finite time asynchronous h control for markov jump repeated scalar non linear systems with input constraints finite time control issue for a quite comprehensive class of system model that is markov jump repeated scalar nonlinear systems mjrsnss has been addressed an asynchronous controller is first proposed in mjrsnss which has less conservatism than mode dependent when the partly available mode information is encountered the input constraints associated with physical limitations in some practical applications have been fully considered which make our model more realistic this paper is concerned with the problem of finite time h control for markov jump repeated scalar nonlinear systems mjrsnss with input constraints the jumps between mjrsnss and desired mode dependent controllers are considered to be nonsynchronous the mode transition of the controllers is governed by a nonstationary markov chain which can model the different degrees of asynchronous jumps between mjrsnss and controllers with the aid of lyapunov krasovskii methodology some h performance criteria for the mjrsnss are proposed based on these criteria sufficient conditions on the existence of the desired controllers are established and then the gains of the controllers can be obtained by solving a convex optimization problem finally an example is presented to illustrate the effectiveness of our method

growth of homogeneous spaces density of discrete subgroups and kazhdan s property t letg be a semisimple lie group with finite center and no compact factors we show that ifh is a closed unimodular subgroup ofg such thatg h has subexponential volume growth thenh is zariski dense ing moreover ifg has kazhdan s property t theng h must have finite volume we extend these results to semisimple groups over a local field

generalized lyapunov criteria on finite time stability of stochastic nonlinear systems abstract this paper considers the problem of finite time stability for stochastic nonlinear systems a general lyapunov theorem of stochastic finite time stability is proposed and an important corollary is obtained some comparisons with the existing results are also given this theorem not only generalizes the classical stochastic finite time theorem but also somewhat shows that brownian noise takes an active role in stochastic finite time stability in addition more general conditions on stochastic finite time stability via multiple lyapunov functions are given to further relax the constraint of the differential operator l v moreover with the help of this criterion it shows that an unstable deterministic system can even be finite time stabilized by brownian noise some concrete examples are constructed to show the significant features of the proposed results and simulations are presented to verify the theoretical analysis

finite time stability and stabilization of time delay systems finite time stability and stabilization of retarded type functional differential equations are developed first a theoretical result on finite time stability inspired by the theory of differential equations using lyapunov functionals is given as it may appear not easily usable in practice we show how to obtain finite time stabilization of linear systems with delays in the input by using an extension of artstein s model reduction to nonlinear feedback with this approach we give an explicit finite time controller for scalar linear systems and for the chain of integrators with delays in the input

finite time stability conditions for non autonomous continuous systems finite time stability is defined for continuous non autonomous systems starting with a result from haimo 1986 we then extend this result to n dimensional non autonomous systems through the use of smooth and non smooth lyapunov functions as in perruquetti and drakunov 2000 one obtains two different sufficient conditions and a necessary one for finite time stability of continuous non autonomous systems

finite time stability of impulsive reaction diffusion systems with and without time delay abstract this paper considers the finite time stability of impulsive reaction diffusion systems irdss we deal with two cases systems without time delay and systems with time delay when there is no delay in the considered system we obtain sufficient conditions to guarantee the finite time stability of irdss via two representations of impulsive sequences when time delay enters into irdss we adopt a comparison method to deal with the finite time stability and provide sufficient conditions ensuring the finite time stability we also present the differences of finite time stability and asymptotic stability for the irdss moreover in our sufficient conditions we show the effects of impulse diffusion and spatial domain on the finite time stability and discuss the effect of time delay on the stability numerical simulations are carried out to show the effectiveness of our obtained results

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

finite time output feedback control for a class of stochastic low order nonlinear systems abstractthis paper discusses the problem of finite time stabilisation for a class of stochastic low order nonlinear systems via output feedback by generalising the adding a power integrator technique constructing an implementable reduced order observer and using the stochastic finite time stability criterion a finite time output feedback controller is presented to guarantee that the closed loop system is finite time stable in probability a simulation example is provided to verify the effectiveness of the proposed design method

on an output feedback finite time stabilization problem studies the problem of finite time output feedback stabilization for the double integrator system a class of output feedback controllers that can achieve global finite time stability for the double integrator system are constructed based on a finite time separation principle furthermore it is shown that the closed loop system resulting from our control law can maintain its local finite time stability regardless of some nonlinear perturbations thus our control law actually applies to a large class of nonlinear second order systems

