stochastic controllability and minimum energy control of systems with multiple delays in control in recent years various controllability problems for different types of linear dynamical systems have been considered in many publications and monographs

quantization based on statistical moments for signal detection design and analysis this paper addresses a signal detection problem based on a class of quantizers the known moments of the underlying noise distribution are used to index a set of quantization points that have been predetermined under an assumed noise model the fact that lower order moments are easy to obtain and that they are required in the implementation and analysis of most threshold detectors makes this approach quite appealing the performance of the resulting quantizers is shown to be relatively insensitive to variations in the underlying noise distribution and to small deviations of the presumed moments the detector s performance in the finite sample size case is investigated and the distribution resulting in the highest false alarm rate is described for both symmetric and asymmetric noise cases by setting the test threshold according to the worst distribution a lower bound on the detector s performance is guaranteed

constrained controllability of nonlinear systems abstract in this paper infinite dimensional dynamical systems described by nonlinear abstract differential equations are considered using the generalized open mapping theorem sufficient conditions for constrained exact local controllability are formulated and proved it is generally assumed that the values of controls are in a convex and closed cone with vertex at zero as an illustrative example a constrained exact local controllability problem for a nonlinear delayed dynamical system is solved in detail some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented

controllability and observability of a class of linear impulsive systems this paper studies the controllability and observability of a class of linear piecewise constant impulsive systems necessary and sufficient criteria for reachability and controllability are established respectively it is proved that the reachability is equivalent to the controllability under some mild conditions then necessary and sufficient criteria for observability and determinability of such systems are established respectively it is also proved that the observability is equivalent to the determinability under some mild conditions our criteria are of geometric type they can be transformed into algebraic type conveniently finally a numerical example is given to illustrate the utility of our criteria

differential algebraic systems as differential equations on manifolds based on the theory of differential equations on manifolds existence and uniqueness results are proved for a class of mixed systems of differential and algebraic equations as they occur in various applications both the autonomous and nonautonomous case are considered moreover a class of algebraically incomplete systems is introduced for which existence and uniqueness results only hold on certain lower dimensional manifolds this class includes systems for which the application of ode solvers is known to lead to difficulties finally some solution approach based on continuation techniques is outlined

spectral tests for observability and detectability of periodic markov jump systems with nonhomogeneous markov chain this paper addresses observability and detectability of discrete time periodic systems with nonhomogeneous markov jump parameter popov belevitch hautus pbh type criteria are proposed for the concerned structural properties it is shown that different from stochastic systems with constant coefficients or homogeneous markov chain the spectral criteria of considered plants do not rely on a single operator but on a finite sequence of linear evolution operators by use of the obtained detectability criterion an extended lyapunov theorem is established which relates asymptotic mean square stability to a periodic lyapunov equation further a difference riccati equation with periodic coefficients is studied and some sufficient conditions are presented for the existence of stabilizing solution

asymptotic expansions of the global error of fixed stepsize methods in his fundamental paper on general fixed stepsize methods skeel 6 studied convergence properties but left the existence of asymptotic expansions as an open problem in this paper we give a complete answer to this question for the special cases of one step and linear multistep methods our proof is shorter than the published ones asymptotic expansions are the theoretical base for extrapolation methods

controllability of measure driven evolution systems with nonlocal conditions this paper investigates complete controllability of semilinear measure driven differential systems with nonlocal conditions without assuming the compactness of the evolution system related to the linear part of the measure system some sufficient conditions for controllability are established by using the measure of noncompactness and the monch fixed point theorem the results obtained here improve and generalize many known results

numerical solution of nonlinear differential equations with algebraic constraints i convergence results for backward differentiation formulas in this paper we investigate the behavior of numerical ode methods for the solution of systems of differential equations coupled with algebraic constraints systems of this form arise frequently in the modelling of problems from physics and engineering we study some particular examples from electrical networks fluid dynamics and constrained mechanical systems we show that backward differentiation formulas converge with the expected order of accuracy for these systems

