stability analysis and control of discrete type 1 and type 2 tsk fuzzy systems part ii control design this paper proposes a new control system design methodology for type 1 and type 2 takagi sugeno kang tsk fuzzy systems that are based on new stability conditions the stability conditions are discussed in a companion paper part i and are used in the proofs of our main results a major advantage of the new methodology is that it does not require a common lyapunov function and is therefore applicable to systems with nonstabilizable consequents our controllers include fuzzy type 1 proportional and proportional integral pi controllers as well as constant state feedback for the same systems the controller results in an exponentially stable system and the designer can specify the rate of exponential convergence the controller designs can be tested by the usage of linear matrix inequalities lmis the design methodology is demonstrated by the usage of simple examples where methods that are based on a common lyapunov function fail and physical systems where the new methodology provides better performance

stabilization of singularly perturbed fuzzy systems this paper presents some novel results for stabilizing singularly perturbed sp nonlinear systems with guaranteed control performance by using takagi sugeno fuzzy model we construct the sp fuzzy spf systems the corresponding fuzzy slow and fast subsystems of the original spf system are also obtained two fuzzy control designs are explored in the first design method we propose the composite fuzzy control to stabilize the spf subsystem with h sup spl infin control performance based on the lyapunov stability theorem the stability conditions are reduced to the linear matrix inequality lmi problem the composite fuzzy control will stabilize the original sp nonlinear systems for all spl epsiv spl isin 0 spl epsiv sup and the upper bound spl epsiv sup can be determined for the second design method we present a direct fuzzy control scheme to stabilize the sp nonlinear system with h sup spl infin control performance by utilizing the lyapunov stability theorem the direct fuzzy control can guarantee the stability of the original sp nonlinear systems for a given interval spl epsiv spl isin spl epsiv spl epsiv the stability conditions are also expressed in the lmis two sp nonlinear systems are adopted to demonstrate the feasibility and effectiveness of the proposed control schemes

robust stabilization of singularly perturbed systems abstract we discuss the problem of designing stabilizing controllers for singularly perturbed systems on the basis of simplified models in 1 it was shown that a constant gain output feedback controller designed on the basis of the simplified model need not stabilize the true system containing both fast and slow modes this phenomenon was then expanded to include the case where the simplified system is strictly proper in 2 the objectives of this note are threefold i to show that given any proper system and any stabilizing controller for it that is proper but not strictly proper there exists a singular perturbation of the system that is destabilized by that controller ii to show that any strictly proper controller for a singularly perturbed system designed on the basis of a reduced order model will stabilize the true system for sufficiently small values of the fast dynamics parameter and iii to provide a characterization in the same spirit as 3 4 of the set of all strictly proper controllers that stabilize a given proper plant by combining these results it is possible to generate the class of all robustly stabilizing controllers for a given singularly perturbed system

stability analysis and synthesis of fuzzy singularly perturbed systems in this paper we investigate the stability analysis and synthesis problems for both continuous time and discrete time fuzzy singularly perturbed systems for continuous time case both the stability analysis and synthesis can be parameterized in terms of a set of linear matrix inequalities lmis for discrete time case only the analysis problem can be cast in lmis while the derived stability conditions for controller design are nonlinear matrix inequalities nmis furthermore a two stage algorithm based on lmi and iterative lmi ilmi techniques is developed to solve the resulting nmis and the stabilizing feedback controller gains can be obtained for both continuous time and discrete time cases the reduced control law which is only dependent on the slow variables is also discussed finally an illustrated example based on the flexible joint inverted pendulum model is given to illustrate the design procedures

on the lyapunov theorem for singular systems in this paper we revisit the lyapunov theory for singular systems there are basically two well known generalized lyapunov equations used to characterize stability for singular systems we start with the lyapunov theorem of the work by lewis we show that the lyapunov equation of that theorem can lead to incorrect conclusion about stability some cases where that equation can be used are clarified we also show that an attempt to correct that theorem with a generalized lyapunov equation similar to the original one leads naturally to the generalized equation of takaba et al

construction of highly nonlinear 1 resilient boolean functions with optimal algebraic immunity and provably high fast algebraic immunity in 2013 tang carlet and tang ieee tit 59 1 653 664 2013 presented two classes of boolean functions the functions in the first class are unbalanced and the functions in the second one are balanced both of those two classes of functions have high nonlinearity high algebraic degree optimal algebraic immunity and high fast algebraic immunity however they are not 1 resilient which represents a drawback for their use as filter functions in stream ciphers in this paper we first propose a large family of 1 resilient boolean functions having high lower bound on nonlinearity optimal algebraic immunity and optimal algebraic degree that is meeting the siegenthaler bound most notably we can mathematically prove that every function in n variables belonging to this family has fast algebraic immunity no less than n 6 which is the first time that an infinite family of 1 resilient functions with provably high fast algebraic immunity has been invented furthermore we exhibit a subclass of the family which has higher lower bound on nonlinearity than all the known 1 resilient functions with potentially optimal algebraic immunity and potentially high fast algebraic immunity

new constructions of resilient functions with strictly almost optimal nonlinearity via non overlap spectra functions abstract the design of n variable t resilient functions with strictly almost optimal sao nonlinearity 2 n 1 2 n 2 n even appears to be a rather difficult task the known construction methods commonly use a rather large number exactly i t 1 n 2 n 2 i of affine subfunctions in n 2 variables which can induce some algebraic weaknesses making these functions susceptible to certain types of guess and determine cryptanalysis and dynamic cube attacks in this paper the concept of non overlap spectra functions is introduced which essentially generalizes the idea of disjoint spectra functions on different variable spaces two general methods to obtain a large set of non overlap spectra functions are given and a new framework for designing infinite classes of resilient functions with sao nonlinearity is developed based on these unlike previous construction methods our approach employs only a few n 2 variable affine subfunctions in the design resulting in a more favourable algebraic structure it is shown that these new resilient sao functions properly include all the existing classes of resilient sao functions as a subclass moreover it is shown that the new class provides a better resistance against fast algebraic attacks than the known functions with sao nonlinearity and in addition these functions are more robust to guess and determine cryptanalysis and dynamic cube attacks

an approach to fuzzy control of nonlinear systems stability and design issues presents a design methodology for stabilization of a class of nonlinear systems first the authors represent a nonlinear plant with a takagi sugeno fuzzy model then a model based fuzzy controller design utilizing the concept of the so called parallel distributed compensation is employed the main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system the design procedure is conceptually simple and natural moreover the stability analysis and control design problems can be reduced to linear matrix inequality lmi problems therefore they can be solved efficiently in practice by convex programming techniques for lmis the design methodology is illustrated by application to the problem of balancing and swing up of an inverted pendulum on a cart

results on highly nonlinear boolean functions with provably good immunity to fast algebraic attacks abstract in the last decade algebraic and fast algebraic attacks are regarded as the most successful attacks on lfsr based stream ciphers since the notion of algebraic immunity was introduced the properties and constructions of boolean functions with maximum algebraic immunity have been researched in a large number of papers however there are few results with respect to boolean functions with provably good immunity against fast algebraic attacks in previous literatures only carlet feng function was proven to have good immunity to fast algebraic attacks in this paper we first study a large family of highly nonlinear boolean functions in terms of the immunity to fast algebraic attacks which includes the functions of tu deng the functions of tang et al and the functions of jin et al based on a sufficient and necessary condition for measuring the immunity of boolean functions against fast algebraic attacks using bivariate polynomial representation we propose an efficient method for estimating the immunity of the functions of such family then we prove that a family of 2 k variable boolean functions including the function recently constructed by tang et al are almost perfect algebraic immune for any integer k 3 more exactly they achieve optimal algebraic immunity and almost perfect immunity to fast algebraic attacks the functions of such family are balanced and have optimal algebraic degree besides we prove a lower bound on their nonlinearity based on the work of tang et al which is better than that of carlet feng function it is also checked for 3 k 9 that the exact nonlinearity of such functions is very good which is slightly smaller than that of carlet feng function and some functions of this family even have a slightly larger nonlinearity than tang s et al function to sum up among the known functions with provably good immunity against fast algebraic attacks the functions of this family make a trade off between the exact value and the lower bound of nonlinearity

hybrid classes of balanced boolean functions with good cryptographic properties abstract cryptographically strong boolean functions play an imperative role in the design of almost every modern symmetric cipher in this context the cryptographic properties of boolean functions such as non linearity algebraic degree correlation immunity and propagation criteria are critically considered in the process of designing these ciphers more recently with the emergence of algebraic and fast algebraic attacks algebraic immunity has also been included as an integral property to be considered as a result several constructions of boolean functions with high non linearity maximal algebraic degree and optimal algebraic immunity have been devised since then this paper focuses on some of these constructions and presents two hybrid classes of boolean functions the functions constructed within these classes possess maximal algebraic degree for balanced functions optimal algebraic immunity high non linearity and good resistance to algebraic and fast algebraic attacks a hybrid class of 1 resilient functions has also been proposed that also possesses high algebraic degree optimal algebraic immunity high non linearity and good resistance to algebraic and fast algebraic attacks

on the construction of cryptographically significant boolean functions using objects in projective geometry spaces recently several construction methods of highly nonlinear boolean functions with relatively good algebraic properties were proposed these approaches manage in optimizing most of the relevant cryptographic criteria but not all of them at the same time usually either the nonlinearity bounds are rather loose though the actual nonlinearity is relatively high or the functions do not provide a good resistance to fast algebraic cryptanalysis in this paper we develop a theoretical framework for using objects in suitable projective geometry spaces for construction of highly nonlinear boolean functions this allows us to establish tight bounds on the nonlinearity using simple counting arguments thus avoiding rather complicated estimates of certain trace sums our method generates a class of almost fully optimized functions that is the functions apart from very high nonlinearity also have the maximum algebraic degree and optimal algebraic immunity compared to the classes of functions proposed by carlet and feng wang and zeng our functions achieve a slightly better nonlinearity which is traded off against a little worse resistance against fast algebraic attacks on the other hand compared to the functions by tang and tu and deng our nonlinearity is somewhat lower but the algebraic properties are slightly better

stability analysis of dynamic interval systems abstract the stability analysis of interval matrices with certain stability margins is considered by means of similarity transformation and gershgorin s theorem new criteria are developed and illustrated by examples we also demonstrate a counter example to a recent result by argoun 1986

minimal penalties for gaussian model selection this paper is mainly devoted to a precise analysis of what kind of penalties should be used in order to perform model selection via the minimiza tion of a penalized least squares type criterion within some general gaussian framework including the classical ones as compared to our previous paper on this topic birge and massart in j eur math soc 3 203 268 2001 more elaborate forms of the penalties are given which are shown to be in some sense optimal we indeed provide more precise upper bounds for the risk of the penalized estimators and lower bounds for the penalty terms showing that the use of smaller penalties may lead to disastrous results these lower bounds may also be used to design a practical strategy that allows to estimate the penalty from the data when the amount of noise is unknown we provide an illustra tion of the method for the problem of estimating a piecewise constant signal in gaussian noise when neither the number nor the location of the change points are known

h sup spl infin optimal control for singularly perturbed systems ii imperfect state measurements for pt i see ibid vol 29 no 2 p 401 423 1993 in this paper we study the h sup spl infin optimal control of singularly perturbed linear systems under general imperfect measurements for both finite and infinite horizon formulations using a differential game theoretic approach we first show that as the singular perturbation parameter say spl epsiv 0 approaches zero the optimal disturbance attenuation level for the full order system under a quadratic performance index converges to a value that is bounded above by and in some cases equal to the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions with the bound being computable independently of e and knowing only the slow and fast dynamics of the system we then construct a controller based on the slow subsystem only and obtain conditions under which it delivers a desired performance level even though the fast dynamics are completely neglected the ultimate performance level achieved by this slow controller can be uniformly improved upon however by a composite controller that uses some feedback from the output of the fast subsystem we construct one such controller via a two step sequential procedure which uses static feedback from the fast output and dynamic feedback from an appropriate slow output each one obtained by solving appropriate spl epsiv independent lower dimensional h sup spl infin optimal control problems under some informational constraints we provide a detailed analysis of the performance achieved by this lower dimensional spl epsiv independent composite controller when applied to the full order system and illustrate the theory with some numerical results on some prototype systems

algebraic immunity for cryptographically significant boolean functions analysis and construction recently algebraic attacks have received a lot of attention in the cryptographic literature it has been observed that a boolean function f used as a cryptographic primitive and interpreted as a multivariate polynomial over f sub 2 should not have low degree multiples obtained by multiplication with low degree nonzero functions in this paper we show that a boolean function having low nonlinearity is also weak against algebraic attacks and we extend this result to higher order nonlinearities next we present enumeration results on linearly independent annihilators we also study certain classes of highly nonlinear resilient boolean functions for their algebraic immunity we identify that functions having low degree subfunctions are weak in terms of algebraic immunity and we analyze some existing constructions from this viewpoint further we present a construction method to generate boolean functions on n variables with highest possible algebraic immunity spl lceil n 2 spl rceil this construction first presented at the 2005 workshop on fast software encryption fse 2005 has been the first one producing such functions these functions are obtained through a doubly indexed recursive relation we calculate their hamming weights and deduce their nonlinearities we show that they have very high algebraic degrees we express them as the sums of two functions which can be obtained from simple symmetric functions by a transformation which can be implemented with an algorithm whose complexity is linear in the number of variables we deduce a very fast way of computing the output to these functions given their input

analysis and design of fuzzy controller and fuzzy observer this paper addresses the analysis and design of a fuzzy controller and a fuzzy observer on the basis of the takagi sugeno t s fuzzy model the main contribution of the paper is the development of the separation property that is the fuzzy controller and the fuzzy observer can be independently designed a numerical simulation and an experiment on an inverted pendulum system are described to illustrate the performance of the fuzzy controller and the fuzzy observer

comments on robust stabilization of a class of uncertain nonlinear systems via fuzzy control quadratic stabilizability h sup spl infin control theory and linear matrix inequalities this paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems first a stability condition for takagi and sugeno s fuzzy model is given in terms of lyapunov stability theory next new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization h sup spl infin control theory and linear matrix inequalities the derived stability conditions are used to analyze the stability of takagi and sugeno s fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems the design method employs the so called parallel distributed compensation important issues for the stability analysis and design are remarked finally three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented

fuzzy regulators and fuzzy observers relaxed stability conditions and lmi based designs this paper presents new relaxed stability conditions and lmi linear matrix inequality based designs for both continuous and discrete fuzzy control systems they are applied to design problems of fuzzy regulators and fuzzy observers first takagi and sugeno s fuzzy models and some stability results are recalled to design fuzzy regulators and fuzzy observers nonlinear systems are represented by takagi sugeno s ts fuzzy models the concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the ts fuzzy models new stability conditions are obtained by relaxing the stability conditions derived in previous papers lmi based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions other lmi s with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the lmi based design procedures

the observer based controller design of discrete time singularly perturbed systems a class of linear shift invariant discrete time singularly perturbed systems with inaccessible states is considered a design technique is formulated by which the stabilizing controller can be formed through the controllers of the slow and fast subsystems sufficient conditions for stability of the closed loop system under this composite controller are given

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

a necessary and sufficient condition for the stability of interval matrices consider the linear dynamical system described by the equation xdot t ax t where a is a constant real matrix with dimensions n n and the elements of matrix a are not known precisely we know only the upper and lower bounds of the intervals in which the elements of matrix a are confined in this paper there is proved a necessary and sufficient condition for the stability of solutions of eqn 1 with incomplete information about the elements of matrix a

constructions of cryptographically significant boolean functions using primitive polynomials it is known that boolean functions used in stream and block ciphers should have good cryptographic properties to resist algebraic attacks up until now there have been several constructions of boolean functions achieving optimum algebraic immunity however most of their nonlinearities are very low carlet and feng studied a class of boolean functions with optimum algebraic immunity and deduced the lower bound of its nonlinearity which is good but not very high moreover the main practical problem with this construction is that it cannot be implemented efficiently in this paper we put forward a new method to construct cryptographically significant boolean functions by using primitive polynomials and construct three infinite classes of boolean functions with good cryptographic properties balancedness optimum algebraic degree optimum algebraic immunity and a high nonlinearity

stability analysis of interval matrices continuous and discrete systems this paper considers the stability properties of dynamical interval systems two new methods of determining an upper bound on interval perturbations are presented one of the methods is applicable to both continuous and discrete systems

stability bounds of singularly perturbed discrete systems the authors propose a systematic approach to determine the exact stability bound of singularly perturbed discrete time systems by combining three conditions of the critical stability criterion with a bialternate product for discrete time systems the stability problems of two types of singularly perturbed discrete time systems can be solved via the derived scheme several examples are given to illustrate the proposed results

h control for fuzzy singularly perturbed systems in this paper both the state feedback and static output feedback h controllers for fuzzy singularly perturbed systems are investigated we give sufficient conditions for the existence of h controller such that the closed loop fuzzy control system is globally stable and achieves a prescribed level of disturbance attenuation for sufficiently small perturbation parameters the linear matrix inequality lmi approach is proposed to obtain the state feedback gains and a homotopy based iterative lmi algorithm is developed to get the static output feedback gains simulation results for two examples are included to demonstrate the effectiveness of the proposed approaches

robustness design of nonlinear dynamic systems via fuzzy linear control this study introduces a fuzzy linear control design method for nonlinear systems with optimal h sup spl infin robustness performance first the takagi and sugeno fuzzy linear model 1985 is employed to approximate a nonlinear system next based on the fuzzy linear model a fuzzy controller is developed to stabilize the nonlinear system and at the same time the effect of external disturbance on control performance is attenuated to a minimum level thus based on the fuzzy linear model h sup spl infin performance design can be achieved in nonlinear control systems in the proposed fuzzy linear control method the fuzzy linear model provides rough control to approximate the nonlinear control system while the h sup spl infin scheme provides precise control to achieve the optimal robustness performance linear matrix inequality lmi techniques are employed to solve this robust fuzzy control problem in the case that state variables are unavailable a fuzzy observer based h sup spl infin control is also proposed to achieve a robust optimization design for nonlinear systems a simulation example is given to illustrate the performance of the proposed design method

lmi based design of stabilizing fuzzy controllers for nonlinear systems described by takagi sugeno fuzzy model abstract there have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controllers this paper reports on a related study of the takagi sugeno ts fuzzy systems and it is shown that the controller synthesis problems for the nonlinear systems described by the ts fuzzy model can be reduced to convex problems involving linear matrix inequalities lmis after classifying the ts fuzzy systems into three families based on how diverse their input matrices are a unique controller synthesis procedure is given for each of the families a numerical example is presented to illustrate the synthesis procedures developed in this paper

control synthesis of singularly perturbed fuzzy systems this paper considers the problem of designing stabilizing and hinfin controllers for nonlinear singularly perturbed systems described by takagi sugeno fuzzy models with the consideration of the bound of singular perturbation parameter e for the synthesis problem of simultaneously designing the bound of e and stabilizing or hinfin controllers linear matrix inequalities lmi based methods are presented for evaluating the upper bound of e subject to stability or a prescribed hinfin performance bound constraint for the resulting closed loop system sufficient conditions are developed respectively for the stabilizing and hinfin control synthesis without the consideration of improving the bound of e new design methods are also given in terms of solutions to a set of lmis examples are given to illustrate the efficiency of the proposed methods

comments on constructions of cryptographically significant boolean functions using primitive polynomials we show that the first of the two constructions by q wang j peng h kan and x xue ieee transactions on information theory vol 56 no 6 pp 3048 3053 2010 of boolean functions satisfying the main criteria for filter functions in stream ciphers is the same as the construction studied by k feng and the author at asiacrypt 2008 lncs 5350 pp 425 440 we observe that the bounds shown on the nonlinearities of the functions in this ieee paper are similar to those shown in the asiacrypt paper we point out that these kinds of functions can be implemented in a more efficient way than usually believed

robust stabilization of a class of singularly perturbed discrete bilinear systems this paper presents two kinds of robust controllers for stabilizing singularly perturbed discrete bilinear systems the first one is an spl epsi dependent controller that stabilizes the closed loop system for all spl epsi spl isin 0 spl epsi sub 0 where spl epsi sub 0 is the prespecified upper bound of the singular perturbation parameter the second one is an spl epsi independent controller which is able to stabilize the system in the entire state space for all spl epsi spl isin 0 spl epsi where spl epsi is the exact upper spl epsi bound the spl epsi can be calculated by the critical stability criterion once the robust controller is determined an example is presented to illustrate the proposed schemes

on symmetric boolean functions with high algebraic immunity on even number of variables in this paper we put forward an efficient method to study the symmetric boolean functions with high algebraic immunity on even number of variables we obtain some powerful necessary conditions for symmetric boolean functions to achieve high algebraic immunity by studying the weight support of some specific types of boolean functions of low degrees with these results we prove that the algebraic immunity of a large class of symmetric correlation immune boolean functions namely the symmetric palindromic functions is not high besides we construct all symmetric boolean functions with maximum algebraic immunity and give a description for those with submaximum algebraic immunity we also determine the hamming weight degrees and nonlinearity of the symmetric boolean functions with maximum algebraic immunity

t s fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems this paper proposes a fuzzy bilinear model for a class of nonlinear systems and a fuzzy controller to stabilize such systems by examination of a modeling problem we describe how to transform a nonlinear system into a bilinear one via taylor s series expansion and then we adopt the takagi sugeno t s fuzzy modeling technique to construct a fuzzy bilinear model for controller design the parallel distributed compensation pdc method is utilized to stabilize the fuzzy bilinear system fbs and some sufficient conditions are derived to guarantee the stability of the overall fuzzy control system via linear matrix inequalities lmis moreover we propound some sufficient conditions for robust stabilization of the fbs with parametric uncertainties finally a numerical example and the van de vusse model are utilized to demonstrate the validity and effectiveness of the proposed fbs

on the stability bounds of singularly perturbed systems the stability bound problem of linear time invariant singularly perturbed systems is considered a set of new stability conditions based on the frequency domain representation is derived the stability criteria can be easily verified by computing certain singular values within finite frequency intervals illustrative examples show that the proposed criteria actually induce a less conservative epsilon bound than the existing criteria and for certain cases an infinite epsilon bound may be obtained

stability bounds of singularity perturbed systems a necessary and sufficient condition is developed for computing the upper bound in sub 0 of the parasitic parameter in in a singularly perturbed system which ensures stability of such a system if 0

a robust h_ infty non pdc design scheme for singularly perturbed t s fuzzy systems with immeasurable state variables this paper addresses an observer based robust h infty fuzzy controller design method for singularly perturbed nonlinear systems with external disturbances which are represented by uncertain takagi sugeno t s fuzzy models for a practical output feedback design the premise variables of the fuzzy controller and the fuzzy observer are considered unknown in general a fuzzy lyapunov function is utilized for the synthesis of the nonparallel distributed compensation based controller the closed loop singularly perturbed t s fuzzy system is asymptotically robustly stable in the absence of disturbances and satisfies an h infty norm condition in the presence of disturbances for all positive values of the singular perturbation parameter within the given desired bound using the descriptor redundancy approach some strict linear matrix inequality lmi conditions are derived for the h infty robustness of the closed loop system when uncertainties are simultaneously considered in all state space matrices of each fuzzy subsystem the main disadvantage of a fuzzy lyapunov function based design is that the bounds on the derivatives of the membership functions must be known a priori inspired by a recent work that provides the bounds of the membership derivatives for a given arbitrary compact set on the state space a new method is proposed that guarantees that the closed loop observer based uncertain singularly perturbed t s fuzzy system remains robustly stable in the compact set using finsler s lemma the resulting design conditions are converted to lmis two numerical examples are provided to show the effectiveness of the proposed method

h control design for fuzzy discrete time singularly perturbed systems via slow state variables feedback an lmi based approach this paper addresses the h control problem via slow state variables feedback for discrete time fuzzy singularly perturbed systems at first a method of evaluating the upper bound of singular perturbation parameter e with meeting a prescribed h performance bound requirement is given subsequently two methods for designing h controllers via slow state variables feedback are presented in terms of solutions to a set of linear matrix inequalities lmis in particular one of them can be used to improve the upper bound of the singular perturbation parameter e finally two numerical examples are given to illustrate the effectiveness of the proposed methods

correcting argoun s approach for the stability of interval matrices recently xu and shao 1989 pointed out that the approach of argoun 1986 for the stability of interval matrices is incorrect this note corrects his approach so that it can be used to check the stability of linear continuous time systems with perturbations

more balanced boolean functions with optimal algebraic immunity and good nonlinearity and resistance to fast algebraic attacks in this paper three constructions of balanced boolean functions with optimal algebraic immunity are proposed it is checked that at least for small numbers of input variables these functions have good behavior against fast algebraic attacks as well other cryptographic properties such as algebraic degree and nonlinearity of the constructed functions are also analyzed lower bounds on the nonlinearity are proved which are similar to the best bounds obtained for known boolean functions resisting algebraic attacks and fast algebraic attacks moreover it is checked that for the number n of variables with 5 n 19 the proposed n variable boolean functions have in fact very good nonlinearity

highly nonlinear boolean functions with optimal algebraic immunity and good behavior against fast algebraic attacks inspired by the previous work of tu and deng we propose two infinite classes of boolean functions of 2k variables where k 2 the first class contains unbalanced functions having high algebraic degree and nonlinearity the functions in the second one are balanced and have maximal algebraic degree and high nonlinearity as shown by a lower bound that we prove as a byproduct we also prove a better lower bound on the nonlinearity of the carlet feng function thanks to a combinatorial fact first conjectured by the authors and later proved by cohen and flori we are able to show that they both possess optimal algebraic immunity it is also checked that at least for numbers of variables n 16 functions in both classes have a good behavior against fast algebraic attacks compared with the known boolean functions resisting algebraic attacks and fast algebraic attacks both of them possess the highest lower bounds on nonlinearity these bounds are however not enough for ensuring a sufficient nonlinearity for allowing resistance to fast correlation attack nevertheless as for previously found functions with the same features there is a gap between the bound that we can prove and the actual values computed for bounded numbers of variables n 38 moreover these values are very good the infinite class of functions we propose in construction 2 presents among all currently known constructions the best provable tradeoff between all the important cryptographic criteria

improving the upper bounds on the covering radii of binary reed muller codes by deriving bounds on character sums of boolean functions and by using the characterizations due to kasami of those elements of the reed muller codes whose hamming weights are smaller than twice and a half the minimum distance we derive an improved upper bound on the covering radius of the reed muller code of order 2 and we deduce improved upper bounds on the covering radii of the reed muller codes of higher orders

a new upper bound on the block error probability after decoding over the erasure channel motivated by cryptographic applications we derive a new upper bound on the block error probability after decoding over the erasure channel the bound works for all linear codes and is in terms of the generalized hamming weights it turns out to be quite useful for reed muller codes for which all the generalized hamming weights are known whereas the full weight distribution is only partially known for these codes the error probability is related to the cryptographic notion of algebraic immunity we use our bound to show that the algebraic immunity of a random balanced m variable boolean function is of order m 2 1 o 1 with probability tending to 1 as m goes to infinity

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods