necessary and sufficient small gain conditions for integral input to state stable systems a lyapunov perspective this paper is concerned with conditions for the stability of interconnected nonlinear systems consisting of integral input to state stable iiss systems with external inputs the treatment of iiss and input to state stable iss systems is unified both necessary conditions and sufficient conditions are investigated using a lyapunov formulation in the presence of model uncertainty this paper proves that for the stability of the interconnected system at least one subsystem is necessarily iss which is a stronger stability property in the set of iiss the necessity of a small gain type property is also demonstrated this paper proposes a common form of smooth lyapunov functions which can establish the iiss and the iss of the interconnection comprising iiss and iss subsystems whenever the small gain type condition is satisfied the result covers situations more general than the earlier study and removes technical conditions assumed in the previous literature global asymptotic stability is discussed as a special case

further results on output feedback stabilization for a class of stochastic nonlinear systems for a class of stochastic nonlinear systems in which the drift and diffusion vector fields depend on the unmeasurable states besides the measurable output the research purpose of this technical note is to find the maximum value interval of observer gain for the desired control performance for this interval the designed output feedback controller ensures that the equilibrium at the origin is globally asymptotically stable in probability and the inverse optimal stabilization in probability is achieved

monomial bent functions in this correspondence we focus on bent functions of the form f 2 n rarr f 2 where x rarr tr alphaxd the main contribution of this correspondence is that we prove that for n 4r r odd the exponent d 2r 1 2 allows the construction of bent functions this open question has been posed by canteaut based on computer experiments as a consequence for each of the well understood families of bent functions we now know an exponent d that yields to bent functions of the given type

three classes of minimal linear codes over the finite fields of odd characteristic minimal linear codes are a special subclass of linear codes and have significant applications in secret sharing and secure two party computation in this paper we focus on constructing minimal linear codes with frac w min w max leq frac p 1 p for any odd prime p based on a generic construction of linear codes where w min and w max denote the minimum and maximum nonzero weights in a code respectively first we present two new infinite families of minimal linear codes with two or three weights by selecting suitable subcode of linear codes which are not minimal second we also present an infinite family of minimal linear codes by employing partial spreads which can be viewed as a generalization of the construction of ding et al in addition we determine the weight distributions of all these minimal linear codes

a homogeneous domination approach to state feedback of stochastic high order feedforward nonlinear systems this paper investigates stochastic high order feedforward nonlinear systems for the first time by introducing the homogeneous domination approach and solving several troublesome obstacles in the design and analysis procedure a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

global finite time stabilisation for a class of stochastic high order time varying nonlinear systems abstractin this paper the problem of global finite time stabilisation by state feedback is investigated for a class of stochastic high order nonlinear systems with time varying nonlinearities based on the generalised stochastic lyapunov theorem on finite time stability and by skillfully using the method of adding a power integrator a continuous state feedback controller is successfully constructed to guarantee that the closed loop system is globally finite time stable in probability finally several simulation examples are provided to illustrate the effectiveness of the proposed method

the concept of exponential input to state stability for stochastic systems and applications to feedback stabilization abstract this paper presents a version of the well known sontag s input to state stability property for stochastic systems this concept is used to derive sufficient conditions for global stabilization for certain class of stochastic nonlinear systems by means of static and dynamic output feedback

stochastic versions of the lasalle theorem the main aim of this paper is to establish stochastic versions of the well known lasalle stability theorem from these stochastic versions follow many classical results on stochastic stability this shows clearly the power of our new results

state feedback control of high order stochastic nonlinear systems with siiss inverse dynamics this technical note considers a class of high order stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics and drift and diffusion terms depending upon the stochastic inverse dynamics and all the states a new design and analysis approach to the problem of state feedback global regulation is developed to guarantee that all the signals of the closed loop system are bounded almost surely and the states can be regulated to zero almost surely

stability of stochastic nonlinear systems with state dependent switching in this paper the problem of stability on stochastic systems with state dependent switching is investigated to analyze properties of the switched system by means of ito s formula and dynkin s formula it is critical to show switching instants being stopping times when the given active region set can be replaced by its interior the local solution of the switched system is constructed by defining a series of stopping times as switching instants and the criteria on global existence and stability of solution are presented by lyapunov approach for the case where the active region set can not be replaced by its interior the switched systems do not necessarily have solutions thereby quasi solution to the underlying problem is constructed and the boundedness criterion is proposed the significance of this paper is that all the results presented depend on some easily verified assumptions that are as elegant as those in the deterministic case and the proofs themselves provide design procedures for switching controls

