dilated lmi characterization for the robust finite time control of discrete time uncertain linear systems this paper provides new dilated linear matrix inequalities lmis characterizations for the finite time boundedness ftb and the finite time stability fts analysis of discrete time uncertain linear systems the dilated lmis are later used to design a robust controller for the finite time control of discrete time uncertain linear systems the relevant feature of the proposed approach is the decoupling between the lyapunov and the system matrices that allows considering a parameter dependent lyapunov function in this way the conservativeness with respect to previous results is decreased numerical examples are used to illustrate the results

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

stability robustness of interval matrices via lyapunov quadratic forms a sufficient condition for the robust stability of a class of interval matrices is derived using the lyapunov approach the matrices considered have elements which are nonlinear functions of a vector of independent and bounded parameters the robust stability condition requires that a quadratic form be positive definite in a finite number of conspicuous points of an enlarged parameter space

brief paper a new concept of invariance for saturated systems in this paper the notions of sns invariance and sns domain of attraction are introduced the sns domain of attraction serves as an estimation of the domain of attraction of a saturated system it is shown that in the case of single input saturated systems any contractive set is contained in the sns domain of attraction another important characteristic of the sns domain of attraction is that it contains any estimation obtained by means of a linear difference inclusion of the saturated system a simple algorithm that converges to the sns domain of attraction is presented an illustrative example is given

very simple methods for all pairs network flow analysis a very simple algorithm for the classical problem of computing the maximum network flow value between every pair of nodes in an undirected capacitated n node graph is presented as in the well known gomory hu method the method given here uses only n 1 maximum flow computations our algorithm is implemented by adding only five simple lines of code to any program that produces a minimum cut a program to produce an equivalent flow tree which is a compact representation of the flow values is obtained by adding only three simple lines of code to any program producing a minimum cut a very simple version of the gomory hu cut tree method that finds one minimum cut for every pair of nodes is also derived and it is shown that the seemingly fundamental operation of that method node contraction is not needed nor must crossing cuts be avoided as a result this version of the gomory hu method is implemented by adding less than ten simple lines of code to any program that produces a minimum cut the algor

a linear programming oriented procedure for quadratic stabilization of uncertain systems abstract this paper gives a new necessary and sufficient condition for linear quadratic stabilization of linear uncertain systems when both the dynamic as well as the control matrix are subject to uncertainty a constructive numerical procedure is defined to check the condition and it furthermore provides a stabilizing linear feedback gain some experiments are presented

an nth step set invariance approach to the analysis and design of discrete time linear systems subject to actuator saturation abstract for a discrete time linear system subject to actuator saturation an analysis and design approach based on n th step set invariance is proposed an n th step invariant set is a set from which all trajectories will enter a contractively invariant set in n steps and thus can be used as an estimate of the domain of attraction such an estimate is less conservative than an estimate obtained on the basis of contractive invariance of ellipsoids which excludes initial conditions from which the trajectories overshoot outside the ellipsoid before converging to the origin in comparison with the existing approach based on conventional set invariance the proposed approach results in a larger domain of attraction and better performance both in the analysis of the closed loop system under a given feedback gain and in the design of feedback gain in comparison with the saturated and nonsaturated sns invariant set approach which is an analysis approach the proposed approach can be used for control design even in the presence of plant uncertainties

searchlight based multi voxel pattern analysis of fmri by cross validated manova abstract multi voxel pattern analysis mvpa is a fruitful and increasingly popular complement to traditional univariate methods of analyzing neuroimaging data we propose to replace the standard decoding approach to searchlight based mvpa measuring the performance of a classifier by its accuracy with a method based on the multivariate form of the general linear model following the well established methodology of multivariate analysis of variance manova we define a measure that directly characterizes the structure of multi voxel data the pattern distinctness d our measure is related to standard multivariate statistics but we apply cross validation to obtain an unbiased estimate of its population value independent of the amount of data or its partitioning into training and test sets the estimate d can therefore serve not only as a test statistic but also as an interpretable measure of multivariate effect size the pattern distinctness generalizes the mahalanobis distance to an arbitrary number of classes but also the case where there are no classes of trials because the design is described by parametric regressors it is defined for arbitrary estimable contrasts including main effects pattern differences and interactions pattern changes in this way our approach makes the full analytical power of complex factorial designs known from univariate fmri analyses available to mvpa studies moreover we show how the results of a factorial analysis can be used to obtain a measure of pattern stability the equivalent of cross decoding

