two conditions concerning common quadratic lyapunov functions for linear systems concerning a pair of linear systems some triangle conditions for the existence of a common quadratic lyapunov function are presented in this paper these conditions are derived from a criterion for judging the semipositiveness of a linear map defined on symmetric matrices

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

stability and stabilization of switched linear time invariant systems with saddle points and switching delays this paper addresses global asymptotic stability gas and stabilization issues of switched linear time invariant lti systems with saddle points and time varying switching delays firstly two criteria of gas are proposed for such switched systems with all subsystems sharing a common unique saddle point under arbitrary periodic quasi periodic switching paths psp qsp secondly by using our stability results we design global asymptotic stabilizing controls gasc periodic quasi periodic stabilizing switching paths pssp qssp and an algorithm of gasc and pssp qssp for the switched systems finally we present a numerical example of a switching multi agent system to illustrate the effectiveness and practicality of our new results

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

eigenvalue based algorithms for testing positive realness of siso systems a computational test for scalar positive real and strictly positive real functions is proposed in this paper the input for this algorithm is state space representation not necessarily minimal it is derived for the discrete time problem based on numerical stable eigenvalue computations the test can be used in the continuous counterpart which is in fact an improvement of an algorithm posed by bai and freund differences between the discrete and continuous time problems are also pointed out

construction of lyapunov krasovskii functionals for switched nonlinear systems with input delay abstract this paper studies the stability issue for switched nonlinear systems with input delay and disturbance it is assumed that for the nominal system an exponential stabilizing controller is predesigned such that the switched system is stable under a certain switching signal and a piecewise lyapunov function for the corresponding closed loop system is known however in the presence of input delay and disturbance the system may be unstable under the same switching signal for this case a new lyapunov krasovskii functional is firstly constructed based on the known lyapunov function then by employing this new functional a new switching signal satisfying the new average dwell time conditions is constructed to guarantee the input to state stability of the system under a certain delay bound the bound on the average dwell time is closely related to the bound on the input delay finally numerical examples are given to illustrate the effectiveness of the proposed theory

on reachability and stabilization of switched linear systems reachability and stabilization issues for switched linear control systems are addressed a necessary and a sufficient condition are presented for reachability under mild assumptions we prove that the switched linear control systems are stabilizable in addition we show that an element driven switching stabilization strategy can be explicitly constructed

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

stability robustness for linear state space models a lyapunov mapping approach some pythagorean like conditions for the existence of a common lyapunov solution for two given matrices are presented these conditions are set on the lyapunov mappings associated with given matrices the key is the semipositiveness of linear mappings defined on symmetric matrices from the viewpoint of the existence of a common lyapunov solution some known stability robustness results are reviewed and refined

stabilization of switched systems with nonlinear impulse effects and disturbances in this note we investigate the stabilization of switched systems with nonlinear impulse effects and disturbances based on the estimate on transition matrices and gronwall inequality feedback laws are designed to achieve the exponential stability of the closed loop system with arbitrary switching frequency

stabilization of switched linear systems in this note we study the stabilization problem of systems that switch among a finite set of controllable linear systems with arbitrary switching frequency for both cases of known and unknown switching functions feedback laws are designed to achieve exponential stability for the later case a method combining on line adaptive estimation and feedback stabilization is developed in the controller design

cpmc automatic object segmentation using constrained parametric min cuts we present a novel framework to generate and rank plausible hypotheses for the spatial extent of objects in images using bottom up computational processes and mid level selection cues the object hypotheses are represented as figure ground segmentations and are extracted automatically without prior knowledge of the properties of individual object classes by solving a sequence of constrained parametric min cut problems cpmc on a regular image grid in a subsequent step we learn to rank the corresponding segments by training a continuous model to predict how likely they are to exhibit real world regularities expressed as putative overlap with ground truth based on their mid level region properties then diversify the estimated overlap score using maximum marginal relevance measures we show that this algorithm significantly outperforms the state of the art for low level segmentation in the voc 2009 and 2010 data sets in our companion papers 1 2 we show that the algorithm can be used successfully in a segmentation based visual object category recognition pipeline this architecture ranked first in the voc2009 and voc2010 image segmentation and labeling challenges