the improved lasalle type theorems for stochastic functional differential equations abstract the main aim of this paper is to improve some results obtained by mao x mao the lasalle type theorems for stochastic functional differential equations nonlinear stud 7 2000 307 328 our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above for example we need only the local lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions to guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation sfde under the weaker conditions imposed in this paper we establish a generalised existence and uniqueness theorem which covers a wider class of nonlinear sfdes as demonstrated by the examples discussed in this paper moreover from our improved results follow some new criteria on the stochastic asymptotic stability for sfdes

several new infinite families of bent functions and their duals bent functions are optimal combinatorial objects since their introduction substantial efforts have been directed toward their study in the last three decades a complete classification of bent functions is elusive and looks hopeless today therefore not only their characterization but also their generation are challenging problems this paper is devoted to the construction of bent functions first we provide several new effective constructions of bent functions self dual bent functions and antiself dual bent functions second we provide seven new infinite families of bent functions by explicitly calculating their dual

output feedback control using small gain conditions for stochastic nonlinear systems with siiss inverse dynamics this article further discusses output feedback control for stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics based on the stochastic lasalle theorem and small gain type conditions on siiss an output feedback controller using the backstepping method is constructively designed to guarantee that all the closed loop signals are bounded almost surely and the stochastic closed loop system is globally asymptotically stable in probability

finite time stabilization of stochastic nonlinear systems in strict feedback form in this paper we investigate the problem of almost surely finite time stabilization of a class of stochastic nonlinear systems based on the recently proposed almost surely finite time stability theorem in yin khoo man and yu 2011 we prove that almost surely global finite time stability of stochastic nonlinear systems in strict feedback form can be guaranteed by a continuous control law a systematic design algorithm is developed for the construction of the controller simulation results are given to illustrate the theoretical analysis

further results on generalized bent functions and their complete characterization this paper contributes to increase our knowledge on generalized bent functions including generalized bent boolean functions and generalized p ary bent functions with odd prime p by bringing new results on their characterization and construction in arbitrary characteristic more specifically we first investigate relations between generalized bent functions and bent functions by the decomposition of generalized bent functions this enables us to completely characterize generalized bent functions and mathbb z p k bent functions by some affine space associated with the generalized bent functions we also present the relationship between generalized bent boolean functions with an odd number of variables and generalized bent boolean functions with an even number of variables based on the well known maiorana mcfarland class of boolean functions we present some infinite classes of generalized bent boolean functions in addition we introduce a class of generalized hyperbent functions that can be seen as generalized dillon s ps functions finally we solve an open problem related to the description of the dual function of a weakly regular generalized bent boolean function with an odd number of variables via the walsh hadamard transform of their component functions and we generalize these results to the case of odd prime

finite time stabilization of stochastic high order nonlinear systems with ft siss inverse dynamics this paper aims to solve the finite time stabilization problem for stochastic high order nonlinear systems with stochastic inverse dynamics by characterizing unmeasured stochastic inverse dynamics with finite time stochastic input to state stability ft siss borrowing from some ideas of the lyapunov function sign function backstepping and ft siss methods and using stochastic finite time stability theory a new design and analysis method is given to guarantee global finite time stability in probability of the closed loop stochastic systems

corrections to stochastic barbalat s lemma and its applications jun 12 1537 1543 the proof of theorem 1 stochastic barbalat s lemma in the paper by wu is incorrect this note provides a new statement of stochastic barbalat s lemma in addition some definitions propositions and proofs are given to replace those in the paper by wu

adaptive backstepping controller design using stochastic small gain theorem a more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper with the concept of input to state practical stability isps and nonlinear small gain theorem being extended to stochastic case by combining stochastic small gain theorem with backstepping design technique an adaptive output feedback controller is proposed it is shown that the closed loop system is practically stable in probability a simulation example demonstrates the control scheme