stability of uncertain systems using lyapunov functions with non monotonic terms abstract this paper is concerned with the problem of robust stability of uncertain linear time invariant systems in polytopic domains the main contribution is to present a systematic procedure to check the stability of the uncertain systems by using an arbitrary number of quadratic functions within higher order derivatives of the vector field in the continuous time case and higher order differences of the vector field in the discrete time case the matrices of the lyapunov function appear decoupled from the dynamic matrix of the system in the conditions this fact leads to sufficient conditions that are given in terms of linear matrix inequalities defined at the vertices of the polytope the proposed method does not impose sign condition constraints in the quadratic functions that compose the lyapunov function individually moreover some of the quadratic functions do not decrease monotonically along trajectories however if the sufficient conditions are satisfied then a monotonic standard lyapunov function that depends on the dynamics of the uncertain system can be constructed a posteriori numerical examples from the literature are provided to illustrate the proposed approach

beyond the flow decomposition barrier we introduce a new approach to the maximum flow problem this approach is based on assigning arc lengths based on the residual flow value and the residual arc capacities our approach leads to an o min n 2 3 m 1 2 m log n 2 m log u time bound for a network with n vertices m arcs and integral arc capacities in the range 1 u this is a fundamental improvement over the previous time bounds we also improve bounds for the gomory hu tree problem the parametric flow problem and the approximate s t cut problem

constrained nonlinear polynomial time delay systems a sum of squares approach to estimate the domain of attraction a sum of squares sos approach is proposed to estimate the domain of attraction doa of regulated nonlinear polynomial time delay systems subject to input constraints it will be shown that the joint use of semialgebraic geometric arguments and semidefinite programming methods provides an efficient tool for lyapunov based control system analysis and design for this class of nonlinear delayed systems specifically a two step procedure is presented which consists of deriving first a lyapunov krasovskii functional controller pair complying with the prescribed constraints and computing then an estimate of the doa

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

robust h estimation of stationary discrete time linear processes with stochastic uncertainties the problem of h filtering of stationary discrete time linear systems with stochastic uncertainties in the state space matrices is addressed where the uncertainties are modeled as white noise the relevant cost function is the expected value with respect to the uncertain parameters of the standard h performance a previously developed stochastic bounded real lemma is applied that results in a modified riccati inequality this inequality is expressed in a linear matrix inequality form whose solution provides the filter parameters the method proposed is applied also to the case where in addition to the stochastic uncertainty other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope the problem of mixed h2 h filtering for the above system is also treated the theory developed is demonstrated by a simple tracking example

asymptotic permutation tests in general factorial designs summary in general factorial designs where no homoscedasticity or a particular error distribution is assumed the well known wald type statistic is a simple asymptotically valid procedure however it is well known that it suffers from a poor finite sample approximation since the convergence to its 2 limit distribution is quite slow this becomes even worse with an increasing number of factor levels the aim of the paper is to improve the small sample behaviour of the wald type statistic maintaining its applicability to general settings as crossed or hierarchically nested designs by applying a modified permutation approach in particular it is shown that this approach approximates the null distribution of the wald type statistic not only under the null hypothesis but also under the alternative yielding an asymptotically valid permutation test which is even finitely exact under exchangeability finally its small sample behaviour is compared with competing procedures in an extensive simulation study

lmi characterization of structural and robust stability the discrete time case abstract this paper extends to the discrete time case some robust stability conditions recently obtained for continuous time systems those conditions are expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable as in the continuous time case parameter dependent lyapunov functions can be constructed and consequently the new approach can yield much sharper and less conservative results than the simultaneous stability approach in particular well known stability problems namely d stability and robust stability in the presence of diagonally structured uncertainty can be more efficiently addressed numerical examples are included to illustrate the advantages of the new stability conditions

