exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

observer based adaptive fuzzy decentralized control for stochastic large scale nonlinear systems with unknown dead zones this paper studies the problem of adaptive fuzzy decentralized output feedback control for a class of uncertain stochastic large scale nonlinear systems the considered systems have unknown nonlinear functions unknown dead zones unmodeled dynamics and unmeasurable state variables therefore fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is established to estimate the unmeasurable states based on the backstepping design and the supply changing function technique a robust adaptive fuzzy decentralized output feedback control approach is developed the proposed control approach can ensure the closed loop system to be input state practically stable isps in probability and accommodate the unmodeled dynamics and unknown dead zones as well the effectiveness of the proposed control approach is illustrated by a simulation example

convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled data systems under dwell time constraints stability analysis and control of linear impulsive systems is addressed in a hybrid framework through the use of continuous time time varying discontinuous lyapunov functions necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas extensions to the stability of aperiodic systems under minimum maximum and ranged dwell times are then derived by exploiting further the particular structure of the stability conditions the results are non conservatively extended to quadratic stability analysis of linear uncertain impulsive systems these stability criteria are in turn losslessly extended to stabilization using a particular yet broad enough class of state feedback controllers providing then a convex solution to the open problem of robust dwell time stabilization of impulsive systems using hybrid stability criteria relying finally on the representability of sampled data systems as impulsive systems the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled data systems are straightforwardly solved using the same ideas several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach

decentralized adaptive fuzzy output feedback control of stochastic nonlinear large scale systems with dynamic uncertainties in this paper centralized and decentralized adaptive fuzzy output feedback control schemes are investigated for a class of stochastic nonlinear interconnected large scale systems with dynamic uncertainties and unmeasured states fuzzy systems are used to approximate the unknown nonlinear functions decentralized k filters are designed to estimate the unmeasured states an available dynamic signal is introduced to dominate the unmodeled dynamics by combining dynamic surface control dsc technique with backstepping design the condition in which the approximation errors are assumed to be bounded is avoided using the defined compact set in the stability analysis the unknown smooth interconnections and black box functions are effectively dealt with using it o formula and chebyshev s inequality it is shown that all the signals in the closed loop system are bounded in probability and the error signals are semi globally uniformly ultimately bounded in mean square or the sense of four moment simulation results demonstrate the effectiveness of the proposed approach

globally stable adaptive backstepping fuzzy control for output feedback systems with unknown high frequency gain sign this paper addresses the problem of globally stable adaptive backstepping output feedback tracking control for a class of nonlinear systems with unknown high frequency gain sign the fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal thus the global stability of closed loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions the other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal which is very important for the choice of the centers and widths of membership functions moreover the nussbaum type function is employed to deal with the unknown high frequency gain sign two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper

stabilization of delay systems delay dependent impulsive control the stabilization problem of delay systems is studied under the delay dependent impulsive control the main contributions of this technical note are that for one thing it shows that time delays in impulse term may contribute to the stabilization of delay systems that is a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks for another it shows the robustness of impulsive control that is the designed control strategy admits the existence of some time delays in impulse term which may do harm to the stabilization in this technical note from impulsive control point of view we firstly propose an impulsive delay inequality then we apply it to the delay systems which may be originally unstable and derive some delay dependent impulsive control criteria to ensure the stabilization of the addressed systems the effectiveness of the proposed strategy is evidenced by two illustrative examples

brief paper robust stability and h control of uncertain impulsive systems with time delay this paper investigates the problems of robust stability stabilization and h control for uncertain impulsive systems with time delay the parametric uncertainties are assumed to be time varying and norm bounded three classes of impulsive systems with time delay are considered the systems with stable stabilizable continuous dynamics and unstable unstabilizable discrete dynamics the systems with unstable unstabilizable continuous dynamics and stable stabilizable discrete dynamics and the systems where both the continuous time dynamics and the discrete time dynamics are stable stabilizable for each class of system by using the lyapunov function and razumikhin type techniques sufficient conditions for robust stability stabilization and h control are developed in terms of linear matrix inequalities numerical examples are given which illustrate the applicability of the theoretical results