output feedback regulation of stochastic nonlinear systems with stochastic iiss inverse dynamics this paper develops a unifying framework for output feedback regulation of stochastic nonlinear systems with more general stochastic inverse dynamics the contributions of this work are characterized by the following novel features 1 motivated by the concept of integral input to state stability iiss in deterministic systems and stochastic input to state stability siss using lyapunov function in stochastic systems a concept of stochastic integral input to state stability siiss using lyapunov function is first introduced two important properties of siiss are obtained i siiss is strictly weaker than siss using lyapunov function ii siiss is stronger than the minimum phase property however only under the minimum phase assumption there is no dynamic output feedback control law for global stabilization in probability 2 almost sure boundedness a reasonable and stronger concept than boundedness in probability is introduced the purpose of introducing the concept is to prove the boundedness and convergence of some signals in the closed loop control system 3 some important mathematical tools which play an essential role in the boundedness and convergence analysis of the closed loop system are established 4 a unifying framework is proposed to design a dynamic output feedback control law which drives the states to the origin almost surely while maintaining all the closed loop signals bounded almost surely

systematic methods of constructing bent functions and 2 rotation symmetric bent functions in this paper we first present two systematic constructions of bent functions by modifying the truth tables of rothaus s bent function and maiorana mcfarland s bent function respectively the number of the newly constructed bent functions by modifying the truth table of rothaus s bent function is also determined the methods of constructing self dual bent functions are then given after the dual functions of these bent functions being determined finally as an application two constructions of 2 rotation symmetric bent functions are presented in this paper

constructing bent functions outside the maiorana mcfarland class using a general form of rothaus in the mid 1960s rothaus proposed the so called most general form of constructing new bent functions by using three initial bent functions whose sum is again bent in this paper we utilize a special case of rothaus construction when two of these three bent functions differ by a suitably chosen characteristic function of an n 2 dimensional subspace this simplification allows us to treat the induced bent conditions more easily also implying the possibility to specify the initial functions in the partial spread class and most notably to identify several instances of the so called non normal bent functions affine inequivalent bent functions within this class are then identified using a suitable selection of initial bent functions within the partial spread class stemming from the complete desarguesian spread it is also shown that when the initial bent functions belong to the class mathcal d then under certain conditions the constructed functions provably do not belong to the completed maiorana mcfarland class we conjecture that our method potentially generates an infinite class of non normal bent functions all tested ten variable functions are non normal but unfortunately they are weakly normal though there are no efficient computational tools for confirming this

time varying state feedback stabilisation of stochastic feedforward nonlinear systems with unknown growth rate abstractwe consider the time varying state feedback stabilisation problem for a class of stochastic feedforward nonlinear systems with unknown growth rate in this paper a new lasalle type theorem for stochastic time varying systems is firstly established by using the generalized weakly positive definite function as an application to deal with serious uncertainties in the unknown growth rate a time varying approach rather than an adaptive one is adopted to design the scheme of a state feedback controller for stochastic feedforward systems based on the established lasalle type theorem it is shown that all signals of the resulting closed loop system converge to zero almost surely illustrative examples are given to verify the theoretical findings

hyperbent functions via dillon like exponents this paper is devoted to hyperbent functions with multiple trace terms including binomial functions via dillon like exponents we show how the approach developed by mesnager to extend the charpin gong family which was also used by wang and coworkers to obtain another similar extension fits in a much more general setting to this end we first explain how the original restriction for charpin gong criterion can be weakened before generalizing the mesnager approach to arbitrary dillon like exponents afterward we tackle the problem of devising infinite families of extension degrees for which a given exponent is valid and apply these results not only to reprove straightforwardly the results of mesnager and wang and coworkers but also to characterize the hyperbentness of several new infinite classes of boolean functions we go into full details only for a few of them but provide an algorithm and the corresponding software to apply this approach to an infinity of other new families finally we compare the asymptotic and practical performances of different characterizations including these in terms of hyperelliptic curves and actually build hyperbent functions in cases which could not be attained through naive computations of exponential sums

constructions of quadratic bent functions in polynomial forms in this correspondence the constructions and enumerations of all bent functions represented by a polynomial form of f x spl sigma sub i 1 sup n 2 1 c sub i tr x sup 1 2 i c sub n 2 tr sub 1 sup n sup 2 x sup 1 2 n 2 c sub i spl isin sub 2 f sub 2 are presented for special cases of n using an iterative approach the construction of bent functions of n variables with degree n 2 is also provided using the constructed quadratic bent functions

algebraic geometric codes on minimal hirzebruch surfaces abstract we define a linear code c t x by evaluating polynomials of bidegree t x in the cox ring on f q rational points of a minimal hirzebruch surface over the finite field f q we give explicit parameters of the code notably using grobner bases the minimum distance provides an upper bound of the number of f q rational points of a non filling curve on a hirzebruch surface