robust l reliable control for uncertain nonlinear switched systems with time delay this paper investigates the robust reliable l control for a class of uncertain switched nonlinear systems with time delay firstly l performance condition for nonlinear switched system with time delay is proposed then a sufficient condition of exponential stability with l performance for switched system is given furthermore a design methodology of the robust l reliable control for switched nonlinear systems with time delay and parameter uncertainties is presented the proposed state feedback controller which guarantees exponential stability of closed loop system can be obtained using a set of linear matrix inequalities lmis finally a numerical example is given to illustrate the effectiveness of the main results

necessary and sufficient conditions for stabilization of discrete time planar switched systems abstract this paper discusses the stabilization problem for single input discrete time planar switched systems we establish necessary and sufficient conditions for the stabilization of planar switched systems a series of linear inequalities are presented for describing the set of all common quadratic lyapunov functions our results are not only easily testable but also constructive

design of strictly positive real systems using constant output feedback the authors present a linear matrix inequality lmi approach to the strictly positive real spr synthesis problem find an output feedback k such that the closed loop system t s is spr the authors establish that if no such constant output feedback k exists then no dynamic output feedback with a proper transfer matrix exists to make the closed loop system spr the existence of k to guarantee the spr property of the closed loop system is used to develop an adaptive control scheme that can stabilize any system of arbitrary unknown order and unknown parameters

numerical solution of hybrid systems of differential algebraic equations abstract we present a mathematical framework for general over and under determined hybrid switched systems of differential algebraic equations hdaes we give a systematic formulation of hdaes and discuss existence and uniqueness of solutions the treatment of the switch points and how to perform consistent initialization at switch points we show how numerical solution methods for daes can be adapted for hdaes and present a numerical results for these methods for the real world example of simulating an automatic gearbox

technical communique on stability of a class of switched nonlinear systems this note is focused on the stability analysis for a class of switched nonlinear systems with disturbance input and delay sufficient conditions in terms of linear inequalities are presented such that the switched system is asymptotically stable for arbitrary switching any admissible sector nonlinearities and disturbances and any constant delay we not only drop a condition of one result given in aleksandrov chen platonov and zhang 2011 but also extend the main result to a more general switched nonlinear system with disturbance input and delay

necessary and sufficient conditions for regional stabilisability of second order switched linear systems with a finite number of subsystems in this paper the switching stabilisation problem of second order switched linear systems is studied by extending the best case switching signal bcss criteria for second order switched linear systems with two subsystems to the general case with any finite number of subsystems necessary and sufficient conditions for regional stabilisability of second order switched linear systems with any finite number of subsystems are proposed in this paper the main idea of this paper is to divide all the subsystems in a region into two groups based on their trajectory directions in that region by comparing pairwise the most stable subsystem for each group in a region can be determined and the bcss analysis among all the subsystems in that region is reduced to the bcss analysis between the two most stable subsystems in that region

improved overshoot estimation in pole placements and its application in observer based stabilization for switched systems in this note we first establish an improved and generalized overshoot estimation in pole placements then this estimation is applied to the observer based output feedback stabilization problem for switched linear systems with arbitrary switching frequency our results complement those results of cheng about the state feedback stabilization of switched linear systems

on quadratic lyapunov functions a topological structure as a subset of 0 2 spl pi sup l spl times spl ropf sub sup n 1 is proposed for the set of quadratic lyapunov functions qlfs of a given stable linear system a necessary and sufficient condition for the existence of a common qlf of a finite set of stable matrices is obtained as the positivity of a certain integral the structure and the conditions are considerably simplified for planar systems it is also proved that a set of block upper triangular matrices share a common qlf if each set of diagonal blocks share a common qlf

