximization algorithm from the dynamical point of view

robust stabilizability for linear systems with both parameter variation and unstructured uncertainty the authors consider the problem of finding a single compensator which stabilizes a plant having both parameter variation and high frequency unstructured uncertainty an uncertain system model is proposed to characterize plants containing those two different uncertainties closed loop stability criteria are then proposed for the model robust stabilizability for single input single output siso systems is studied a number of assumptions describing the set of admissable siso plants are imposed the satisfaction of these assumptions guarantees the existence of a proper stable compensator c s achieving robust stabilization the algorithm used for controller design is recursive in nature and allows the designer to select one compensator coefficient at a time also the minimum order of the desired stabilizer c s depends only on the largest relative degree of the nominal plants which often leads to a lower order compensator

the solution of a transcendental problem and its applications in simultaneous stabilization problems a complete solution for a special transcendental problem in system theory is given one of the interpretations of this transcendental problem is the following simultaneous stabilization problem under what conditions can two linear plants be simultaneously stabilized by a single compensator having no real poles in the closed right half of the complex plane these conditions are completely general and therefore encompass unstable non minimum phase plants as well it is shown that the simultaneous stabilizability of two given plants via such a restricted compensator depends solely on the locations of the real zeros of the two plants and their difference plant in the closed right half of the complex plane for two plants satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is provided and illustrated a computationally checkable necessary condition for simultaneous stabilization of three plants is also given

robust feedback synthesis for nonlinear integro differential equation models using generalized describing functions we propose a technique for synthesizing robust feedback systems for plants described by nonlinear integro differential equations nide with considerable coefficient uncertainties the technique is based on the concept of generalized frequency response functions gfrf and exploits recent results that enable ready derivation of these from the nide description of the plant a powerful synthesis procedure that combines the gfrf and quantitative feedback theory qft technique is given the proposed procedure has several advantages over the existing nonlinear qft methods a nonlinear chemical reactor example is solved using the procedure and is found to yield satisfactory results

interpretation of non linear frequency response functions analytical and graphical methods of interpreting generalised frequency response functions for non linear systems are derived it is shown that non linear phenomena can be classified into intra kernel and inter kernel interference and that worst case responses can be computed the results are illustrated using several discrete and continuous time non linear systems

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

extensions of the small mu test for robust stability the notion of a topologically arcwise connected set is used to develop a general graph topology based robustness test the test provides a switching criterion among different inequality tests and possibly among different nominal models when it is applied to extend the small mu test the result reduces conservatism and allows a more natural application of the test