systematic constructions of rotation symmetric bent functions 2 rotation symmetric bent functions and bent idempotent functions rotation symmetric bent functions and their generation two rotation symmetric bent functions are two classes of cryptographically significant boolean functions however few constructions have been presented in the literature which either have restriction on integer n or have algebraic degree no more than 4 in this paper for any even integer n ge 4 three classes of bent functions are presented respectively most notably the proposed n variable rotation symmetric bent functions and two rotation symmetric bent functions can have any possible algebraic degree ranging from 2 to n 2 besides we obtain bent idempotent functions with the maximal algebraic degree n 2

bent function sequences in this paper we construct a new family of nonlinear binary signal sets which achieve welch s lower bound on simultaneous cross correlation and autocorrelation magnitudes given a parameter n with n 0 pmod 4 the period of the sequences is 2 n 1 the number of sequences in the set is 2 n 2 and the cross auto correlation function has three values with magnitudes leq 2 n 2 1 the equivalent linear span of the codes is bound above by sum i 1 n 4 left stackrel n i right these new signal sets have the same size and correlation properties as the small set of kasami codes but they have important advantages for use in spread spectrum multiple access communications systems first the sequences are balances which represents only a slight advantage second the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly hopped from sequence to sequence for code division multiple access operation most importantly the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it this high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing

state dependent scaling problems and stability of interconnected iiss and iss systems this paper addresses the problem of establishing stability of nonlinear interconnected systems this paper introduces a mathematical formulation of the state dependent scaling problems whose solutions directly provide lyapunov functions proving stability properties of interconnected dissipative systems in a unified manner stability criteria are interpreted as sufficient conditions for the existence of solutions to the state dependent scaling problems computing solutions to the problems is straightforward for systems covered by classical stability criteria it however could be too difficult for systems with strong nonlinearity the main purpose of this paper is to demonstrate the effectiveness beyond formal applicability by focusing on interconnected integral input to state stable iiss systems and input to state stable iss systems this paper derives small gain type theorems for interconnected systems involving iiss systems from the state dependent scaling formulation this paper provides solutions and lyapunov functions explicitly the new framework seamlessly generalizes the iss small gain theorem and classical stability criteria such as the lp small gain theorem the passivity theorems the circle and popov criteria state dependence of the scaling is crucial for effective treatment of essential nonlinearities while constants are sufficient for classical nonlinearities

bent and hyper bent functions in polynomial form and their link with some exponential sums and dickson polynomials bent functions are maximally nonlinear boolean functions with an even number of variables they were introduced by rothaus in 1976 for their own sake as interesting combinatorial objects but also because of their relations to coding theory reed muller codes and applications in cryptography design of stream ciphers they have attracted a lot of research specially in the last 15 years the class of bent functions contains a subclass of functions introduced by youssef and gong in 2001 the so called hyper bent functions whose properties are still stronger and whose elements are still rarer than bent functions bent and hyper bent functions are not classified a complete classification of these functions is elusive and looks hopeless so it is important to design constructions in order to know as many of hyper bent functions as possible this paper is devoted to the constructions of bent and hyper bent boolean functions in polynomial forms we survey and present an overview of the constructions discovered recently we extensively investigate the link between the bentness property of such functions and some exponential sums involving dickson polynomials and give some conjectures that lead to constructions of new hyper bent functions

optimal codebooks from binary codes meeting the levenshtein bound in this paper a generic construction of codebooks based on binary codes is introduced with this generic construction a few previous constructions of optimal codebooks are extended and a new class of codebooks almost meeting the levenshtein bound is presented exponentially many codebooks meeting or almost meeting the levenshtein bound from binary codes are obtained in this paper the codebooks constructed in this paper have alphabet size 4 as a byproduct three bounds on the parameters of binary codes are derived

a note on the lasalle type theorems for stochastic differential delay equations the main aim of this note is to improve some results obtained in the author s earlier paper 1999 j math anal appl 236 350 369 from the improved result follow some useful criteria on the stochastic asymptotic stability and boundedness

stochastic input to state stability and applications to global feedback stabilization notions of stochastic input to state stability are introduced and their lyapunov characterizations are established these notions constitute extensions of the deterministic iss proposed by e sonta

dissipativity based small gain theorems for stochastic network systems in this paper some small gain theorems are proposed for stochastic network systems which describe large scale systems with interconnections uncertainties and random disturbances by the aid of conditional dissipativity and showing times of stochastic interval small gain conditions proposed for the deterministic case are extended to the stochastic case when some design parameters are tunable in practice we invaginate a simpler method to verify small gain condition by selecting one subsystem as a monitor compared with the existing results the existence and uniqueness of solution and ultimate uniform boundedness of input are removed from requirements of input to state stability and small gain theorems