stability condition for sampled data based control of linear continuous switched systems abstract most practical systems are continuous in nature but with discrete sampled feedback when digital control is utilized this paper investigates the stabilization problem of switched linear continuous time systems with sampled data based control for both known and unknown arbitrary switching processes on the basis of lyapunov stability theory a sufficient global exponential stability condition related to dwell time and sampling period is established for the latter case on line one step adaptive estimation algorithm is derived and integrated with sampled feedback for control design validation and verification of the established result are conducted through cruise control of train systems

necessary and sufficient conditions for regional stabilisability of generic switched linear systems with a pair of planar subsystems in this article the regional stabilisability issues of a pair of planar lti systems are investigated through the geometrical approach and easily verifiable necessary and sufficient conditions are derived the main idea of the article is to characterise the best case switching signals based upon the variations of the constants of the integration of the subsystems the conditions are generic as all possible combinations of the subsystem dynamics are considered

object proposal with kernelized partial ranking abstract object proposals are an ensemble of bounding boxes with high potential to contain objects in order to determine a small set of proposals with a high recall a common scheme is extracting multiple features followed by a ranking algorithm which however incurs two major challenges 1 the ranking model often imposes pairwise constraints between each proposal rendering the problem away from an efficient training testing phase 2 linear kernels are utilized due to the computational and memory bottleneck of training a kernelized model in this paper we remedy these two issues by suggesting a kernelized partial ranking model in particular we demonstrate that i our partial ranking model reduces the number of constraints from o n2 to o nk where n is the number of all potential proposals for an image but we are only interested in top k of them that has the largest overlap with the ground truth ii we permit non linear kernels in our model which is often superior to the linear classifier in terms of accuracy for the sake of mitigating the computational and memory issues we introduce a consistent weighted sampling cws paradigm that approximates the non linear kernel as well as facilitates an efficient learning in fact as we will show training a linear cws model amounts to learning a kernelized model extensive experiments demonstrate that equipped with the non linear kernel and the partial ranking algorithm recall at top k proposals can be substantially improved

on stability of switched homogeneous nonlinear systems in this paper the problem of stability of switched homogeneous systems is addressed first of all if there is a quadratic lyapunov function such that nonlinear homogeneous systems are asymptotically stable a matrix lyapunov like equation is obtained for a stable nonlinear homogeneous system using semi tensor product of matrices and lyapunov equation of linear system is just its particular case following the previous results a sufficient condition is obtained for stability of switched nonlinear homogeneous systems and a switching law is designed by partition of state space in particular a constructive approach is provided to avoid chattering phenomena which is caused by the switching rule then for planar switched homogeneous systems an lmi approach to stability of planar switched homogeneous systems is presented similar to the condition for linear systems the lmi type condition is easily verifiable an example is given to illustrate that candidate common lyapunov function is a key point for design of switching law

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

properties of linear switching time varying discrete time systems with applications abstract we study two discrete time linear switching time varying lstv structures each of which consists of a periodic switch connected to several linear time invariant lti systems such structures can be used to represent any linear periodically time varying lptv systems we give basic properties associated with the lstv structures in terms of their lti building blocks and then apply the results to solve a general approximation problem how to optimally approximate an lptv system with period p by an lptv system with period p the optimality is measured using h 2 norms the study is extended to general multirate periodic systems

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

technical communique a new stability analysis of switched systems in this paper we present a new stability analysis of switched systems we introduce the concepts of minimum maximum holding time and redundancy as a tool for lyapunov stability the presented results are more practical than the existing stability analyses that introduce multiple lyapunov functions

stabilization of planar switched systems this paper considers the problem of stabilization of single input planar switched systems we assume the switching law is observable a formula is presented which provides a necessary and sufficient condition for the system to be quadratically stabilizable a set of linear inequalities are given to describe the set of all quadratic lyapunov functions the solvability and the control design technique are clearly described in a straightforward computation algorithm

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

stability of switched systems a lie algebraic condition we present a sucient condition for asymptotic stability of a switched linear system in terms of the lie algebra generated by the individual matrices namely if this lie algebra is solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of linear systems satisfying this condition possesses a quadratic common lyapunov function we also discuss the implications of this result for switched nonlinear systems c 1999 elsevier science b v all rights reserved