stability analysis and design of impulsive control systems with time delay a class of impulsive control systems with time varying delays is considered by establishing an impulsive delay differential inequality we analyze the global exponential stability of the impulsive delay systems and estimate the exponential convergence rate on the basis of the analysis a design procedure of impulsive controller is presented the designed impulsive controller not only can globally exponentially stabilize the time delay systems but also can control the exponential convergence rate of the systems two numerical examples are given to illustrate the effectiveness of the method

dwell time based stabilisation of switched linear delay systems using clock dependent lyapunov krasovskii functionals dwell time stability conditions of the switched delay systems are derived using multiple clock dependent lyapunov krasovskii functionals the corresponding conditions are approximated by both using

sampled data h8 state feedback control of systems with state delays in the present paper we adopt the second approach to the nite horizon sampled data state delay h 1 control problem note that in the case of state delays the lifting technique leads to complicated discrete system with in nite dimensional state variable we obtain the piecewise constant state feedback controllers by solving coupled rpdes between sampling and updating the terminal conditions at the sampling instants we derive an asymptotic approximation to the solution of these rpdes by expanding it in the powers of the largest delay the resulting approximation is obtained by solving uncoupled low order partial dia erential equations the performance of the system with the controller that has been obtained using the zero approximation the one that corresponds to zero delay is analysed when the open loop system possesses a non zero delay bounded real lemmas for systems with state delays and jumps are obtained 2 problem formulation

design of a unified adaptive fuzzy observer for uncertain nonlinear systems this paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems more precisely we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high gain or a sliding mode observer by selecting its gain appropriately additionally we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances we also show that the observation error is ultimately bounded using a lyapunov approach without having recourse to the usual strictly positive real spr condition or a suitable observation error filtering the effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature

stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function a more general class of stochastic non linear systems with unmodelled dynamics and uncertain non linear functions are considered in this paper with the concept of isps being extended to stochastic case by combining changing supply function technique with backstepping design technique an adaptive output feedback controller is proposed it is shown that all the solutions of the closed loop system are uniformly bounded in probability and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability a simulation example demonstrates the control scheme

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

delay dependent stability and hybrid l2 l2 gain analysis of linear impulsive time delay systems a continuous timer dependent lyapunov like functional approach abstract this paper presents a new approach for analyzing delay dependent stability and hybrid l 2 l 2 gain performance of linear impulsive delay systems the new approach is inspired by the delay partitioning method the timer dependent lyapunov functional method and the looped functional method in the delay partitioning framework a new type of timer dependent lyapunov functional is constructed which depends on the partition on impulse intervals and also on impulse dynamics different from the previous discontinuous lyapunov functionals the introduced lyapunov functional is continuous along the trajectories of the considered impulsive delay system consequently two different problems of exponential stability and hybrid l 2 l 2 gain performance are tackled by using the same class of lyapunov functionals it is shown that the positive definiteness of this lyapunov functional inside impulse intervals is not necessary for proving exponential stability by use of new integral inequalities based techniques delay dependent criteria for exponential stability and finite hybrid l 2 l 2 gain are established in terms of linear matrix inequalities numerical examples are provided to illustrate the efficiency of the new approach

brief paper output feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable this brief paper investigates the problem of output feedback stabilization for a class of high order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input based on the ideas of the homogeneous systems theory and the adding a power integrator technique an output feedback controller is constructed to ensure that the equilibrium at the origin of the closed loop system is globally asymptotically stable gas in probability the efficiency of the output feedback controller is demonstrated by a simulation example

stability and boldsymbol l_ 1 gain analysis for positive takagi sugeno fuzzy systems with impulse this paper is concerned with the stability analysis and l 1 gain characterization for positive takagi sugeno fuzzy systems subject to impulse effects the main tool utilized is the construction of an impulse time dependent discretized copositive lyapunov function where the impulse interval partitioning idea is exploited to derive less conservative results for the disturbance free case stability criteria are developed to guarantee global exponential stability of the concerned systems under ranged and constant dwell time constraints the analysis of the influence of the discretizing parameter on the reduction of conservativeness is performed we further employ the proposed impulse time dependent discretized copositive lyapunov function to analyze the l 1 gain performance for the case where external disturbances are considered by performing a grid search for a scalar in an interval all the proposed criteria can be checked via linear programming finally numerical simulations are discussed to illustrate the effectiveness of the theoretical results

adaptive fuzzy output feedback control of mimo nonlinear systems with unknown dead zone inputs this paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi input and multi output mimo strict feedback nonlinear systems with both unknown nonsymmetric dead zone inputs and immeasurable states in this research fuzzy logic systems are utilized to evaluate the unknown nonlinear functions and a fuzzy adaptive state observer is established to estimate the unmeasured states based on the information of the bounds of the dead zone slopes as well as treating the time varying inputs coefficients as a system uncertainty a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique it is shown that the proposed control approach can assure that all the signals of the resulting closed loop system are semiglobally uniformly ultimately bounded it is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters simulation examples are also provided to illustrate the effectiveness of the proposed approach

stability and l2 gain analysis for impulsive delay systems an impulse time dependent discretized lyapunov functional method abstract the problems of exponential stability and l 2 gain for a class of time delay systems with impulsive effects are studied the main tool used is the construction of an impulse time dependent complete lyapunov functional by dividing the impulse interval and delay interval into several segments the matrix functions of this functional are chosen to be continuous piecewise linear moreover an impulse time dependent weighting factor is introduced to coordinate the dynamical behavior of the nondelayed and integral terms of this functional along the trajectories of the system by applying this functional delay dependent sufficient conditions for exponential stability and l 2 gain are derived in terms of linear matrix inequalities as by products new delay independent sufficient conditions for the same problems are also derived the efficiency of the proposed results is illustrated by numerical examples

stabilizing transmission intervals for nonlinear delayed networked control systems in this note we consider a nonlinear process with delayed dynamics to be controlled over a communication network in the presence of disturbances and study robustness of the resulting closed loop system with respect to network induced phenomena such as sampled distorted delayed and lossy data as well as scheduling protocols for given plant controller dynamics and communication network properties e g propagation delays and scheduling protocols we quantify the control performance level in terms of mathcal l p gains as the transmission interval varies maximally allowable transfer interval mati labels the greatest transmission interval for which a prespecified mathcal l p gain is attained the proposed methodology combines impulsive delayed system modeling with lyapunov razumikhin techniques to allow for matis that are smaller than the communication delays other salient features of our methodology are the consideration of variable delays corrupted data and employment of model based estimators to prolong matis the present stability results are provided for the class of uniformly globally exponentially stable uges scheduling protocols the well known round robin rr and try once discard tod protocols are examples of uges protocols finally a nonlinear example is provided to demonstrate the benefits of the proposed approach

a performance approach to fuzzy control design for nonlinear systems abstract this paper presents a systematic methodology to the design of a decentralized fuzzy logic controller for large scale nonlinear systems a new method which is based on a performance index of sliding mode control is used to derive fuzzy rules and an adaptive algorithm is used to reduce the chattering phenomenon the simulation results of a two inverted pendulum system and a two link manipulator demonstrate that the attractive features of the proposed approach include a smaller residual error and robustness against nonlinear interactions

uniform asymptotic stability of impulsive delay differential equations abstract in this paper criteria on uniform asymptotic stability are established for impulsive delay differential equations using lyapunov functions and razumikhin techniques it is shown that impulses do contribute to yield stability properties even when the underlying system does not enjoy any stability behavior some examples are also discussed to illustrate the theorems

stable adaptive fuzzy sliding mode control of interconnected systems the problem of stable adaptive fuzzy control for a class of interconnected systems with unknown control gains is studied in this paper by using fuzzy modeling method a design scheme of an adaptive fuzzy controller is proposed the design is capable of incorporating linguistic and numerical information into controllers by theoretical analysis the closed loop adaptive fuzzy control system is proved to be globally stable in the sense that all signals involved are bounded with tracking errors converging to a neighborhood of zero

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network

a novel control design on discrete time takagi sugeno fuzzy systems with time varying delays this paper focuses on analyzing a new model transformation of discrete time takagi sugeno t s fuzzy systems with time varying delays and applying it to dynamic output feedback dof controller design a new comparison model is proposed by employing a new approximation for time varying delay state and then a delay partitioning method is used to analyze the scaled small gain of this comparison model a sufficient condition on discrete time t s fuzzy systems with time varying delays which guarantees the corresponding closed loop system to be asymptotically stable and has an induced l2 disturbance attenuation performance is derived by employing the scaled small gain theorem then the solvability condition for the induced l2 dof control is also established by which the dof controller can be solved as linear matrix inequality optimization problems finally examples are provided to illustrate the effectiveness of the proposed approaches

actions of taft s algebras on finite dimensional algebras abstract let f be a field containing a primitive m th root of the unit we characterize the actions of a taft s algebra h m of a certain order m on finite dimensional arbitrary algebras we describe the action in terms of gradings and actions by skew derivations moreover we prove the associative algebra u t 2 of 2 2 upper triangular matrices with entries from f does not generate a variety of h m module algebras of almost polynomial growth

robust control on saturated markov jump systems with missing information in this paper a robust h controller is designed for saturated markov jump systems with uncertainties and time varying transition probabilities the time varying transition probability uncertainty is described as a polytope set stochastic stability is analyzed for the underlying systems by lyapunov function approach and a sufficient condition is derived to design controllers such that the resulting closed loop system is stochastically stable and a prescribed h performance is also achieved furthermore the attraction domain of this markov jump system is estimated and evaluated a simulation example is given to show the effectiveness of the developed techniques

exponential stability of linear delay impulsive differential equations for an impulsive delay differential equation with bounded delay and bounded coefficients the following result is established if each solution is bounded on 0 together with its derivative for each bounded right hand side then the equation is exponentially stable an explicit stability theorem is presented

decentralized adaptive output feedback controller design for stochastic nonlinear interconnected systems in this paper the controller design for a class of stochastic interconnected systems with both parametric uncertainties and unknown nonlinear interactions is presented the diffusion terms considered are dependent on the outputs of local subsystems and allowed to be unbounded first by employing decentralized state observers totally decentralized adaptive tracking controllers with suitable parameter adaptive laws are designed to ensure the boundedness in probability of all the signals in the closed loop system it is shown that the tracking errors converge to small residual sets around the origin then for systems with relaxed diffusion vector fields a decentralized adaptive stabilizing scheme is proposed to ensure the boundedness in probability of all signals in the closed loop system

lyapunov based sufficient conditions for stability of hybrid systems with memory hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena in this note we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions these generalized solutions motivated by studying robustness and well posedness of such systems are defined on hybrid time domains and parameterized by both continuous and discrete time we establish lyapunov based sufficient conditions for asymptotic stability using both lyapunov razumikhin functions and lyapunov krasovskii functionals examples are provided to illustrate these conditions

fuzzy adaptive observer backstepping control for mimo nonlinear systems in this paper a fuzzy adaptive backstepping output feedback control approach is developed for a class of multi input and multi output mimo nonlinear systems with unmeasured states using fuzzy logic systems to approximate the unknown nonlinear functions a fuzzy adaptive observer is designed for state estimation as well as system identification combining with the backstepping design techniques a fuzzy adaptive output feedback control is constructed recursively it is proved that the proposed fuzzy adaptive control approach can guarantee the semi global uniform ultimate boundedness for all the signals and the tracking error to a small neighborhood of the origin simulation studies illustrate the effectiveness of the proposed approach

brief paper exponential stability of nonlinear time delay systems with delayed impulse effects the problem of exponential stability for nonlinear time delay systems with delayed impulses is addressed in this paper lyapunov based sufficient conditions for exponential stability are derived respectively for two kinds of delayed impulses i e destabilizing delayed impulses and stabilizing delayed impulses it is shown that if a nonlinear impulsive time delay system without impulse input delays is exponentially stable then under some conditions its stability is robust with respect to small impulse input delays moreover it is also shown that for a stable nonlinear impulsive time delay system if the magnitude of the delayed impulses is sufficiently small then under some conditions the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays the efficiency of the proposed results is illustrated by three numerical examples

constructive necessary and sufficient condition for the stability of quasi periodic linear impulsive systems the technical note provides a computation oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems whose impulsions are assumed to occur quasi periodically based on the set theoretic conditions for robust stability of uncertain linear systems the existence of polyhedral lyapunov functions is proved to be necessary and sufficient for global exponential stability of quasi periodic linear impulsive systems a constructive method is developed for testing the stability of the system and for computing set induced polyhedral lyapunov functions the method leads to an algorithm whose complexity is similar to the standard algorithm related to discrete time parametric uncertain systems with the state matrix belonging to a convex polytopic set

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