asymptotic stability in the pth moment for stochastic differential equations with levy noise abstract this paper is devoted to study a class of stochastic differential equations with levy noise in comparison to the standard gaussian noise levy noise is more versatile and interesting with a wider range of applications however levy noise makes the analysis more difficult owing to the discontinuity of its sample paths in this paper we attempt to overcome this difficulty we propose several sufficient conditions under which we investigate the long time behavior of the solution including the asymptotic stability in the pth moment and almost sure stability also we discuss two types of continuity of the solution continuous in probability and continuous in the pth moment finally we provide two examples to illustrate the effectiveness of the theoretical results

almost sure exponential stability of dynamical systems driven by levy processes and its application to control design for magnetic bearings abstracta lyapunov type theorem is developed to study well posedness and almost surely k exponential stability of dynamical systems driven by levy processes sufficient conditions imposed by the t

control of nonlinear systems with output tracking error constraints and its application to magnetic bearings a constructive method is presented to design controllers that force the output of nonlinear systems in a strict feedback form to track a bounded and sufficiently smooth reference trajectory asymptotically under a suitable condition on the initial output tracking error the proposed controllers guarantee the output tracking error within a symmetric or an asymmetric pre specified limit range and boundedness of all signals of the closed loop system a transformation is introduced to take care of the output tracking error constraint smooth and or p times differentiable step functions are proposed and incorporated in the output tracking error transformation to overcome difficulties due to the asymmetric limit range on the output tracking error as a result there are no switchings in the proposed controllers despite the asymmetric limit range the proposed control design is then applied to design a tracking controller for active magnetic bearings as an illustrating application

dead beat control of linear discrete time systems the paper considers the problem of determining the various classes of state feed back dead beat controllers for linear multivariable discrete time systems unlike earlier work attention is not restricted to the special case of minimum time dead beat controllers a general dead beat control problem is posed and solved the solution is based principally on an approach of closed loop eigenstructure assignment the minimum of free parameters in each class are specified and used in an explicit parametric form for the feedback gain matrix the concept of the greatest minimum of free parameters is introduced finally the method is illustrated by a numerical example

the stability with general decay rate of neutral stochastic functional hybrid differential equations with levy noise abstract this paper is concerned with the existence and uniqueness the almost sure stability with general decay rate including almost sure exponential stability almost sure polynomial stability and almost sure logarithmic stability for the global solution of nonlinear neutral stochastic functional hybrid differential equations with levy noise the key technique used is the method of lyapunov function nonnegative semi martingale convergence theorem and the theory of m matrix we use auxiliary functions to dominate the corresponding lyapunov function and the diffusion operator our conditions on the diffusion operator are weaker than those in the related existing works finally one example is given to show the effectiveness of the obtained theory

cluster backbone and elastic backbone structures of the multiple invasion percolation we study the cluster the backbone and the elastic backbone structures of the multiple invasion percolation for both the perimeter and the optimized versions we investigate the behavior of the mass the number of red sites i e sites through which all the current passes and loops of those structures their corresponding scaling exponents are also estimated by construction the mass of the optimized model scales exactly with the gyration radius of the cluster we verify that this also happens to the backbone our simulation shows that the red sites almost disappear indicating that the cluster has achieved a high degree of connectivity

stability analysis for stochastic hybrid systems this survey addresses stability analysis for stochastic hybrid systems shs which are dynamical systems that combine continuous change and instantaneous change and that also include random effects we re emphasize the common features found in most of the models that have appeared in the literature which include stochastic switched systems markov jump systems impulsive stochastic systems switching diffusions stochastic impulsive systems driven by renewal processes diffusions driven by levy processes piecewise deterministic markov processes general stochastic hybrid systems and stochastic hybrid inclusions then we review many of the stability concepts that have been studied including lyapunov stability lagrange stability asymptotic stability and recurrence next we detail lyapunov based sufficient conditions for these properties and additional relaxations of lyapunov conditions many other aspects of stability theory for shs like converse lyapunov theorems and robustness theory are not fully developed hence we also formulate some open problems to serve as a partial roadmap for the development of the underdeveloped pieces