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

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

dissipativity based sliding mode control of switched stochastic systems this technical brief is concerned with dissipativity analysis and dissipativity based sliding mode control smc of continuous time switched stochastic systems firstly a sufficient condition is proposed to guarantee the mean square exponential stability and strict dissipativity for the switched stochastic system then an integral type sliding surface function is designed for establishing a sliding mode dynamics which can be formulated by a switched stochastic system with an external disturbance uncertainty dissipativity analysis and synthesis are both investigated for the sliding mode dynamics and consequently sufficient conditions are derived which pave the way for solving the dissipativity analysis and control problems moreover a smc law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time finally the efficiency of the theoretical findings is demonstrated by an illustrative example

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

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

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

output tracking control of nonlinear switched cascade systems using a variable structure control method this article is concerned with the output tracking control problem for a class of nonlinear switched cascade systems under some average dwell time based switching laws firstly stabilisation problem of this class of switched systems is considered then the result is extended to the output tracking control problem based on the variable structure control technique and the characteristic of the system the variable structure controllers and the average dwell time are designed the effectiveness of the proposed design approach is illustrated with simulation results

strictly positive real transfer functions revisited the two most commonly used definitions of strictly positive real spr transfer functions are reviewed contrary to what has been suggested in the literature it is proven that the least restrictive weak definition of the two is clearly related to the yacubovich kalman lemma the relationship between time and frequency domain conditions pertaining to the weak definition of spr systems is established

hamilton paths in grid graphs a grid graph is a node induced finite subgraph of the infinite grid it is rectangular if its set of nodes is the product of two intervals given a rectangular grid graph and two of its nodes we give necessary and sufficient conditions for the graph to have a hamilton path between these two nodes in contrast the hamilton path and circuit problem for general grid graphs is shown to be np complete this provides a new relatively simple proof of the result that the euclidean traveling salesman problem is np complete

robust stability of uncertain discrete impulsive switching systems this paper studies discrete impulsive switching systems and uncertain linear discrete switching systems it establishes some stability and robust stability criteria for such systems by using the method of lyapunov functions and linear matrix inequalities lmi these criteria are verifiable by using the lmi toolbox of matlab

fault tolerant hamiltonicity in a class of faulty meshes abstract this paper addresses the hamiltonian properties of rectangular meshes with faulty nodes we present a necessary and sufficient condition for an m n mesh m 4 and n 4 are even with two faulty nodes to have a fault free hamiltonian cycle which generalizes a result owing to kim and yoon j s kim s h yoon embedding of rings in 2 d meshes and tori with faulty nodes journal of systems architecture 43 9 1997 643 654 we also describe an efficient scheme for constructing such a fault free hamiltonian cycle if there is

canonical forms of generic piecewise linear continuous systems this technical note reports a simple but effective strategy to derive a single coordinate transformation of a generic n dimensional piecewise linear continuous vector field that puts both of its subsystems into the same observer or control canonical form the only hypothesis required is that both subsystems are either observable or controllable to derive the result the structure of the system is used in order to prove that it suffices to consider the same transformation for both subsystems the theoretical results are illustrated by means of the colpitts oscillator as a practical case of study

controllability of switched bilinear systems the controllability of switched bilinear systems sblss is considered three kinds of controllabilities including weak controllability approximate controllability and global controllability are investigated one by one sets of easily verifiable sufficient conditions are obtained for each case which are applicable to a large class of switched bilinear systems

stability analysis of stochastic hybrid jump linear systems using a markov kernel approach in this paper the state dynamics of a supervisor implemented with a digital sequential system are represented with a finite state machine fsm the supervisor monitors a symbol sequence derived from a linear closed loop system s performance and generates a switching signal for the closed loop system the effect of random events on the performance of the closed loop system is analyzed by adding an exogenous markov process input to the fsm and by appropriately augmenting a switched system representation of the supervisor and the closed loop system for this class of hybrid jump linear systems the switching signal is in general a non markovian process making it hard to analyze its stability properties this is ameliorated by introducing a sufficient mean square stability test that uses only upper bounds on the one step transition probabilities of the switching signal these bounds are explicitly derived from a markov kernel associated with the hybrid system model this stability test becomes necessary and sufficient when the switching signal is markovian to determine tighter stability bounds procedures to determine the upper bound transition probability matrices when the fsm has a moore or a mealy type output map are presented two examples illustrate the applicability of the presented results