simultaneous stabilization and robust control of polynomial nonlinear systems using sos techniques this technical note is concerned with the simultaneous stabilization and robust performance control for a class of polynomial nonlinear systems building on the tenets of state dependent polynomial lyapunov functions we present sufficient conditions for simultaneous stabilization with and without hinfin performance these conditions can be verified by the recently developed sum of squares technique which essentially solves a linear matrix inequality feasibility problem

an improved lmi condition for robust d stability of uncertain polytopic systems a sufficient condition for robust d stability of linear systems with polytope type uncertainties is proposed the result is based on a linear parameter dependent lyapunov function obtained from the feasibility test of a set of linear matrix inequalities lmis defined at the vertices of the polytope this improved lmi condition encompasses previous results based on additional inequalities as well as results based on extra variables

characterizing the shape of anatomical structures with poisson s equation poisson s equation a fundamental partial differential equation in classical physics has a number of properties that are interesting for shape analysis in particular the equipotential sets of the solution graph become smoother as the potential increases we use the displacement map the length of the streamlines formed by the gradient field of the solution to measure the complexity or smoothness of the equipotential sets and study its behavior as the potential increases we believe that this function complexity f potential which we call the shape characteristic is a very natural way to express shape robust algorithms are presented to compute the solution to poisson s equation the displacement map and the shape characteristic we first illustrate our technique on two dimensional synthetic examples and natural silhouettes we then perform two shape analysis studies on three dimensional neuroanatomical data extracted from magnetic resonance mr images of the brain in the first study we investigate changes in the caudate nucleus in schizotypal personality disorder spd and confirm previously published results on this structure in the second study we present a data set of caudate nuclei of premature infants with asymmetric white matter injury our method shows structural shape differences that volumetric measurements were unable to detect

robust spl hscr sub spl infin filtering for discrete time linear systems with uncertain time varying parameters this paper deals with the problem of robust spl hscr sub spl infin filtering for linear discrete time state space models with uncertain time varying parameters the parameters enter affinely into the state space model matrices and their admissible values and variations are assumed to belong to given intervals a method is derived for designing a linear stationary asymptotically stable filter with a prescribed spl hscr sub spl infin performance in spite of large parameter uncertainty the proposed method incorporates information on available bounds on both the admissible values and variation of the uncertain parameters and is based on a lyapunov function with quadratic dependence on the parameters the filter design is given in terms of linear matrix inequalities

brief paper stability and stabilization of discrete time periodic linear systems with actuator saturation this paper is concerned with the problems of stability and stabilization for discrete time periodic linear systems subject to input saturation both local results and global results are obtained for local stability and stabilization the so called periodic invariant set is used to estimate the domain of attraction the conditions for periodic invariance of an ellipsoid can be expressed as linear matrix inequalities lmis which can be used for both enlarging the domain of attraction with a given controller and synthesizing controllers the periodic enhancement technique is introduced to reduce the conservatism in the methods as a by product less conservative results for controller analysis and design for discrete time time invariant systems with input saturation are obtained for global stability by utilizing the special properties of the saturation function a saturation dependent periodic lyapunov function is constructed to derive sufficient conditions for guaranteeing the global stability of the system the corresponding conditions are expressed in the form of lmis and can be efficiently solved several numerical and practical examples are given to illustrate the theoretical results proposed in the paper

robust control of multi input periodic discrete time systems with saturating actuators this paper proposes the use of a time varying sliding surface for robust transient shaping of periodic linear discrete time plants subject to saturating actuators in the presence of bounded matched uncertainties a constructive procedure is presented and ultimate boundedness of state trajectories is proved