lyapunov conditions for finite time stability of time varying time delay systems in this paper we develop the lyapunov razumikhin method to finite time stability fts and finite time contractive stability ftcs of time delay systems several lyapunov based sufficient conditions for establishing these fts properties are obtained then the theoretical results are applied to fts and ftcs for a class of linear time varying ltv time delay system the efficiency of the proposed criteria is illustrated by three numerical examples where a stabilizing memoryless controller for ftcs of a second order ltv system with time delay is proposed

further results on global adaptive stabilisation for a class of uncertain stochastic nonlinear systems this paper considers the global adaptive stabilisation for a class of uncertain stochastic nonlinear systems comparing with the existing relevant literature the systems under investigation allow more serious unknowns uncertainties more importantly by remarkably reducing the dimension of dynamic compensator for system unknowns from n to 2 and considerably diminishing the overparametrisation in the existing literature this paper proposes an improved design scheme for adaptive state feedback controllers it is turned out that with the designed controller in loop all the closed loop system states are globally bounded and the original system states converge to the origin both in the sense of probability one a simulation example is also given to demonstrate the effectiveness of the theoretical results

decentralised adaptive output feedback stabilisation for stochastic time delay systems via lasalle yoshizawa type theorem abstractthis paper deals with the decentralised output feedback stabilisation problem for a class of large scale stochastic time delay nonlinear systems a general theorem is firstly given to guarantee the global existence and uniqueness of the solution for stochastic time delay systems in addition a stochastic version of the well known lasalle yoshizawa theorem with time varying delay is initially proposed for the controller design and stability analysis then for a class of large scale stochastic systems with time varying delays totally decentralised adaptive delay dependent controllers are designed by using k filter and backstepping approach via lasalle yoshizawa type theorem and constructing a general lyapunov function it is shown that all signals in the closed loop system are bounded almost surely and the solution is almost surely asymptotically stable finally a simulation example is given to illustrate the effectiveness of the results of this paper

finite time stabilizability detectability and dynamic output feedback finite time stabilization of linear systems in this note we deal with linear systems and we extend to the finite time setting the concepts of stabilizability and detectability it will be shown that similarly to what happens in the classical lyapunov framework even in the finite time context stabilizability and detectability play a role into the existence of stabilizing dynamical controllers we prove that a dynamic output feedback controller which finite time stabilizes the overall closed loop system exists if and only if the open loop system is finite time detectable and stabilizable plus a further linear matrix inequality coupling condition we also show that in the finite time context the equivalence between stabilizability via output feedback and stabilizability via observer based controllers is no longer true

global fixed time stabilization for switched stochastic nonlinear systems under rational switching powers abstract this note studies global fixed time stabilization for switched stochastic nonlinear systems under rational switching powers with the aid of stochastic fixed time stability theorem a new control approach is presented to ensure that the system state globally reaches zero almost surely in fixed time independent of initial conditions the developed scheme is used to controller design of the liquid level system

on nonsingular terminal sliding mode control of nonlinear systems this paper proposes a method to overcome the singularity problem of terminal sliding mode control systems the system behaviors in both the reaching phase and the ideal sliding mode are analyzed a global nonsingular terminal sliding mode control strategy for nonlinear systems is developed and it is shown that the proposed control strategy can eliminate the singularity while guaranteeing the finite time reachability of the systems to the terminal sliding mode surface and the finite time convergence of the systems towards the origin along the terminal sliding mode surface

fixed time stability theorem of stochastic nonlinear systems to solve the fixed time stability problem for stochastic systems which has not been investigated due to the difficulty caused by the existence of stochastic the fixed time stability is investigat

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

finite time stabilization of switched stochastic nonlinear systems with mixed odd and even powers this paper investigates the finite time stabilization of a class of switched stochastic nonlinear systems in p normal form where the power orders of the system are dependent upon the switching signal and the system structure is in non triangular form compared with the existing results some power orders of the system are allowed to be even under suitable assumptions a state feedback control law with state dependent switching is designed by using the convex combination method and the adding a power integrator technique it is shown that the resulting closed loop system is finite time stable in probability simulation results of a continuously stirred tank reactor cstr system are provided to show the effectiveness and applicability of the proposed method