stability and stabilisation of planar switched linear systems via lasalle s invariance principle this paper investigates the problem of uniformly asymptotical stability uas and stabilisation of planar switched linear systems using lasalle s invariance principle of switched systems first we show that a common weak quadratic lyapunov function wqlf is enough to assure the uas of a switched linear system with stable modes then the necessary and sufficient conditions for the existence of common wqlf are obtained secondly we consider the problem of uniformly asymptotical stabilisation uasz of single input planar switched linear systems necessary and sufficient conditions for the closed loop system with proper feedback to share a common wqlf are presented it is also proved that a common wqlf is enough to assure the uas of the closed loop system

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

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

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

frequency domain conditions for strictly positive real functions frequency domain conditions for strictly positive real spr functions which appear in literature are often only necessary or only sufficient this point is raised in 1 2 where necessary and sufficient conditions in the s domain are given for a transfer function to be spr in this note the points raised in 1 i2 are clarified further by giving necessary and sufficient conditions in the frequency domain for transfer functions to be spr these frequency domain conditions are easier to test than those given in the s domain or time domain 1 2

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

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

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

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

on a class of marginally stable positive real systems a class of marginally stable positive real systems is defined which is less restrictive than the previously published definitions of strictly positive real systems a minimal realization and state space characterization of such systems are presented and it is proven that controllers belonging to this class robustly stabilize positive real plants

time domain and frequency domain conditions for strict positive realness the author states various time domain and frequency domain conditions pertaining to multivariate strict positive real systems and establishes the relationship between these conditions their relationship is clarified by means of a three tier diagram each tier represents a set of equivalent conditions successively stronger than the lower tier the main theorem in the present study can be considered as the positive realness lemma for strictly positive real systems

efficient subwindow search a branch and bound framework for object localization most successful object recognition systems rely on binary classification deciding only if an object is present or not but not providing information on the actual object location to estimate the object s location one can take a sliding window approach but this strongly increases the computational cost because the classifier or similarity function has to be evaluated over a large set of candidate subwindows in this paper we propose a simple yet powerful branch and bound scheme that allows efficient maximization of a large class of quality functions over all possible subimages it converges to a globally optimal solution typically in linear or even sublinear time in contrast to the quadratic scaling of exhaustive or sliding window search we show how our method is applicable to different object detection and image retrieval scenarios the achieved speedup allows the use of classifiers for localization that formerly were considered too slow for this task such as svms with a spatial pyramid kernel or nearest neighbor classifiers based on the lambda2 distance we demonstrate state of the art localization performance of the resulting systems on the uiuc cars data set the pascal voc 2006 data set and in the pascal voc 2007 competition

object proposal generation using two stage cascade svms object proposal algorithms have shown great promise as a first step for object recognition and detection good object proposal generation algorithms require high object detection recall rate as well as low computational cost because generating object proposals is usually utilized as a preprocessing step the problem of how to accelerate the object proposal generation and evaluation process without decreasing recall is thus of great interest in this paper we propose a new object proposal generation method using two stage cascade support vector machines svms where in the first stage linear filters are learned for predefined quantized scales aspect ratios independently and in the second stage a global linear classifier is learned across all the quantized scales aspect ratios for calibration so that all the windows from the first stage can be compared properly the windows with highest scores from the second stage are kept as inputs to our new efficient proposal calibration algorithm to improve their localization quality significantly resulting in our final object proposals we explain our scale aspect ratio quantization scheme and investigate the effects of combinations of ell 1 and ell 2 regularizers in cascade svms with without ranking constraints in learning comprehensive experiments on voc2007 dataset are conducted and our method is comparable with the current state of the art methods with much better computational efficiency