unified framework for robust estimation of brain networks from fmri using temporal and spatial correlation analyses there is a rapidly growing interest in the neuroimaging field to use functional magnetic resonance imaging fmri to explore brain networks i e how regions of the brain communicate with one another this paper presents a general and novel statistical framework for robust and more complete estimation of brain functional connectivity from fmri based on correlation analyses and hypothesis testing in addition to the ability of examining the correlations with each individual seed as in the standard and existing methods the proposed framework can detect functional interactions by simultaneously examining multiseed correlations via multiple correlation coefficients spatially structured noise in fmri is also taken into account during the identification of functional interconnection networks through noncentral f hypothesis tests the associated issues for the multiple testing and the effective degrees of freedom are considered as well furthermore partial multiple correlations are introduced and formulated to measure any additional task induced but not stimulus locked relation over brain regions so that we can take the analysis of functional connectivity closer to the characterization of direct functional interactions of the brain evaluation for accuracy and advantages and comparisons of the new approaches in the presented general framework are performed using both realistic synthetic data and in vivo fmri data

absolute exponential stability of recurrent neural networks with generalized activation function in this paper the recurrent neural networks rnns with a generalized activation function class is proposed in this proposed model every component of the neuron s activation function belongs to a convex hull which is bounded by two odd symmetric piecewise linear functions that are convex or concave over the real space all of the convex hulls are composed of generalized activation function classes the novel activation function class is not only with a more flexible and more specific description of the activation functions than other function classes but it also generalizes some traditional activation function classes the absolute exponential stability aest of the rnn with a generalized activation function class is studied through three steps the first step is to demonstrate the global exponential stability ges of the equilibrium point of original rnn with a generalized activation function being equivalent to that of rnn under all vertex functions of convex hull the second step transforms the rnn under every vertex activation function into neural networks under an array of saturated linear activation functions because the ges of the equilibrium point of three systems are equivalent the next stability analysis focuses on the ges of the equilibrium point of rnn system under an array of saturated linear activation functions the last step is to study both the existence of equilibrium point and the ges of the rnn under saturated linear activation functions using the theory of m matrix in the end a two neuron rnn with a generalized activation function is constructed to show the effectiveness of our results

a parameter dependent approach to robust h_ infty filtering for time delay systems this paper is concerned with the problem of robust h infin filtering for linear continuous time systems with polytopic parameter uncertainties and time varying delay in the state we utilize the polynomially parameter dependent idea to solve the robust h infin filtering problem with new linear matrix inequality conditions obtained for the existence of admissible filters these conditions are developed based on homogeneous polynomially parameter dependent matrices of arbitrary degree the delay dependence and polynomial parameter dependence guarantee the proposed approach to be potentially less conservative which is shown via a numerical example

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

a fuzzy lyapunov function approach to estimating the domain of attraction for continuous time takagi sugeno fuzzy systems this paper deals with stability analysis and control design problems for continuous time takagi sugeno t s fuzzy systems the first aim is to present less conservative linear matrix inequality lmi conditions to design controllers and assess the stability the second relevant contribution is to present a new strategy to find an inner estimate of the domain of attraction da via lmis the results are based on the fuzzy lyapunov functions flfs and non parallel distributed compensation non pdc approaches finally examples illustrate the effectiveness and merits of the proposed methods

a polynomial time algorithm to find the shortest cycle basis of a graph define the length of a basis of the cycle space of a graph to be the sum of the lengths of all cycles in the basis an algorithm is given that finds a cycle basis with the shortest possible length in o m 3 n operations where m is the number of edges and n is the number of vertices this is the first known polynomial time algorithm for this problem edges may be weighted or unweighted also the shortest cycle basis is shown to have at most 3 n 1 n 2 2 edges for the unweighted case o mn 2 algorithm to obtain a suboptimal cycle basis of length o n 2 for unweighted graphs is also given

distances and inference for covariance operators a framework is developed for inference concerning the covariance operator of a functional random process where the covariance operator itself is an object of interest for statistical analysis distances for comparing positive definite covariance matrices are either extended or shown to be inapplicable to functional data in particular an infinite dimensional analogue of the procrustes size and shape distance is developed convergence of finite dimensional approximations to the infinite dimensional distance metrics is also shown for inference a frechet estimator of both the covariance operator itself and the average covariance operator is introduced a permutation procedure to test the equality of the covariance operators between two groups is also considered additionally the use of such distances for extrapolation to make predictions is explored as an example of the proposed methodology the use of covariance operators has been suggested in a philological study of cross linguistic dependence as a way to incorporate quantitative phonetic information it is shown that distances between languages derived from phonetic covariance functions can provide insight into the relationships between the romance languages