controllability of non linear impulsive stochastic systems in this article we consider the finite dimensional dynamical control systems described by non linear impulsive stochastic differential equations sufficient conditions for the complete and approximate controllability of non linear impulsive stochastic systems are formulated and proved under the natural assumption that the corresponding linear system is appropriately controllable

brief paper complete controllability of impulsive stochastic integro differential systems this paper is concerned with the controllability of impulsive stochastic integro differential systems sufficient conditions of complete controllability for impulsive stochastic integro differential systems are obtained by using schaefer s fixed point theorem a numerical example is provided to show the effectiveness of the proposed results

constrained controllability of linear impulse differential systems considers the following linear impulse differential control system x spl dot a t x t spl ne t sub k spl delta x b sub k x t sub k c sub k u sub k t t sub k where the control sequences u sub k belong to some set of admissible controllers that is restricted either by norm or by range the authors then give a necessary and sufficient condition for global null controllability of time varying systems and some sufficient conditions for global null controllability for time invariant systems with special structures

on concepts of controllability for deterministic and stochastic systems the new necessary and sufficient conditions which are formulated in terms of convergence of a certain sequence of operators involving the resolvent of the negative of the controllability operator are found for deterministic linear stationary control systems to be completely and approximately controllable respectively these conditions are applied to study the s controllability a property of attaining an arbitrarily small neighborhood of each point in the state space with a probability arbitrarily close to one and c controllability the s controllability fortified with some uniformity of stochastic systems it is shown that the s controllability the c controllability of a partially observable linear stationary control system with an additive gaussian white noise disturbance on all the intervals 0 t for t 0 is equivalent to the approximate complete controllability of its deterministic part on all the intervals 0 t for t 0

controllability of semilinear stochastic systems in hilbert spaces we study the weak approximate and complete controllability properties of semilinear stochastic systems assuming controllability of the associated linear systems the results are obtained by using the banach fixed point theorem applications to stochastic heat equation are given

controllability of linear stochastic systems abstract we discuss several concepts of controllability for stochastic systems and derive sufficient and in most cases also necessary algebraic conditions for the controllability of the state and the output of white and colored noise linear systems these criteria reduce to the well known deterministic ones in the absence of noise

controllability of linear stochastic systems we discuss several concepts of controllability for partially observable stochastic systems complete controllability approximate controllability and stochastic controllability we show that complete and approximate controllability notions are equivalent and in turn they are equivalent to the stochastic controllability for linear stochastic systems controlled with gaussian processes we derive necessary and sufficient conditions for these concepts of controllability these criteria reduce to the well known rank condition

robust fuzzy design for nonlinear uncertain stochastic systems via sliding mode control this paper deals with the sliding mode control smc problem for nonlinear stochastic time delay systems by means of fuzzy approach the takagi sugeno t s fuzzy stochastic time delay model with parametric uncertainties and unknown nonlinearities is presented a sufficient condition for the exponential stability in mean square of the sliding motion is also derived moreover it is shown that when the linear matrix inequalities lmis with equality constraint are feasible the designs of both sliding surface and sliding mode controller can be easily obtained via convex optimization a simulation example illustrating the proposed method is given

one step and extrapolation methods for differential algebraic systems the paper analyzes one step methods for differential algebraic equations dae in terms of convergence order in view of extrapolation methods certain perturbed asymptotic expansions are shown to hold for the special dae extrapolation solver based on the semi implicit euler discretization the perturbed order pattern of the extrapolation tableau is derived in detail the theoretical results lead to modifications of the known code the efficiency of the modifications is illustrated by numerical comparisons over critical examples mainly from chemical combustion