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

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

on kalman yakubovich popov lemma for stabilizable systems the kalman yakubovich popov kyp lemma has been a cornerstone in system theory and network analysis and synthesis it relates an analytic property of a square transfer matrix in the frequency domain to a set of algebraic equations involving parameters of a minimal realization in time domain this note proves that the kyp lemma is also valid for realizations which are stabilizable and observable

a converse lyapunov theorem for a class of dynamical systems which undergo switching the authors investigate the stability of a system in which the dynamics at any instant in time will follow one of a fixed set of vector fields they allow switching between members of the family of vector fields to be completely random the focus of this paper is to prove a converse lyapunov theorem for this class of systems

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

delay independent criteria for exponential admissibility of switched descriptor delayed systems this paper deals with the uniform exponential admissibility problem for switched descriptor systems with time varying delays a criterion for regularity impulsiveness free of each subsystem is presented a solution to switching impulsiveness free for switched descriptor systems is provided a novel type of piecewise lyapunov functionals is introduced this type of lyapunov functionals can efficiently overcome the switching jump of adjacent lyapunov functionals at switching times by applying this type of lyapunov functionals and algebraic manipulations the delay independent conditions for uniform exponential admissibility is established on the minimum dwell time

affine characterizations of minimal and mode dependent dwell times for uncertain linear switched systems an alternative approach for minimum and mode dependent dwell time characterization for switched systems is derived while minimum dwell time results require the subsystems to be asymptotically stable mode dependent dwell time results can consider unstable subsystems and dwell times within a possibly unbounded range of values the proposed approach is related to lyapunov looped functionals a new type of functionals leading to stability conditions affine in the system matrices unlike standard results for minimum dwell time these conditions are expressed as infinite dimensional lmis which can be solved using recent polynomial optimization techniques such as sum of squares the specific structure of the conditions is finally utilized in order to derive dwell time stability results for uncertain switched systems several examples illustrate the efficiency of the approach

hamiltonian properties of honeycomb meshes meshes are widely used topologies for networks on chip noc honeycomb meshes have better topological properties than meshes in order to communicate efficiently in a linear or cyclic manner it is benefited that there is a hamiltonian path or hamiltonian cycle in noc in this paper we give a necessary and sufficient condition for the existence of hamiltonian path between any pair of vertices in a honeycomb mesh and for the existence of hamiltonian path in a honeycomb mesh with one faulty vertex besides we give a systematic method to construct a hamiltonian path in honeycomb meshes

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

the set of stable switching sequences for discrete time linear switched systems in this paper we study the characterization of the asymptotical stability for discrete time switched linear systems we first translate the system dynamics into a symbolic setting under the framework of symbolic topology then by using the ergodic measure theory a lower bound estimate of hausdorff dimension of the set of asymptotically stable sequences is obtained we show that the hausdorff dimension of the set of asymptotically stable switching sequences is positive if and only if the corresponding switched linear system has at least one asymptotically stable switching sequence the obtained result reveals an underlying fundamental principle a switched linear system either possesses uncountable numbers of asymptotically stable switching sequences or has none of them provided that the switching is arbitrary we also develop frequency and density indexes to identify those asymptotically stable switching sequences of the system

convex lifted conditions for robust l 2 stability analysis and l 2 stabilization of linear discrete time switched systems with minimum dwell time constraint stability analysis of discrete time switched systems under minimum dwell time is studied using a new type of lmi conditions these conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed in geromel and colaneri 2006b the convexification of the conditions is performed by a lifting process which introduces a moderate number of additional decision variables the convexity of the conditions can be exploited to extend the results to uncertain systems control design and 2 gain computation without introducing additional conservatism several examples are presented to show the effectiveness of the approach

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

strictly positive real matrices and the lefschetz kalman yakubovich lemma the authors give necessary and sufficient conditions in the frequency domain for rational matrices to be strictly positive real based on this result the matrix form of the lefschetz kalman yakubovich lemma is proved which gives necessary and sufficient conditions for strictly positive real transfer matrices in the state space realization form