brief robust h filtering for uncertain impulsive stochastic systems under sampled measurements this paper is concerned with the problem of robust h filtering for uncertain impulsive stochastic systems under sampled measurements the parameter uncertainties are assumed to be time varying norm bounded the aim is to design a stochastically stable filter using the locally sampled measurements which ensures both the robust stochastic stability and a prescribed level of h performance for the filtering error dynamics for all admissible uncertainties a sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given an example is provided to demonstrate the effectiveness of the proposed approach

digital computation of linear canonical transforms we deal with the problem of efficient and accurate digital computation of the samples of the linear canonical transform lct of a function from the samples of the original function two approaches are presented and compared the first is based on decomposition of the lct into chirp multiplication fourier transformation and scaling operations the second is based on decomposition of the lct into a fractional fourier transform followed by scaling and chirp multiplication both algorithms take n log n time where n is the time bandwidth product of the signals the only essential deviation from exactness arises from the approximation of a continuous fourier transform with the discrete fourier transform thus the algorithms compute lcts with a performance similar to that of the fast fourier transform algorithm in computing the fourier transform both in terms of speed and accuracy

discrete time adaptive iterative learning control for high order nonlinear systems with unknown control directions an adaptive iterative learning control method is proposed for a class of nonlinear strict feedback discrete time systems with random initial conditions and iteration varying desired trajectories an n step ahead predictor approach is employed to estimate the future states in the control design discrete nussbaum gain method is utilised to deal with the lack of a priori knowledge of control directions the proposed control algorithm guarantees the boundedness of all the signals in the controlled system the tracking error converges to zero asymptotically along the iterative learning axis except for beginning states affected by random initial conditions the effectiveness of the proposed control scheme is verified through numerical simulation

stability of discrete time delayed impulsive linear systems with application to multi tracking this paper studies the stability issue for discrete time delayed impulsive systems ddis the ddis model is formulated from a discrete time delayed system with impulses by using the matrix spectrum theory the estimates of solution with growth exponent are derived for delayed difference inequalities based on these results two types of criteria on exponential stability with an estimated convergence rate have been established for ddis the first type investigates the effect of destabilising impulses while the second is for the case in which the impulses stabilise the unstable discrete time delayed systems as the application the stability results are used to solve the multi tracking issue for discrete time dynamical networks by mixed impulsive networked control minc in which the impulsive control signals are transmitted via a communication network the effect of data dropout of impulsive control signals is also investigated and the maximal allowable dropout rate is estimated for the designed minc

finite time coordination in multiagent systems using sliding mode control approach abstract finite time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time in this paper we use the notion of finite time stability to apply it to the problem of coordinated motion in multiagent systems specifically we consider a group of agents described by fully actuated euler lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady state distances between the neighboring agents in finite time we use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph laplacian matrix furthermore using sliding mode control approach we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state sliding mode control is known to drive the system states to the sliding surface in finite time the key feature of our approach is in the design of non smooth sliding surfaces such that while on the sliding surface the error states converge to the origin in finite time thus ensuring finite time coordination among the agents in the network in addition we discuss the case of switching communication topologies in multiagent systems finally we show the efficacy of our theoretical results using an example of a multiagent system involving planar double integrator agents

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

on q extended eigenvectors of the integral and finite fourier transforms mehta has shown that eigenvectors of the n n finite fourier transform can be written in terms of the standard hermite eigenfunctions of the quantum harmonic oscillator 1987 j math phys 28 781 here we construct a one parameter family of q extensions of these eigenvectors based on the continuous q hermite polynomials of rogers in the limit when q 1 these q extensions coincide with mehta s eigenvectors and in the continuum limit as n they give rise to q extensions of eigenfunctions of the fourier integral transform

stability of solutions for stochastic impulsive systems via comparison approach this note studies stability problem of solutions for stochastic impulsive systems by employing lyapunov like function method and it s formula comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established based on these comparison principles the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system as the application the stability results are used to design impulsive control for the stabilization of unstable stochastic systems finally one example is given to illustrate the obtained results

continuous global stabilisation of high order time delay nonlinear systems this paper studies the global stabilisation problem for a class of high order nonlinear systems with multiple time delays a distinct property of the systems to be investigated is that powers on the upper bound restrictions of nonlinearities are allowed to take values on a continuous interval by introducing the sign functions and using the generalised method of adding a power integrator this paper successfully designs a continuous global state feedback controller independent of time delays moreover a novel lyapunov krasovskii functional is constructed to prove the globally asymptotic stability of the resulting closed loop system