static output feedback control synthesis for linear systems with time invariant parametric uncertainties this technical note is concerned with the problem of designing robust static output feedback controllers for linear discrete and continuous time systems with time invariant polytopic uncertainties sufficient conditions for static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities furthermore the results are also extended to h2 static output feedback controller designs numerical examples are given to illustrate the effectiveness of the proposed design methods

design of distributed decentralized estimators for formations with fixed and stochastic communication topologies this paper proposes a solution to the problem of synthesizing distributed decentralized estimators for a formation of agents the collected dynamics of the formation are modeled by a discrete lti system in the considered estimation structure each agent of the formation carries an estimate of the entire formation state agents of the formation can communicate information between each other through unidirectional links modeled with a fixed or a stochastic communication topology the design procedures are based on a set of convex optimization problems with linear matrix inequalities and result in the suboptimal choice of estimator gains which stabilize the estimation error dynamics and minimize a norm of the estimation error correlation matrix

a note on sampled data stabilization of lti systems with aperiodic sampling in this technical note we are concerned with linear matrix inequality lmi approaches for solving sampled data state feedback control design problems of linear time invariant systems this short contribution discusses a simple alternative to a family of lmi approaches based on the polytopic linear difference inclusion representation of the original problem with the aid of the so called matrix dilation technique the proposed condition is capable of being directly derived from the discrete time lyapunov inequality without the polytopic modeling finally numerical experiments are given to illustrate the results

brief stability analysis of discrete time systems with actuator saturation by a saturation dependent lyapunov function in this paper stability of discrete time linear systems subject to actuator saturation is analyzed using a saturation dependent lyapunov function this saturation dependent lyapunov function captures the real time information on the severity of actuator saturation and leads to less conservative estimate of the domain of attraction which is based on the solution of an lmi optimization problem numerical examples are presented to show the effectiveness of the proposed method

augmented lyapunov function approach to l2 gain analysis for discrete time systems with saturation nonlinearities abstract this paper presents a method for l 2 gain analysis of discrete time systems with saturation nonlinearity by using an augmented lyapunov functional by using sector and slope properties of the saturation nonlinearity the l 2 gain performance criterion is obtained via lmi formulation the proposed lyapunov function have augmented quadratic form with states as well as the sector bounded nonlinear function numerical examples show that the proposed method is less conservative than the existing ones

analysis and design for discrete time linear systems subject to actuator saturation we present a method to estimate the domain of attraction for a discrete time linear system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis the following surprising result is revealed for systems with single input suppose that an ellipsoid is made invariant with a linear feedback then it is invariant under the saturated linear feedback if and only if there exists a saturated nonlinear feedback which makes the ellipsoid invariant finally the set invariance condition is extended to determine invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements

robust permutation tests for correlation and regression coefficients abstractgiven a sample from a bivariate distribution consider the problem of testing independence a permutation test based on the sample correlation is known to be an exact level test however when used to test the null hypothesis that the samples are uncorrelated the permutation test can have rejection probability that is far from the nominal level further the permutation test can have a large type 3 directional error rate whereby there can be a large probability that the permutation test rejects because the sample correlation is a large positive value when in fact the true correlation is negative it will be shown that studentizing the sample correlation leads to a permutation test which is exact under independence and asymptotically controls the probability of type 1 or type 3 errors these conclusions are based on our results describing the almost sure limiting behavior of the randomization distribution we will also present asymptotically robust randomization tests for regression coeffi

periodically time varying cal h _ infty memory filter design for discrete time lti systems with polytopic uncertainty this technical note focuses on the development of a general periodically time varying memory filter ptvmf to improve the robust h filtering performance for discrete time linear time invariant lti systems with polytopic parameter uncertainties a sufficient condition to design the h ptvmf is given in terms of convex optimizations expressed as linear matrix inequalities lmis finally examples demonstrate its potential less conservatism