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

stochastic nonlinear stabilization i a backstepping design while the current robust nonlinear control toolbox includes a number of methods for systems affine in deterministic bounded disturbances the problem when the disturbance is unbounded stochastic noise has hardly been considered we present a control design which achieves global asymptotic lyapunov stability in probability for a class of strict feedback nonlinear continuous time systems driven by white noise in a companion paper we develop inverse optimal control laws for general stochastic systems affine in the noise input and for strict feedback systems a reader of this paper needs no prior familiarity with techniques of stochastic control

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

finite time stability of discrete autonomous systems abstract finite time stability involves dynamical systems whose trajectories converge to a lyapunov stable equilibrium state in finite time in this paper we address finite time stability of discrete time dynamical systems specifically we show that finite time stability leads to uniqueness of solutions in forward time furthermore we provide lyapunov and converse lyapunov theorems for finite time stability of discrete autonomous systems involving scalar difference fractional inequalities and minimum operators in addition lower semicontinuity of the settling time function capturing the finite settling time behavior of the dynamical system is studied and illustrated through several examples in particular it is shown that the regularity properties of the lyapunov function and those of the settling time function are related consequently converse lyapunov theorems for finite time stability of discrete time systems can only assure the existence of lower semicontinuous lyapunov functions

finite time stabilization of weak solutions for a class of non local lipschitzian stochastic nonlinear systems with inverse dynamics in this paper finite time stabilization is investigated for a class of non local lipschitzian stochastic nonlinear systems with stochastic inverse dynamics different from the existing work about finite time control to guarantee the existence of the solution under mild conditions we study the stabilization in the sense of weak solution we first present a finite time stability theory under the framework of weak solution then for a class of stochastic nonlinear systems with stochastic inverse dynamics a finite time controller via state feedback is constructively designed under the assumption that the stochastic inverse dynamics is stochastic input to state stable the trivial weak solution of the closed loop system is proved to be globally finite time stable in probability finally a simulation example is given to illustrate the efficiency of the proposed design procedure

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

some properties of finite time stable stochastic nonlinear systems in this paper we study some properties of finite time stable stochastic nonlinear systems we begin by showing several continuous dependence theorems of solutions on initial values under some conditions on the coefficients of stochastic systems we then derive some regular properties of its stochastic settling time for a finite time stable stochastic nonlinear system we show continuity positive definiteness and boundedness of the expected stochastic settling time under appropriate conditions finally a lyapunov function is constructed by making use of the expectation of the stochastic settling time and the infinitesimal generator of the stochastic system defined on the lyapunov function is also given and hence resulting in a converse lyapunov theorem of finite time stochastic stability

output tracking of high order stochastic nonlinear systems with application to benchmark mechanical system this note considers output tracking of high order stochastic nonlinear systems without imposing any restriction on the high order and the drift and diffusion terms by using the backstepping design technique a smooth state feedback controller is given to guarantee that the solution process is bounded in probability and the error signal between the output and the reference signal can be regulated into a small neighborhood of the origin in probability a practical example of stochastic benchmark mechanical system and simulation are provided to demonstrate the effectiveness of the control scheme

brief paper finite time stability and instability of stochastic nonlinear systems this paper presents a new definition of finite time stability for stochastic nonlinear systems this definition involves stability in probability and finite time attractiveness in probability an important lyapunov theorem on finite time stability for stochastic nonlinear systems is established a theorem extending the stochastic lyapunov theorem is also proved moreover an example and a lemma are presented to illustrate the scope of extension a useful inequality extended from bihari s inequality is derived which plays an important role in showing the lyapunov theorem finally a lyapunov theorem on finite time instability is proved which states that almost surely globally asymptotical stability is not equivalent to finite time stability for some stochastic systems two simulation examples are given to illustrate the theoretical analysis

finite time stability and stabilization of ito stochastic systems with markovian switching mode dependent parameter approach this technical note is concerned about the finite time stability and stabilization for ito stochastic systems with markovian switching a mode dependent parameter approach is proposed to give a sufficient condition for finite time stability and its superiority to common parameter approach is analyzed moreover the finite time stabilization is studied and two new sufficient conditions for the existence of state and output feedback controllers are presented in terms of coupled matrix inequalities a n mode algorithm is given for solving the obtained matrix inequalities arising from finite time stability stabilization finally an example is employed to illustrate the effectiveness of our obtained results