brief paper state feedback stabilization of linear impulsive systems we address the fundamental problem of state feedback stabilization for a class of linear impulsive systems featuring arbitrarily spaced impulse times and possibly singular state transition matrices specifically we show that a strong reachability property enables a state feedback law to be constructed that yields a uniformly exponentially stable closed loop system the approach adopts a receding horizon strategy involving a weighted reachability gramian in a manner reminiscent of well known results for time varying linear systems for both continuous and discrete time cases

improved stability criteria for a class of neural networks with variable delays and impulsive perturbations this paper further investigates the problem of stability analysis for a kind of neural networks with variable delays and nonlinear impulses with the help of m matrix the homeomorphism theory some effective inequalities and analysis techniques certain novel criteria on the existence uniqueness and exponential stability of the equilibrium point have been established moreover these criteria possess adjustable real parameters which extend and improve many existing results in the literature in the end two numerical examples are provided to illustrate the validation of the theoretical results

euler integration over definable functions we extend the theory of euler integration from the class of constructible functions to that of tame r valued functions definable with respect to an o minimal structure the corresponding integral operator has some unusual defects it is not a linear operator however it has a compelling morse theoretic interpretation in addition it is an advantageous setting in which to integrate in applications to diffused and noisy data in sensor networks

compositional contraction analysis of resetting hybrid systems this note develops sufficient conditions for exponential convergence of resetting hybrid nonlinear dynamical systems using nonlinear contraction theory the analysis first develops a unified formulation of continuous time and discrete time nonlinear dynamics based on a differential transition matrix this yields enhanced dwell time based conditions for stability of such systems analogous to those existing for switched systems it turns out that such dwell time based conditions unlike their counterparts for switched systems include arbitrary stability conditions as a special case and are less conservative and much simpler to verify

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

fractional discrete q fourier transforms the discrete fourier transform dft matrix has a manifold of fractionalizations that depend on the choice of its eigenbases one prominent basis is that of mehta functions here we examine a family of fractionalizations of the dft stemming from q extensions of this basis although closed expressions are given many results of our analysis derive from numerical computation and display thus we suggest that the account of fractional fourier transformations applied on signals as presented by other authors typically of a centred rectangle function may be biased because the support of the function lies in the central part of the domain only the phase and amplitude of the whole fractional dft matrices reveal the location of departures from the continuous kernel of the fractional fourier integral transform whose phase and constant amplitude are well known

jacobi ϑ functions and discrete fourier transforms properties of the jacobi 3 function and its derivatives under discrete fourier transforms are investigated and several interesting results are obtained the role of modulo n equivalence classes in the theory of functions is stressed an important conjecture is studied

the discrete harmonic oscillator harper s equation and the discrete fractional fourier transform certain solutions to harper s equation are discrete analogues of and approximations to the hermite gaussian functions they are the energy eigenfunctions of a discrete algebraic analogue of the harmonic oscillator and they lead to a definition of a discrete fractional fourier transform ft the discrete fractional ft is essentially the time evolution operator of the discrete harmonic oscillator

stability theory of hybrid dynamical systems with time delay by defining the bounded time lag space and other related concepts this note formulates the notion of hybrid dynamical systems with time delay which provides a unified framework for describing a large class of systems and is suitable for qualitative analysis it also investigates stability properties of invariant sets by the method of lyapunov functions and the razumihin techniques criteria on uniform stability and uniform asymptotic stability are established for hybrid dynamical systems with time delay those criteria are then applied to conduct stability analysis for impulsive delay differential systems and nonlinear sampled data feedback control systems with time delay

asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented we consider two possible input nonlinearities that is backlash like hysteresis and symmetric dead zone which can be simultaneously dealt with by using the proposed compensation controllers the knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required only the boundedness of the reference signal is assumed the nussbaum gain approach is employed to remove the assumption on the control gain sign the first scheme is based on the backstepping technique the final step of the recursive design is crucial for the closed loop stability in the second scheme a direct adaptive control law is designed the controller has a simple structure and only one adaptation parameter is updated in both controllers it is shown that asymptotic tracking is ensured two numerical examples are provided to show the effectiveness of the theor

stability analysis of systems with impulse effects the authors establish conditions for the uniform stability and the uniform asymptotic stability of equilibria of systems with impulse effects described by systems of nonlinear time varying ordinary differential equations under mild additional assumptions these sufficient conditions turn out to be necessary as well for the case of time invariant systems with impulse effects described by nonlinear ordinary differential equations the above results are used to establish conditions under which the uniform asymptotic stability of equilibria can be deduced from the linearizations of such systems

adaptive stabilisation for a large class of high order uncertain non linear systems the problem of global adaptive stabilisation by state feedback is investigated for a class of high order non linear systems with uncertain control coefficients and zero dynamics first some appropriate unknown parameters are introduced to obtain the updating laws when adapting control design then by the flexible way of combining adding a power integrator with adaptive technique and the idea of changing supply functions the requirement on the uncertain control coefficients is relaxed and a recursive design procedure is successfully developed to achieve a continuous adaptive stabilising controller finally an example is provided to illustrate the correctness of the theoretical results

an invariance principle for nonlinear hybrid and impulsive dynamical systems in this paper we develop an invariance principle for dynamical systems possessing left continuous flows specifically we show that left continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems as a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems namely state dependent impulsive dynamical systems these results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems

digital computation of the fractional fourier transform an algorithm for efficient and accurate computation of the fractional fourier transform is given for signals with time bandwidth product n the presented algorithm computes the fractional transform in o nlogn time a definition for the discrete fractional fourier transform that emerges from our analysis is also discussed

robust exponential stabilization for large scale uncertain impulsive systems with coupling time delays abstract in this paper we aim to study robust exponential stabilization for a large scale uncertain impulsive system with coupling time delays furthermore we also provide an estimation of the rate of convergence of exponential stabilization by utilizing the lyapunov method and razumikhin technique we shall design the feedback hybrid controllers in terms of linear matrix inequalities under which the robust exponential stability is achieved for a closed loop large scale uncertain impulsive system with coupling time delays moreover we shall also use the results obtained to design impulsive controllers for a large scale uncertain continuous system under which the closed loop continuous system achieves robust and exponential stability to illustrate our results one example is solved

eigenvalues and eigenvectors of the finite fourier transform the eigenvalues and eigenvectors of the n n unitary matrix of finite fourier transform whose j k element is 1 n 1 2 exp 2 i n jk i 1 1 2 is determined in doing so a multitude of identities some of which may be new are encountered a conjecture is advanced

adaptive nonlinear output feedback dynamic surface control with unknown high frequency gain sign in this paper an adaptive dynamic surface control dsc for a class of nonlinear systems with unknown high frequency gain hfg sign is proposed the novelty of our scheme is that we separate the first virtual control signal from the hfg which enables us to estimate the hfg directly as a result the traditional nussbaum function nf approach is abandoned by using the proposed dsc the adaptive laws are needed only at the first design step and the explosion of terms in backstepping control can be eliminated which greatly reduces the computational burden in particular based on an initialisation technique we prove that the performance of the system tracking error can be guaranteed even when the hfg sign is unknown it is shown that all signals of the closed loop system are semi globally uniformly bounded simulation results illustrate that the proposed scheme is more applicable than that of the nf based backstepping control

discrete fractional fourier transform based on orthogonal projections the continuous fractional fourier transform frft performs a spectrum rotation of signal in the time frequency plane and it becomes an important tool for time varying signal analysis a discrete fractional fourier transform has been developed by santhanam and mcclellan see ibid vol 42 p 994 98 1996 but its results do not match those of the corresponding continuous fractional fourier transforms we propose a new discrete fractional fourier transform dfrft the new dfrft has dft hermite eigenvectors and retains the eigenvalue eigenfunction relation as a continous frft to obtain dft hermite eigenvectors two orthogonal projection methods are introduced thus the new dfrft will provide similar transform and rotational properties as those of continuous fractional fourier transforms moreover the relationship between frft and the proposed dfrft has been established in the same way as the conventional dft to continuous fourier transform

the discrete fractional fourier transform we propose and consolidate a definition of the discrete fractional fourier transform that generalizes the discrete fourier transform dft in the same sense that the continuous fractional fourier transform generalizes the continuous ordinary fourier transform this definition is based on a particular set of eigenvectors of the dft matrix which constitutes the discrete counterpart of the set of hermite gaussian functions the definition is exactly unitary index additive and reduces to the dft for unit order the fact that this definition satisfies all the desirable properties expected of the discrete fractional fourier transform supports our confidence that it will be accepted as the definitive definition of this transform

fundamental properties of reset control systems reset controllers are linear controllers that reset some of their states to zero when their input is zero we are interested in their feedback connection with linear plants and in this paper we establish fundamental closed loop properties including stability and asymptotic tracking this paper considers more general reset structures than previously considered allowing for higher order controllers and partial state resetting it gives a testable necessary and sufficient condition for quadratic stability and links it to both uniform bounded input bounded state stability and steady state performance unlike previous related research which includes the study of impulsive differential equations our stability results require no assumptions on the evolution of reset times