stability of networked control systems with asynchronous renewal links an impulsive systems approach we consider networked control systems in which sensors actuators and controller transmit through asynchronous communication links each introducing independent and identically distributed intervals between transmissions we model these scenarios through impulsive systems with several reset maps triggered by independent renewal processes i e the intervals between jumps associated with a given reset map are identically distributed and independent of the other jump intervals for linear dynamic and reset maps we establish that mean exponential stability is equivalent to the spectral radius of an integral operator being less than one we also prove that the origin of a non linear impulsive system is locally stable with probability one if its local linearization about the zero equilibrium is mean exponentially stable which justifies the importance of studying the linear case the applicability of the results is illustrated through an example using a linearized model of a batch reactor

the n steps invasion percolation model abstract a new kind of invasion percolation is introduced in order to take into account the inertia of the invader fluid the inertia strength is controlled by the number n of pores or steps invaded after the perimeter rupture the new model belongs to a different class of universality with the fractal dimensions of the percolating clusters depending on n a blocking phenomenon takes place in two dimensions it imposes an upper bound value on n for pore sizes larger than the critical threshold the acceptance profile exhibits a permanent tail

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

stability analysis of neutral stochastic differential delay equations driven by levy noises abstract this paper mainly analyzes the well posedness and the stability analysis for the global solution of neutral stochastic differential delay equations nsddes driven by levy noises by using an integral lemma and a lyapunov function approach the existence and uniqueness theorem is proved then by using the inequality technique and the stochastic analysis theory the exponential stability in pth p 2 moment of such equations is discussed by using another integral lemma and using the baralat lemma as well as the stochastic analysis the almost surely asymptotic stability is also studied finally one example is given to check the effectiveness of the findings derived

on eigenstructure assignment in linear multivariable systems the eigenvalue assignment approach of brogan 1 2 is generalized and extended to the assignment of the entire closed loop eigenstructure of linear multivariable systems the set of assignable eigenvectors and generalized eigenvectors emerges naturally in the solution and is given moreover in an explicit parametric form two numerical examples are worked out to demonstrate the application of the procedure

parameterization of the class of deadbeat controllers this technical note deals with the problem of parameterizing the class of deadbeat controllers for a given system through the minimum of parameters it is shown that if n and m are dimensions of the state vector and control vector respectively and the i s are the controllability indexes then almost the whole class of deadbeat controllers is explicitly parameterizable through mn mu 1 3 mu 2 2m 1 mu m parameters

parametric time optimal control of linear discrete time systems by state feedback part 2 irregular kronecker invariants in an earlier paper part 1 a parametric state feedback time optimal control law was devised for the regular kronecker invariants on the basis of parametrization of the vector companion form the present paper describes a straight forward technique for obtaining the parametric feedback matrix by exploiting the parametric vector companion forms in the case of irregular kronecker invariants hidden properties of vector companion forms are also given which result in entirely different and interesting techniques for parametrization of the control law an illustrative example is presented

stochastic stabilization of hybrid differential equations this paper aims to determine whether or not a stochastic state feedback control can stabilize a given linear or nonlinear hybrid system new methods are developed and sufficient conditions on the stability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization by stochastic feedback controls two types of structure controls namely state feedback and output injection are discussed our stabilization criteria are in terms of linear matrix inequalities lmis whence the feedback controls can be designed more easily in practice a couple of examples and computer simulations are worked out to illustrate our theory

volterra integral approach to impulsive renewal systems application to networked control we analyze impulsive systems with independent and identically distributed intervals between transitions our approach involves the derivation of novel results for volterra integral equations with positive kernel we highlight several applications of these results and show that when applied to the analysis of impulsive systems they allow us to i provide necessary and sufficient conditions for mean square stability stochastic stability and mean exponential stability which can be equivalently tested in terms of a matrix eigenvalue computation an lmi feasibility problem and a nyquist criterion condition ii assess performance of the impulsive system by computing a second moment lyapunov exponent the applicability of our results is illustrated in a benchmark problem considering networked control systems with stochastically spaced transmissions for which we can guarantee stability for inter sampling times roughly twice as large as in previous papers