representations of fundamental groups of manifolds with a semisimple transformation group group 1 m and the lie groups that can act on m more precisely let g be a connected semisimple lie group of higher real rank and suppose g acts continuously on a topological manifold m preserving a finite measure the main theme of this paper is that the representation theory of 7r i m in low dimensions is to a large extent controlled by that of g the latter of course being well understood in particular under natural hypotheses e g that the action of g on m is engaging i e there is no loss of ergodicity in passing to finite covers see definition 3 1 below we prove that if g has no nontrivial

global regulation for a class of stochastic high order nonlinear systems with multiple unknown control directions this paper concerns the global regulation for a class of stochastic high order nonlinear systems which admit more general system form than the existing works for details except for the serious sy

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

finite time boundary control for delay reaction diffusion systems abstract this paper considers finite time stabilization and h performance for delay reaction diffusion systems by boundary control first a full domain controller is designed and sufficient conditions are obtained to achieve finite time stability using finite time stability lemma and wirtinger s inequality method then a boundary controller furnished with sufficient conditions to achieve finite time stability is presented when taking into consideration external noise on a delay reaction diffusion system finite horizon h boundary control with a criterion that guarantees the h performance of delay reaction diffusion systems is proposed how to handle neumann boundary conditions and mixed boundary conditions are discussed numerical simulations are carried out to verify the effectiveness of our theoretical results

on different generalizations of episturmian words in this paper we study some classes of infinite words generalizing episturmian words and analyse the relations occurring among such classes in each case the reversal operator r is replaced by an arbitrary involutory antimorphism q of the free monoid a in particular we define the class of q words with seed whose standard elements q standard words with seed are constructed by an iterative q palindrome closure process starting from a finite word u 0 called the seed when the seed is empty one obtains q words episturmian words are exactly the r words one of the main theorems of the paper characterizes q words with seed as infinite words closed under q and having at most one left special factor of each length n n where n is some nonnegative integer depending on the word when n 0 we call such words q episturmian further results on the structure of q episturmian words are proved in particular some relationships between q words with or without seed and q episturmian words are shown

finite time control of switched stochastic nonlinear systems abstract this manuscript studies a finite time tracking problem of switched stochastic nonlinear uncertain systems by utilizing a comparison theorem and a mean value theorem of integrals a significant finite time stability criterion for stochastic nonlinear systems is first set up then combining a common lyapunov function method and an adaptive fuzzy control approach a novel common control scheme is formed under the proposed adaptive mechanism the system performance is achieved in finite time by using the universal approximation ability the nonlinear functions and their bounding functions may be completely unknown to the designer which is more in line with reality than the existing finite time researches for stochastic nonlinear systems

finite time input to state stability and applications to finite time control design this paper extends the well known concept sontag s input to state stability iss to finite time control problems in other words a new concept finite time input to state stability ftiss is proposed and then is applied to both the analysis of finite time stability and the design of finite time stabilizing feedback laws of control systems with finite time stability nonsmoothness has to be considered and serious technical challenges arise in the design of finite time controllers and the stability analysis of the closed loop system it is found that ftiss plays an important role as the conventional iss in the context of asymptotic stability analysis and smooth feedback stabilization moreover a robust adaptive controller is proposed to handle nonlinear systems with parametric and dynamic uncertainties by virtue of ftiss and related arguments

stabilization by artificial wiener processes in this technical note we restage the positive effects of gaussian white noises for continuous time driftless input affine nonholonomic systems compared with previous studies we found that the positive effects are hidden in the shadows of nonuniqueness of stochastic integrals over multi dimensional wiener processes furthermore we found that the positive effects are artificially restaged by numerical calculations with use of euler scheme for ordinary differential equations our results demonstrate that the positive effects act as hidden independent control inputs for nonholonomic systems this implies that our results provide a constructive procedure for designing control inputs such that the origins become p th moment exponentially or finite time stable