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

nonlinear boundary value problem of first order impulsive functional differential equations this paper discusses nonlinear boundary value problem for first order impulsive functional differential equations we establish several existence results by using the lower and upper solutions and monotone iterative techniques two examples are discussed to illustrate the efficiency of the obtained results

step size adjustment and extrapolation for time stepping schemes in non smooth dynamics in this paper we use step size adjustment and extrapolation methods to improve moreau s time stepping scheme for the numerical integration of non smooth mechanical systems i e systems with impact and friction the scheme yields a system of inclusions which is transformed into a system of projective equations these equations are solved iteratively switching points are time instants for which the structure of the mechanical system changes for example time instants for which a sticking friction element begins to slide we show how switching points can be localized and how these points can be resolved by choosing a minimal step size in order to improve the integration of non smooth systems in the smooth parts we show how the time stepping method can be used as a base integration scheme for extrapolation methods which allow for an increase in the integration order switching points are processed by a small time step while time intervals during which the structure of the system does not change are computed with a larger step size and improved integration order the overall algorithm which consists of a time stepping module an extrapolation module and a step size adjustment module is discussed in detail and some examples are given

input to state stability of impulsive and switching hybrid systems with time delay this paper investigates input to state stability iss and integral input to state stability iiss of impulsive and switching hybrid systems with time delay using the method of multiple lyapunov krasovskii functionals it is shown that even if all the subsystems governing the continuous dynamics in the absence of impulses are not iss iiss impulses can successfully stabilize the system in the iss iiss sense provided that there are no overly long intervals between impulses i e the impulsive and switching signal satisfies a dwell time upper bound condition moreover these impulsive iss iiss stabilization results can be applied to systems with arbitrarily large time delays conversely in the case when all the subsystems governing the continuous dynamics are iss iiss in the absence of impulses the iss iiss properties can be retained if the impulses and switching do not occur too frequently i e the impulsive and switching signal satisfies a dwell time lower bound condition several illustrative examples are presented with their numerical simulations to demonstrate the main results

optimal projection for multidimensional signal detection the concept of projection in which a set of samples is represented by a single sample can be used to reduce the dimensionality of the data thereby simplifying the detection process a projection method that maximizes the probability of signal detection for a fixed probability of false alarm is derived samples containing signal plus noise and noise alone are assumed to be independently and identically distributed but are otherwise arbitrary only one sample in the set of samples projected onto a single sample may contain the signal it is shown that for high signal to noise ratios the optimal projection algorithm can be approximated as the maximum value projection scheme and for low signal to noise ratios it can be viewed as a summation projection algorithm an example is presented of a computationally efficient 3 d line segment detector that uses maximum value projection the algorithm is useful for optically detecting meteors satellites and other moving targets that move in a straight path across many frames of data

null controllability of an infinite dimensional sde with state and control dependent noise abstract we consider a controlled stochastic linear differential equation with state and control dependent noise in a hilbert space h we investigate the relation between the null controllability of the equation and the existence of the solution of singular riccati operator equations moreover for a fixed interval of time the null controllability is characterized in terms of the dual state examples of stochastic pdes are also considered

linearly implicit extrapolation methods for differential algebraic systems we consider the numerical solution of implicit differential equations in which the solution derivative appears multiplied by a solution dependent singular matrix we study extrapolation methods based on two linearly implicit euler discretizations their error behaviour is explained by perturbed asymptotic expansions

approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained but approximate controllability of semilinear control systems usually requires some complicated and limited assumptions in this paper we show the approximate controllability of the abstract semilinear deterministic and stochastic control systems under the natural assumption that the associated linear control system is approximately controllable the results are obtained using new properties of symmetric operators which are proved in this paper compact semigroups the schauder fixed point theorem and or the contraction mapping principle

controllability of non linear stochastic systems complete controllability of a semi linear stochastic system assuming controllability of the associated linear sytem is studied it is also shown that a non linear stochastic system is locally null controllable provided that the corrsponding linearized system is controllable