further results on adaptive state feedback stabilization for stochastic high order nonlinear systems this paper aims to relax the results in xie and tian 2009 from the following two aspects completely removing the power order restriction and largely relaxing the growth conditions of nonlinear functions by using the backstepping design method and homogeneous domination technique this paper investigates the problem of adaptive state feedback stabilization for a class of stochastic high order nonlinear systems with nonlinear parameterization the closed loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely the efficiency of the adaptive state feedback controller is demonstrated by a simulation example

practical output feedback risk sensitive control for stochastic nonlinear systems with stable zero dynamics this paper addresses the design problem of practical or satisfaction output feedback controls for stochastic strict feedback nonlinear systems in observer canonical form with stable zero dynamics under long term average tracking risk sensitive cost criteria the cost function adopted here is of the quadratic integral type usually encountered in practice rather than the quartic integral one used to avoid difficulty in control design and performance analysis of the closed loop system a sequence of coordinate diffeomorphisms is introduced to separate the zero dynamics from the entire system so that the transformed system has an appropriate form suitable for integrator backstepping design for any given risk sensitivity parameter and desired cost value by using the integrator backstepping methodology an output feedback control is constructively designed such that a the closed loop system is bounded in probability and b the long term average risk sensitive cost is upper bounded by the desired value in addition this paper does not require the uniform boundedness of the gain functions of the system noise furthermore an example is given to show the effectiveness of the theory

an iiss framework for stochastic robustness of interconnected nonlinear systems this paper addresses integral input to state stability iiss for stochastic nonlinear dynamical systems and develops lyapunov type criteria the developments offer an iiss small gain framework for verifying robustness of interconnected systems with respect to disturbances the framework not only includes input to state stability iss as a special case but also highlights fundamental differences between the stochastic and deterministic systems in particular dealing with nonlinearities in interconnection gives rise to a unique issue of degradation in the presence of stochastic noises this paper addresses this issue by coping judiciously with the effect of the gradient of lyapunov functions of subsystems through diffusion fields in composing a lyapunov function of the entire system this paper employs two types of robustness notions and demonstrates that the influence of the stochastic degradation on one notion is considerably different from the influence on the other notion in dealing with interconnected systems

brief paper small gain control method for stochastic nonlinear systems with stochastic iiss inverse dynamics this paper investigates the small gain type conditions on stochastic iiss siiss systems and makes full use of these conditions in the design and analysis of the controller the contributions are as follows 1 a new proof of the stochastic lasalle theorem is provided 2 the small gain type conditions on siiss are developed and their relationship is discussed 3 based on the stochastic lasalle theorem and siiss small gain type conditions the adaptive controllers are designed to guarantee that all of the closed loop signals are bounded almost surely and the stochastic closed loop systems are globally asymptotically stable in probability

reduced order observer based output feedback regulation for a class of nonlinear systems with iiss inverse dynamics global asymptotic regulation via output feedback based on a reduced order observer is considered for a class of nonlinear systems with integral input to state stable iiss inverse dynamics the contributions are that 1 we further consider the conditions on changing supply rates in iiss systems and discuss the necessity of some conditions by constructing a counter example 2 for a more general class of nonlinear systems with iiss inverse dynamics a reduced order observer is introduced and by the combined approach of backstepping and changing iiss supply rates an output feedback controller is given to drive the output of system to the origin asymptotically and maintain other closed loop signals bounded

output feedback stabilization using small gain method and reduced order observer for stochastic nonlinear systems this technical note further investigates more general stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics and focuses on solving the following problems 1 a class of counterexamples which are different from that in are reconstructed to discuss the relationship between two small gain type conditions on siiss and 2 under the weaker conditions on nonlinearities based on a reduced order observer small gain type condition on siiss and stochastic lasalle theorem an output feedback controller is constructed to guarantee the global asymptotical stability in probability of the closed loop stochastic system

finite time stabilisation of a class of stochastic nonlinear systems with dead zone input this paper addresses the problem of finite time stabilisation by state feedback for a class of stochastic nonlinear systems in strict feedback form remarkably the system under consideration posse

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

state feedback stabilization for stochastic feedforward nonlinear systems with time varying delay this paper investigates a class of stochastic feedforward nonlinear systems with time varying delay by introducing the homogeneous domination approach to stochastic systems a state feedback controller is constructed to render the closed loop system globally asymptotically stable in probability