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

new lyapunov conditions of stochastic finite time stability and instability of nonlinear time varying sdes in this paper we further consider the problem of stochastic finite time stability and instability of nonlinear stochastic differential equations sdes with time varying drift and diffusion terms

finite time state feedback stabilisation of stochastic high order nonlinear feedforward systems abstractthis paper studies the finite time state feedback stabilisation of stochastic high order nonlinear feedforward systems based on the stochastic lyapunov theorem on finite time stability by using the homogeneous domination method the adding one power integrator and sign function method constructing a c2 lyapunov function and verifying the existence and uniqueness of solution a continuous state feedback controller is designed to guarantee the closed loop system finite time stable in probability

convergence rates of stochastic homogeneous systems abstract this study considers stochastic homogeneous systems and focuses on the relation between their homogeneity and the convergence rates we give a definition of stochastic homogeneous systems with weighted dilations as an extension of deterministic homogeneous systems we also introduce the stability properties such as exponential rational and finite time stability with respect to homogeneous norms as a main result we show that their homogeneous degrees imply the convergence rates of asymptotically stable systems based on the result we also deal with the stabilization of stochastic homogeneous control systems we provide a design method of homogeneous feedback laws with homogeneous control lyapunov functions which guarantees the convergence rates

finite time stability and stabilization of a class of continuous systems abstract finite time stability is investigated for continuous system x f x which satisfies uniqueness of solutions in forward time a necessary and sufficient condition for finite time stability is given for this class of systems using lyapunov functions then a necessary and sufficient condition is developed for finite time stabilization of class cl k affine systems x f x g x u involving a class cl 0 settling time function for the closed loop system finally an explicit feedback control is addressed by using a control lyapunov function verifying a certain inequality

adaptive finite time control of stochastic nonlinear systems with actuator failures abstract this paper investigates a finite time tracking control of stochastic nonlinear systems with actuator failures as the nonlinearities and actuator failures are completely unknown the existing control methods are unavailable by applying an approximation property of fuzzy logic systems an adaptive finite time control strategy is presented since the existing finite time stability criterion can not deal with the finite time control under the effect of approximation error lemma 5 is first established under the proposed scheme the actuator failures are compensated successfully and the finite time tracking performance and stability of stochastic nonlinear system are assured based on lemma 5 and jessen s inequality the finite time stability of stochastic nonlinear systems is proved

global finite time stabilisation for a class of stochastic nonlinear systems by output feedback in this paper the problem of global finite time stabilisation by output feedback is considered for a class of stochastic nonlinear systems first based on homogeneous systems theory and the adding a power integrator technique a homogeneous reduced order observer and control law are constructed in a recursive manner for the nominal system then the homogeneous domination approach is used to deal with the nonlinearities in drift and diffusion terms it is shown that the proposed output feedback control law can guarantee that the closed loop system is global finite time stable in probability finally simulation examples are carried out to demonstrate the effectiveness of the proposed control scheme

unitary spectrum and the fundamental group for actions of semisimple lie groups suppose a locally compact group g acts on a separable metrizable space m preserving a finite measure then there is an associated unitary representation of g on lz m o the square integrable functions orthogonal to the constants this representation will in general be far from irreducible and in fact when g is not compact need not have any irreducible subrepresentations thus in the decomposition of lz g o into irreducible constituents one not only requires a direct integral rather than a direct sum but the associated spectral measure on the unitary dual g say for type i groups will except in special circumstances have no atoms the point of this paper is to give natural and general conditions mostly involving just rq m under which there will be an infinite atomic spectrum i e the spectral measure has infinitely many atoms the basic example of actions in which the spectrum is purely atomic i e when the representation is a direct sum of irreducible representations is the case of m g f where f c g is a cocompact discrete subgroup in this case assuming 9 g to be simply connected we have 7tl m f the first results of this paper show that when g is a simple lie group with r rank g 2 we can deduce that any action of g on a compact manifold m with fundamental group isomorphic to such a f and satisfying a natural hypothesis of either a geometric or ergodic theoretic nature must also have an infinite atomic spectrum in fact under certain natural hypotheses the same is true as long as there is a surjection of hi m onto f to formulate this more precisely let f c ad g be a cocompact lattice and let pr be the unitary representation of ad g on l2 ad g f o we recall that an action of a group on a manifold or more generally on a standard space in the sense of 4 is called engaging if there is no loss of ergodicity in passing to finite covers see i 4 for discussion