global inverse optimal stabilization of stochastic nonholonomic systems abstract optimality has not been addressed in existing works on control of stochastic nonholonomic systems this paper presents a design of optimal controllers with respect to a meaningful cost function to globally asymptotically stabilize in probability nonholonomic systems affine in stochastic disturbances the design is based on the lyapunov direct method the backstepping technique and the inverse optimal control design a class of lyapunov functions which are not required to be as nonlinearly strong as quadratic or quartic is proposed for the control design thus these lyapunov functions can be applied to design of controllers for underactuated stochastic mechanical systems which are usually required lyapunov functions of a nonlinearly weak form the proposed control design is illustrated on a kinematic cart of which wheel velocities are perturbed by stochastic noise

invasion percolation between two sites in two three and four dimensions abstract the mass distribution of invaded clusters in non trapping invasion percolation between an injection site and an extraction site has been studied in two three and four dimensions this study is an extension of the recent study focused on two dimensions by araujo et al a d araujo t f vasconcelos a a moreira l s lucena j s andrade jr phys rev e 72 2005 041404 with respect to higher dimensions the mass distribution exhibits a power law behavior p m m it has been found that the index for p e p c p c being the percolation threshold of a regular percolation appears to be independent of the value of p e and is also independent of the lattice dimensionality when p e p c appears to depend marginally on the lattice dimensionality and the relation 1 being the exponent associated with cluster size distribution of a regular percolation via n s s appears to be valid

on the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps this paper is concerned with the stability and numerical analysis of solution to highly nonlinear stochastic differential equations with jumps by the ito formula stochastic inequality and semi martingale convergence theorem we study the asymptotic stability in the p th moment and almost sure exponential stability of solutions under the local lipschitz condition and nonlinear growth condition on the other hand we also show the convergence in probability of numerical schemes under nonlinear growth condition finally an example is provided to illustrate the theory

the discrete linear time invariant time optimal control problem an overview a review of two decades of investigation into one of the fundamental problems of control theory the discrete linear time invariant time optimal control problem is presented two classes of multi input time optimal controller one based on system controllability and the other on eigenvalue assignment are considered in some detail also discussed are the dual state reconstruction problem the deadbeat control of linear systems with inaccessible state and other extensions the exposition is a unifying one and involves only that matrix algebra commonly encountered in control theory

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

stabilization and destabilization of hybrid systems of stochastic differential equations this paper aims to determine whether or not a stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system new methods are developed and sufficient conditions on the stability and instability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization and destabilization

stochastic hybrid systems with renewal transitions moment analysis with application to networked control systems with delays we consider stochastic hybrid systems shss for which the lengths of times that the system stays in each mode are independent random variables with given distributions we propose an approach based on a set of volterra equations to compute any statistical moment of the state of the shs moreover we provide a method to compute the lyapunov exponents of a given degree i e the exponential rate of decrease or increase at which statistical moments converge to zero or to infinity respectively we also discuss how by computing the statistical moments one can provide information about the probability distribution of the state of the shs the applicability of the results is illustrated in the analysis of a networked control problem with independently distributed intervals between data transmissions and delays

practical asymptotic stability of stochastic systems driven by levy processes and its application to control of tora systems two lyapunov type theorems are developed to investigate global practical asymptotic stability in probability for sdes driven by non vanishing levy processes which can be either affine or non a

a general riccati equation solution to the deadbeat control problem it is well known that the state of a controllable system can be driven to zero in minimum time for arbitrary initial condition by the time varying kalman gain sequence computed via a singular riccati equation this paper shows how a constant deadbeat control feedback which will accomplish the same result in the same minimum time can always be found via the same riccati equation

deadbeat control and tracking of discrete time systems a new approach for forcing the state of a linear discrete time system to zero in a minimum number of steps is discussed the problem is formulated as the solution to a steady state optimal control problem with no cost on the control this problem in turn is set up as the solution to an associated eigenvalue problem no special assumption on the open loop system matrix and or the ratio of the number of states to controls is required stable numerical techniques are presented for solving for the feedback gain robust deadbeat tracking is also discussed