practical stability controllability and optimal control of stochastic markovian jump systems with time delays the notions of the practical stability in probability and in the pth mean and the practical controllability in probability and in the pth mean are introduced for some stochastic systems with markovian jump parameters and time varying delays sufficient conditions on such practical properties are obtained by using the comparison principle and the lyapunov function methods besides for a class of stochastic nonlinear systems with markovian jump parameters and time varying delays existence conditions of optimal control are discussed particularly for linear systems optimal control and the corresponding index value are presented for a class of quadratic performance indices with jumping weighted parameters

extrapolation at stiff differential equations asymptotic expansions of the global error of numerical methods are well understood if the differential equation is non stiff this paper is concerned with such expansions for the implicit euler method the linearly implicit euler method and the linearly implicit mid point rule when they are applied tostiff differential equations in this case perturbation terms are present whose dominant one is given explicitly this permits us to better understand the behaviour ofextrapolation methods at stiff differential equations numerical examples supporting the theoretical results are included

the drazin inverse in multibody system dynamics the numerical analysis of multibody system dynamics is based on the equations of motion as differential algebraic systems a thorough analysis of the linearized equations and their solution theory leads to an equivalent system of ordinary differential equations which gives deeper insight into the derivation of integration schemes and into the stabilization approaches the main tool is the drazin inverse a generalized matrix inverse which preserves the eigenvalues the results are illustrated by a realistic truck model finally the approach is extended to the nonlinear index 2 formulation

on controllability conception for stochastic systems the controllability notions for partially observed stochastic systems are defined their relation with complete and approximate controllabilities is shown in particular it is proven that the approximate controllability condition is necessary and the complete controllability condition is sufficient for the partially observed linear gaussian control system to attain the arbitrarily small neighborhood of each point in the state space with probability arbitrarily closely to one

detection performance characteristics for a system with quantizers or ing and accumulator the false alarm and detection probabilities of an n channel system subject to l 1 level quantization or ing and accumulation of m time samples are evaluated exactly with no gaussian assumptions for arbitrary values of n l m and for a quantizer with arbitrary breakpoint locations the channel noises are independent but can have arbitrary statistics the signal occupies one unknown possibly changing channel if present two ffts suffice to sweep out a complete detection probability versus threshold curve the optimum placement of quantizer breakpoints for a fixed total number of levels l 1 is a subtle one and shown to depend on n m and the desired level of performance a simple rule of thumb is presented which yields near optimum capability over the useful range of the operating characteristics

controllability of stochastic linear systems in the paper necessary and sufficient conditions for various types of stochastic controllability of the linear stochastic system of the form d x ax d t bu d t c d w r x 0 x 0 are given some possible extensions are indicated as well

on the stability of volterra runge kutta methods we investigate the stability of extended runge kutta methods for volterra integral equations of the second kind as test equations we choose linear convolution equations with positive definite l 1 kernels our results are strongly connected with the contractivity of runge kutta methods for nonlinear dissipative differential equations

controllability of linear impulsive stochastic systems in hilbert spaces this paper is concerned with the controllability of linear impulsive stochastic systems lisss in hilbert spaces for this class of systems the concepts of null controllability and approximate null controllability are introduced to overcome the difficulties related we construct the adjoint systems and the quasi backward stochastic systems of lisss necessary and sufficient conditions for the null controllability and the approximate null controllability are developed by utilizing our introduced quasi backward stochastic systems furthermore an equivalence is established between the null controllability of lisss and some initial state of quasi backward stochastic systems

ode methods for the solution of differential algebraic systems in this paper we study the numerical solution of the differential algebraic systems f t y y 0 many of these systems can be solved conveniently and economically using a range of ode methods others can be solved only by a small subset of ode methods and still others present insurmountable difficulty for all current ode methods we examine the first two groups of problems and indicate which methods we believe to be best for them then we explore the properties of the third group which cause the methods to fail we describe a reduction technique which allows systems to be reduced to ones that can be solved it also provides a tool for the analytical study of the structure of systems