a new discrete time stabilizability condition for linear parameter varying systems we introduce a new condition for the stabilizability of discrete time linear parameter varying lpv systems in the form of linear matrix inequalities lmis a distinctive feature of the proposed condition is the ability to handle variation in both the dynamics as well as in the input matrix without resorting to dynamic augmentation or iterative procedures we show that this new condition contains the existing poly quadratic stabilizability result as a particular case a numerical example illustrates the results

brief positive polynomial matrices and improved lmi robustness conditions recently several new lmi conditions for stability of linear systems have been proposed introducing additional slack variables to reduce the gap between conservative convex quadratic stability conditions and intractable non convex robust stability conditions in this paper we show that these improved lmi conditions can be derived with the help of some basic results on positive polynomial matrices the approach allows us to derive in a unifying way results in the state space and polynomial frameworks applications to robust stability analysis and robust stabilization of systems with multi linear parametric uncertainty are fully described

stability and performance analysis of saturated systems via partitioning of the virtual input space this paper revisits the problem of estimating the domain of attraction and the nonlinear l 2 gain for systems with saturation nonlinearities we construct a virtual input space from the algebraic loop contained in systems and divide this virtual input space into several regions in one of these regions none of the virtual inputs saturate in each of the remaining regions there is a unique virtual input that saturates everywhere with the time derivative of its saturated signal being zero these special properties of the virtual inputs in different regions of the virtual input space are combined with an existing piecewise quadratic lyapunov function that contains the information of virtual input saturation to arrive at a set of less conservative stability and performance conditions from which we can obtain a larger level set of the piecewise quadratic lyapunov function as an estimate of the domain of attraction and a tighter scalar function of the bound on the l 2 norm of the exogenous input as an estimate of the local nonlinear l 2 gain simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction and a significantly tighter estimate of the nonlinear l 2 gain than the existing methods

stochastic stabilization of a class of nonhomogeneous markovian jump linear systems this paper deals with the problem of stochastic stability analysis and control synthesis of a class of markovian jump linear systems mjls with time varying transition probabilities tps in the discrete time domain the time varying character is considered to be in a polytopic sense the approach followed in this note is based on the use of a parameter dependent stochastic lyapunov function we give a stability condition in terms of a linear matrix inequality lmi feasibility problem the obtained results are illustrated in a numerical example

robust filtering for uncertain nonlinearly parameterized plants we address the robust filtering problem for a wide class of systems whose state space data assume a very general nonlinear dependence in the uncertain parameters our resolution methods rely on new linear matrix inequality characterizations of spl hscr sub 2 and spl hscr sub spl infin performances which in conjunction with suitable linearization transformations of the variables give rise to practical and computationally tractable formulations for the robust filtering problem

a generalization of kharitonov s four polynomial concept for robust stability problems with linearly dependent coefficient perturbations kharitonov s four polynomial concept is generalized to the case of linearly dependent coefficient perturbations and more general zero location regions to this end a specially constructed scalar function of a scalar variable is instrumental to the robustness analysis the present work is motivated by two fundamental limitations of kharitonov s theorem namely 1 the theorem only applies to polynomials with independent coefficient perturbations and 2 it only applies to zeros in the left hand plane

a new decentralised controller design method for a class of strongly interconnected systems abstractin this paper two interconnected structures are first discussed under which some closed loop subsystems must be unstable to make the whole interconnected system stable which can be viewed as a kind of strongly interconnected systems then comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown a new approach for the design of decentralised controllers is presented by determining the lyapunov function structure previously which allows the existence of unstable subsystems by fully utilising the orthogonal space information of input matrix some new understandings are presented for the construction of lyapunov matrix this new method can deal with decentralised state feedback static output feedback and dynamic output feedback controllers in a unified framework furthermore in order to reduce the design conservativeness and deal with robustness a new robust decentralised controller design method is given by combining with the parameter depend