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

global stability and stabilization of more general stochastic nonlinear systems abstract this paper considers the global stability and stabilization of more general stochastic nonlinear systems due to the absence of the conventional assumptions e g lipschitz condition the stochastic nonlinear systems under investigation may have more than one weak solution however the most associated results are only applicable to the stochastic systems having a unique strong solution and therefore it is meaningful to refine and extend the relevant concepts and methods to the more general case in this paper the concepts of stochastic stability in the more general sense are first introduced to cover the stochastic nonlinear systems having more than one weak solution then the generalized stochastic barbashin krasovskii theorem and lasalle theorem are established which present the criterions of stochastic stability for more general stochastic nonlinear systems as one of the main contributions in this paper we rigorously prove the generalized stochastic barbashin krasovskii theorem moreover based on the generalized theorems the output feedback and state feedback stabilization are accomplished respectively for two classes of high order stochastic nonlinear systems under rather weaker assumptions comparing to the existing literature

finite time stability and settling time estimation of nonlinear impulsive systems abstract this paper studies the problem of finite time stability fts for nonlinear impulsive systems based on impulsive control theory several lyapunov based fts theorems involving stabilizing impulses and destabilizing impulses are established respectively our proposed results provide sufficient conditions for estimating the settling time with respect to suitable classes of impulse time sequences it is shown that the settling time of nonlinear impulsive systems depends not only on the initial state but also on the impulse effect as compared with the case without using stabilizing impulses a smaller bound of setting time can be derived when a fts system is subject to stabilizing impulses conversely a larger bound of settling time can be derived when the fts system is subject to destabilizing impulses as compared with the case without using destabilizing impulses as a special case we extend the ideas to nonlinear impulsive delay systems and derive some delay independent fts results examples and their simulations are given to demonstrate the applicability of the proposed results

new criteria on finite time stability of fractional order hopfield neural networks with time delays in this article the finite time stability fts of fractional order hopfield neural networks with time delays fhnntds is studied a widely used inequality in investigating the stability of the fractional order neural networks is fractional order gronwall inequality related to the mittag leffler function which cannot be directly used to study the stability of the factional order neural networks with time delays in the existing works related to fractional order gronwall inequality with time delays the order 0 was divided into two cases 0 0 5 and 0 5 in this article a new fractional order gronwall integral inequality with time delay and the unified form for all the fractional order 0 is developed which can be widely applied to investigate fts of various fractional order systems with time delays based on this new inequality a new criterion for the fts of fhnntds is derived compared with the existing criteria in which fractional order 0 1 was divided into two cases 0 0 5 and 0 5 1 the obtained results in this article are presented in the unified form of fractional order 0 1 and convenient to verify more importantly the criteria in this article are less conservative than some existing ones finally two numerical examples are given to demonstrate the validity of the proposed results

backstepping controller design for nonlinear stochastic systems under a risk sensitive cost criterion this paper develops a methodology for recursive construction of optimal and near optimal controllers for strict feedback stochastic nonlinear systems under a risk sensitive cost function criterion the design procedure follows the integrator backstepping methodology and the controllers obtained guarantee any desired achievable level of long term average cost for a given risk sensitivity parameter theta furthermore they lead to closed loop system trajectories that are bounded in probability and in some cases asymptotically stable in the large these results also generalize to nonlinear systems with strongly stabilizable zero dynamics a numerical example included in the paper illustrates the analytical results

finite time stability theorems of homogeneous stochastic nonlinear systems abstract the purpose of this paper is to study finite time stability of a class of homogeneous stochastic nonlinear systems modeled by stochastic differential equations an existence result of weak solutions for stochastic differential equations with continuous coefficients is derived as a preparation for discussing stochastic nonlinear systems then a generalization of finite time stochastic stability theorem is given by using some properties of homogeneous functions and homogeneous vector fields it is proved that a homogeneous stochastic nonlinear system is finite time stable if its coefficients have negative degrees of homogeneity and there exists a sufficiently smooth and homogeneous lyapunov function such that the infinitesimal generator of the stochastic system acting on it is negative definite in the case when the drift coefficient of a stochastic system is homogeneous and has a negative degree of homogeneity it can be shown that the stochastic system is also finite time stable under appropriate conditions two examples are provided as illustrations

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

finite time stabilization of high order stochastic nonlinear systems in strict feedback form this paper deals with the problem of finite time stabilization for a class of high order stochastic nonlinear systems in strict feedback form by using ito s formula mathematical induction and backstepping design method a novel state feedback controller is constructed to guarantee that the closed loop high order nonlinear system has a unique solution and the solution of the closed loop high order nonlinear system is finite time stable a systematic design algorithm is developed for the construction of the backstepping controller finally the effectiveness of the state feedback controller is illustrated by two examples