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

output feedback stabilization of stochastic high order nonlinear systems under weaker conditions under the weaker conditions on the power order and the nonlinear functions this paper investigates the output feedback stabilization problem for a class of stochastic high order nonlinear systems based on the backstepping design method and homogeneous domination technique the closed loop system can be proved to be globally asymptotically stable in probability

stochastic barbalat s lemma and its applications in the deterministic case a significant improvement on stability analysis of nonlinear systems is caused by introducing barbalat s lemma into control area after lyapunov s second method and lasalle s theorem were established this note considers the extension of barbalat s lemma to the stochastic case to this end the uniform continuity and the absolute integrability are firstly described in stochastic forms it is nevertheless a small generalization upon the existing references since our result can be used to adapted processes which are not necessarily ito diffusions when it is applied to ito diffusion processes many classical results on stochastic stability are covered as special cases

stability of stochastic nonlinear systems in cascade with not necessarily unbounded decay rates this paper develops tools to verify stability and robustness of cascaded nonlinear stochastic systems based on lyapunov functions constituent systems are formulated in terms of integral input to state stability iiss and input to state stability iss which are popular notions for both stochastic and deterministic systems this paper highlights differences between the stochastic and the deterministic cases in contrast to deterministic systems it is demonstrated that assuming iss systems having unbounded decay rates in dissipation inequalities is restrictive taking this fact into account stability criteria are formulated without assuming unboundedness of decay rates so that iss systems with bounded decay rates and iiss systems which are not iss are covered in a unified manner stability criteria for stochastic cascades involve the growth rate conditions at connecting channels this paper clarifies how noise diffusion fields affect the growth rate conditions and the influence depends on definition of stochastic robustness

decentralized adaptive output feedback stabilization for large scale stochastic nonlinear systems in this paper the problem of decentralized adaptive output feedback stabilization is investigated for large scale stochastic nonlinear systems with three types of uncertainties including parametric uncertainties nonlinear uncertain interactions and stochastic inverse dynamics under the assumption that the inverse dynamics of the subsystems are stochastic input to state stable an adaptive output feedback controller is constructively designed by the backstepping method it is shown that under some general conditions the closed loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability in addition the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin the contributions of the work are characterized by the following novel features 1 even for centralized single input single output systems this paper presents a first result in stochastic nonlinear adaptive output feedback asymptotic stabilization 2 the methodology previously developed for deterministic large scale systems is generalized to stochastic ones at the same time novel small gain conditions for small signals are identified in the setting of stochastic systems design 3 both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states 4 parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields which may appear nonlinearly 5 the concept of stochastic input to state stability and the method of changing supply functions are adapted for the first time to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control

further results on niho bent functions this paper consists of two main contributions first the niho bent function consisting of 2r exponents discovered by leander and kholosha is studied the dual of the function is found and it is shown that this new bent function is not of the niho type second all known univariate representations of niho bent functions are analyzed for their relation to the completed maiorana mcfarland class m in particular it is proven that two families do not belong to the completed class m the latter result gives a positive answer to an open problem whether the class h of bent functions introduced by dillon in his thesis of 1974 differs from the completed class m

a unifying framework for global regulation via nonlinear output feedback from iss to iiss this paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input to state stable inverse dynamics subject to possibly unknown control direction the contribution of the paper is two fold firstly we consider the problem of global regulation instead of global asymptotic stabilization gas for systems with generalized dynamic uncertainties it is shown by an elementary example that gas is not solvable using conventional smooth output feedback secondly we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system using our framework most of the known classes of output feedback form systems are broadened in several directions unmeasured states and unknown parameters can appear nonlinearly restrictive matching and growth assumptions are removed the dynamic uncertainty satisfies the weaker condition of sontag s integral input to state stability and the sign of high frequency gain may be unknown a constructive strategy is proposed to design a dynamic output feedback control law that drives the state to the origin while keeping all other closed loop signals bounded

several new classes of bent functions from dillon exponents several new classes of binary and p ary regular bent functions are obtained in this paper the bentness of all these functions is determined by some exponential sums over finite fields most of which have close relations with the well known kloosterman sums

bent functions with 2 r niho exponents in this note a new primary construction of bent functions consisting of a linear combination of 2r niho exponents is presented this construction generalizes one of the constructions proven by h dobbertin g leander a canteaut c carlet p felke and p gaborit