on robust stability and set invariance of switched linear parameter varying systems in this paper we address the problem of robust stability and set invariance of switched linear parameter varying lpv systems affected by bounded disturbances a switched lpv system is a collection of single lpv subsystems with a switching rule that decides which subsystem is active at each time this framework is useful for lpv systems with large parameter variation range for which it may be difficult to assess or guarantee stability over the whole parameter range our first contribution is to derive a result for a single lpv system that extends and generalises previous work for switched systems our second and main contribution is to apply this seed result in the derivation of dwell time type conditions on the switched lpv switching rule which ensure robust closed loop stability and set invariance of the trajectories of the switched lpv system across the whole parameter range as an application of the results we consider the problem of reference tracking for lpv systems using switched lpv state fe

properties of gomory hu co cycle bases let d v a be a directed graph with non negative arc weights we study the problem of computing certain special co cycle bases of d in particular a minimum weight weakly fundamental co cycle basis a co cycle in d corresponds to a cut in the underlying undirected graph and a 1 0 1 arc incidence vector is associated with each co cycle where the 1 coordinates are used for the arcs crossing the cut the weight of a co cycle c is the sum of the weights of those arcs a such that c a 1 the vector space over q generated by the arc incidence vectors of the co cycles is the co cycle space of d the co cycle space of d can also be defined as the orthogonal complement of the cycle space of d a set of linearly independent co cycles that span the co cycle space is a co cycle basis of d the problem of computing a co cycle basis c 1 c k such that the sum of weights of the co cycles in the basis is the least possible is the minimum co cycle basis problem a co cycle basis c 1 c k is weakly fundamental if for every i there is an arc a i such that c i a i 1 while c j a i 0 for j i the minimum cycle basis problem in directed and undirected graphs is a well studied problem and while polynomial time algorithms are known for these problems the problem of computing a minimum weight weakly fundamental cycle basis has recently been shown to be apx hard we show that the co cycle basis corresponding to the cuts of a gomory hu tree t of the underlying undirected graph of d is a minimum weight weakly fundamental co cycle basis of d this is in fact a minimum co cycle basis of d and it is also totally unimodular thus this is a special co cycle basis that simultaneously answers several questions in the domain of co cycle bases it is known that there is no such special cycle basis for general graphs

a new robust d stability condition for real convex polytopic uncertainty abstract the problem of robust d stability analysis with respect to real convex polytopic uncertainties is tackled a new lmi based sufficient condition for the existence of parameter dependent lyapunov functions is proposed this condition generalises previously published conditions numerical comparisons with quadratic stability results as well as previous results based on parameter dependent lyapunov functions illustrate the relevance of this new condition finally this result appears to be promising for robust multi objective performance analysis and control synthesis purposes

local stabilization of discrete time linear systems with saturating controls an lmi based approach deals with the problem of local stabilization of linear discrete time systems subject to control saturation a linear matrix inequalities based framework is proposed in order to compute a saturating state feedback that stabilizes the system with respect to a given set of admissible initial states and in addition guarantees some dynamical performances when the system operates in the zone of linear behavior i e when the controls are not saturated

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

finite time h control for a class of discrete time switched singular time delay systems subject to actuator saturation this paper concerns with the finite time h control problem for a class of discrete time switched singular time delay with actuator saturation not only linear matrix inequality conditions for the systems but also average dwell time of switching signal is given to guarantee regular causal and finite time boundedness for the discrete time switched singular time delay system moreover sufficient conditions are presented to ensure the h disturbance attenuation level and the design method of h controller is developed by solving linear matrix inequalities lmi optimization problem without any decompositions of system matrices and equivalent transformation furthermore the function in the proof procedure belongs to multiple lyapunov like functions whose advantage lies in their flexibility finally numerical examples are employed to verify the effectiveness of the proposed methods and to illustrate the significant improvement on the conservativeness of some reported results in the literature

gain scheduled output control design for a class of discrete time nonlinear systems with saturating actuators this paper deals with the stabilization of a class of nonlinear discrete time systems under control saturations including time varying parameter dependency the control law studied consists of the gain scheduled feedback of the measured output and of the nonlinearity present in the dynamics of the controlled system furthermore the saturations are taken into account by modeling the nonlinear saturated system through a dead zone nonlinearity satisfying a modified sector condition thus as for precisely known systems linear matrix inequality lmi stabilization conditions are proposed for such a generic system these conditions can be cast into convex programming problems for design purposes an illustrative example stresses the efficiency of the main result

periodic memory state feedback controller new formulation analysis and design results this paper proposes a unified setup for robust stability and performance analysis and synthesis for periodic polytopic discrete time systems relying on a general formulation for state feedback periodic memory controllers and a new time lifting new sufficient lmi conditions for the existence of robust stability certificates and h2 guaranteed cost control laws are derived comparisons of the efficiency of different controller structures illustrate these developments on a numerical example

selective hbox scr h _2 and hbox scr h _ infty stabilization of takagi sugeno fuzzy systems this paper presents new results concerning the stability analysis and design of state feedback controllers for continuous time takagi sugeno t s fuzzy systems via fuzzy lyapunov functions the membership functions of the t s fuzzy systems are modeled in a space that is defined by the cartesian product of simplexes called a multisimplex if the time derivatives of the membership functions are bounded the bounds are used to construct a polytope that models the space of the time derivatives of the membership functions linear matrix inequality lmi relaxations that are based on polynomial matrices are provided for stability analysis and controller design extensions for the design of control laws that minimize upper bounds to h2 and h norms are also given the main novelty of this method is that it allows one to synthesize control gains which depends only on some premise variables that are selected by the designer numerical experiments illustrate the flexibility and advantages of the proposed method

discrete time l and l2 norm vanishment and low gain feedback with their applications in constrained control the existing low gain feedback which is a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero has been designed in very specific ways in this paper by recognizing the l and l 2 slow peaking phenomenon that exists in discrete time systems under low gain feedback more general notions of l and l 2 norm vanishment are considered so as to provide a full characterization of the nonexistence of slow peaking phenomenon in some measured signals low gain feedback that does not lead to l and l 2 slow peaking in the control input are respectively referred to as l and l 2 low gain feedback based on the notions of l and l 2 vanishment not only can the existing low gain feedback be recognized as an l low gain feedback but also a new design approach referred to as the l 2 low gain feedback approach is developed for discrete time linear systems parallel to the effectiveness of l low gain feedback in magnitude constrained control the l 2 low gain feedback is instrumental in the control of discrete time systems with control energy constraints the notions of l and l 2 vanishment also result in a systematic approach to the design of l and l 2 low gain feedback by providing a family of solutions including those resulting from the existing design methods

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

robust control of uncertain discrete time markovian jump systems with actuator saturation in this paper the robust stochastic stabilization problem for the class of discrete time uncertain markovian jump linear systems mjls with actuator saturation is considered the definition of domain of attraction in mean square sense doa mss is introduced to analyze the stochastic stability of the closed loop system by using a class of stochastic lyapunov function which is dependent on the jump mode and saturation function design procedures for both the mode dependent and mode independent state feedback controllers are developed based on the linear matrix inequality lmi approach finally a numerical example is provided to show the usefulness of the proposed techniques

anti windup strategies for discrete time switched systems subject to input saturation this paper deals with the design of anti windup compensator for discrete time switched systems subject to input saturation the cases of static and dynamic anti windup controllers are addressed aiming at maximising the estimate of the basin of attraction of the origin for the closed loop system two aspects of the switching law are taken into account during the design either it is arbitrary or it is a part of the complete control law theoretical conditions allowing to synthesise the anti windup compensator are mainly described through linear matrix inequalities computational oriented conditions are then provided to solve convex optimisation problems that are able to give a constructive solution

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

parameter dependent lyapunov functions for discrete time systems with time varying parametric uncertainties abstract in this paper we consider discrete time systems with polytopic time varying uncertainty we look for a class of parameter dependent lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter we show that extending the new discrete time stability condition proposed by de oliveira et al systems control lett 36 1999 135 to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a lyapunov function this allows to check asymptotic stability of the system under study the obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem