stabilization of neural network based control systems via event triggered control with nonperiodic sampled data this paper focuses on a problem of event triggered stabilization for a class of nonuniformly sampled neural network based control systems nnbcss first a new event triggered data transmission mechanism is designed based on the nonperiodic sampled data different from the previous works the proposed triggering scheme enables the nnbcss design to enjoy the advantages of both nonuniform and event triggered sampling schemes second under the nonperiodic event triggered data transmission scheme the nonperiodic sampled data three layer fully connected feedforward neural network tlfcffnn based event triggered controller is constructed and the resulting closed loop tlfcffnn based event triggered control system is modeled as a state delay system based on time delay system modeling approach then the stability criteria for the closed loop system is formulated using lyapunov krasovskii functional approach third the sufficient conditions for the codesign of the tlfcffnn based controller and triggering parameters are given in terms of solvability of matrix inequalities to guarantee the asymptotical stability of the closed loop system and an upper bound on the given cost function while reducing the updates of the controller finally three numerical examples are provided to illustrate the effectiveness and benefits of the proposed results

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

a convex programming approach to h2 control of discrete time markovian jump linear systems in this paper we consider the h control problem for the class of discrete time 2 linear systems with parameters subject to markovian jumps using a convex programming approach we generalize the definition of the h norm from the deter2 ministic case to the markovian jump case and set a link between this norm and the observability and controllability gramians conditions for existence and derivation of a mean square stabilizing controller for a markovian jump linear system using convex analysis are established the main contribution of the paper is to provide a convex programming formulation to the h control problem so that several 2 important cases to our knowledge not analysed in previous work can be addressed regarding the transition matrix p for the markov chain two ij situations are considered the case in which it is exactly known and the case in which it is not exactly known but belongs to an appropriated convex set regarding the state variable and the jump variable the cases in which t

event driven multi consensus of multi agent networks with repulsive links due to diversification in environment a network of agents may have several emergent behaviors this paper introduces an event driven paradigm for realizing multi consensus which as a generic version of group cluster consensus depends both on the initial underlying topology and initial states for the network feature we resort to a distributed event driven paradigm since event driven control has advantages on communication reduction and control energy saving moreover to relax assumption on network topology repulsive links are exploited at event instants to facilitate multiple coordination to realize multi consensus we design a distributed event driven controller based on coupled intra subgroup and extra subgroup information in this context with different control strengths the finial value of man would be varying this phenomenon matches the principle of multi consensus in the current study based on lasalle s invariance principle we prove that under the proposed event driven configuration the joint cooperation and competition contributes to multi consensus provided that the sampling period is no larger than a positive threshold it is shown there is no further requirement on network topologies in pursuit of multiple coordination this paper studies multiple coordination of multi agent networks under an event driven paradigm for an undirected connected graph a node clustering scheme is first adopted to ensure a relatively strong degree of connectivity within each potential subgroup and some repulsive effect is used to deal with the extra subgroup links to reduce unnecessary communication a distributed event driven controller is designed via coupled intra subgroup and extra subgroup information based on the lasalle s invariance principle it is shown that under the proposed event driven control configuration multi agent networks can realize multi consensus without any balanced requirement on the underlying topologies simulation work is presented to validate the theoretical results

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

a new necessary and sufficient condition for static output feedback stabilizability and comments on stabilization via static output feedback in this paper a counterexample of the above mentioned paper by trofino neto et al ibid vol 38 1993 is reported it is pointed out that one of the conditions for a linear system to be stabilizable via static output feedback is not correct a modified necessary and sufficient condition for this problem is also presented

event triggered consensus control for discrete time stochastic multi agent systems this paper is concerned with the event triggered consensus control problem for a class of discrete time stochastic multi agent systems with state dependent noises a novel definition of consensus in probability is proposed to better describe the dynamics of the consensus process of the addressed stochastic multi agent systems the measurement output available for the controller is not only from the individual agent but also from its neighboring ones according to the given topology an event triggered mechanism is adopted with hope to reduce the communication burden where the control input on each agent is updated only when a certain triggering condition is violated the purpose of the problem under consideration is to design both the output feedback controller and the threshold of the triggering condition such that the closed loop system achieves the desired consensus in probability first of all a theoretical framework is established for analyzing the so called input to state stability in probability issip for general discrete time nonlinear stochastic systems within such a theoretical framework some sufficient conditions on event triggered control protocol are derived under which the consensus in probability is reached furthermore both the controller parameter and the triggering threshold are obtained in terms of the solution to certain matrix inequalities involving the topology information and the desired consensus probability finally a simulation example is utilized to illustrate the usefulness of the proposed control protocol

the rotation number in one dimensional maps definition and applications a rotation number in the case of one dimensional maps is introduced as is shown this rotation number is equivalent to the already known rotation number in the case of two dimensional maps the definition of the rotation number is given in two steps first it is defined for periodic orbits inside a window of organized motion wom we show that in this case our definition coincides with the definition of the over rotation number then our definition is further generalized for chaotic orbits outside the woms thus we obtain a unified definition of the rotation number for the whole area of the chaotic zone of the bifurcation diagram having a number of useful applications namely it can be used as a tool to distinguish whether an orbit is contained within a wom or not as a tool of numerical location of the bifurcation points of the band mergings as well as of the boundary points of a wom finally a method of numerical calculation of the percentage of the cumulative width of the woms in every particular segment chaotic band of the chaotic zone is given

periodically time varying memory static output feedback control design for discrete time lti systems this paper addresses the problem of static output feedback sof stabilization for discrete time lti systems we approach this problem using the recently developed periodically time varying memory state feedback controller ptvmsfc design scheme a bilinear matrix inequality bmi condition which uses a pre designed ptvmsfc is developed to design the periodically time varying memory sof controller ptvmsofc the bmi condition can be solved by using bmi solvers alternatively we can apply two steps and iterative linear matrix inequality algorithms that alternate between the ptvmsfc and ptvmsofc designs finally an example is given to illustrate the proposed methods

asynchronous h filtering for 2d discrete markovian jump systems with sensor failure this paper investigates the problem of the asynchronous h filtering for a class of two dimensional 2d markovian jump systems with sensor failure the asynchronous phenomenon is considered to be random mismatch between system modes and candidate filters the mismatch behavior is assumed to be stochastic with a certain probability and a new markov chain is proposed to model the jumping process of the filtering error system besides a switching method is proposed to dealing with the sensor failure sufficient conditions for the existence of a desired filter such that the filtering error system is stochastically stable with a guaranteed h performance index are obtained in the form of linear matrix inequalities lmis two examples are provided to illustrate the effectiveness and advantage of the proposed method

event based state estimation of linear dynamic systems with unknown exogenous inputs in this work an event based optimal state estimation problem for linear time varying systems with unknown inputs is investigated by treating the unknown input as a process with a non informative prior the event based minimum mean square error mmse estimator is obtained in a recursive form it is shown that for the general time varying case the closed loop matrix of the optimal event based estimator is exponentially stable and the estimation error covariance matrix is asymptotically bounded for each sample path of the event triggering process the results are also extended to the multiple sensor scenario where each sensor is allowed to have its own event triggering condition the efficiency of the proposed results is illustrated by a numerical example and comparative simulation with the mmse estimators obtained based on time triggered measurements the results are potentially applicable to event based secure state estimation of cyber physical systems

h control for markovian jump systems with partially unknown transition rates via an adaptive method abstract this paper investigates the problem of the h control for a class of continuous time markovian jump systems with partially unknown transition rates an adaptive h performance index is defined to describe the disturbance attenuation performance of markovian jump systems by combining the linear matrix inequality lmi approach for designing h controllers and the adaptive method for estimating the unknown terms a new method for designing the h controllers is proposed where an estimation of the transition rate matrix is given and the controller parameter matrices are dependent on the known transition rates and the estimations of the unknown terms the sufficient conditions for the existence of the adaptive state feedback controller and the adaptive dynamic output feedback controller are proposed and the estimations of the unknown transition rates are obtained from the adaptive laws it is shown that the proposed adaptive controllers provide better performance than the traditional fixed gain controllers a practical example is provided to illustrate the effectiveness and advantage of the proposed method

h sub spl infin state feedback control for discrete singular systems deals with the problem of state feedback h sub spl infin control for discrete singular systems it is not assumed that the singular system under consideration is necessarily regular the problem we address is the design of a state feedback controller such that the resulting closed loop system is not only regular causal and stable but also satisfies a prescribed h sub spl infin norm bound condition in terms of certain matrix inequalities a necessary and sufficient condition for the solution to this problem is obtained and a suitable state feedback control law is also given

optimization of static output feedback using substitutive lmi formulation this note proposes a new design tool for optimizing static output feedback using a linear matrix inequality lmi formula called substitutive lmi a matrix inequality derived from static output feedback is not usually linear adding a positive definite term including auxiliary variables the matrix inequality is transformed into an lmi with respect to the positive definite matrix and the static output feedback gain an iterative calculation algorithm is given to solve the substitutive lmi in this note designs of the static output feedback gain are shown in the frame of h sub spl infin and h sub 2 syntheses a numerical example is shown to demonstrate the effectiveness of the proposed technique

a constructive method to static output stabilisation of markov jump systems this paper is concerned with the static output feedback stabilisation of markov jump systems transition probabilities are assumed to be incomplete namely they may be known uncertain with known lower and upper bounds and unknown to linearise the nonlinearities induced by unknown transition probabilities a linearisation is developed to solve the static output feedback problem by means of linear matrix inequalities a constructive method is proposed to separate the controller gain matrices from lyapunov variables based on the linearisation and the separation sufficient conditions are established to guarantee that the closed loop system is stochastically stable by the designed static output feedback controller the obtained results are further extended to deal with norm bounded or polytopic uncertainties on system matrices numerical examples are given to demonstrate the effectiveness of the proposed method

self triggered consensus for multi agent systems with zeno free triggers in this technical note a self triggered consensus algorithm for multi agent systems has been proposed each agent receives the state information of its neighbors and computes the average state of its neighborhood based on this average state the event trigger is designed to determine when the agent updates its control input and transmits the average state to its neighbors by specifying a strictly positive minimal inter event time for each agent zeno behavior can be avoided then by solving quadratic equations related to the event condition the self triggered consensus algorithm is developed by directly computing the event time instants with a set of iterative procedures it has been proved that with the proposed zeno free algorithm the agent group can achieve consensus asymptotically compared with the existing works the proposed algorithm is simpler in formulation and computation moreover it has been showed that agents need less time to achieve consensus with considerable reduction of the number of triggering events controller updates and information transmission as a result more energy can be saved using the proposed algorithm in practical multi agent systems

static output feedback control of markov jump linear systems without mode observation in this paper we address infinite horizon optimal control of markov jump linear systems mjls via static output feedback because the jump parameter is assumed not to be observed the optimal control law is nonlinear and intractable therefore we assume the regulator to be linear under this assumption we first present sufficient feasibility conditions for static output feedback stabilization of mjls with nonobserved mode in the mean square sense in terms of linear matrix inequalities lmis however these conditions depend on the particular state space representation i e a coordinate transform can make the lmis feasible while the original lmis are infeasible to avoid the issues with the ambiguity of the state space representation we therefore present an iterative algorithm for the computation of the regulator gain the algorithm is shown to converge if the mjls is stabilizable via mode independent static output feedback however convergence of the algorithm is not sufficient for the stability of the closed loop which requires an additional stability check after the regulator gains have been computed a numerical example demonstrates the application of the presented results

new approach to mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems this paper revisits the problem of mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems differing from previous results in the quadratic framework the filter design makes full use of the parameter dependent stability idea not only is the filter dependent of the parameters which are assumed to reside in a polytope and be measurable online but in addition the lyapunov matrices are different for the entire polytope domain as well as for different channels with respect to the mixed performances these ideas are realized by introducing additional slack variables to the well established performance conditions and by employing new bounding techniques which results in a much less conservative filter design method a numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method

robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties this paper studies the static output feedback sof control problem of continuous time linear systems with polytopic uncertainties novel lmi conditions with a line search over a scalar variable for designing robust sof controllers are proposed where the uncertain output matrix of the considered system is allowed to be not of full row rank in particular it is shown that the new method can give less or at least the same conservative results than those methods by inserting a matrix equality constraint between system output matrix and lyapunov matrix furthermore the result is extended to the case of h control numerical examples are given to illustrate the effectiveness of the proposed method

quantized saturated control for sampled data systems under noisy sampling intervals a confluent vandermonde matrix approach in this paper a unified framework is established to investigate both the quantized and the saturated control problems for a class of sampled data systems under noisy sampling intervals a random variable obeying the erlang distribution is used to describe the noisy sampling intervals in virtue of the matrix exponential the sampled data control system is transformed into an equivalent discrete time stochastic system and the aim of this paper is to design a quantized saturated sampled data controller such that the resulting discrete time stochastic system is stochastically stable when the sampling error follows the erlang distribution in order to deal with the case of multiple control inputs a confluent vandermonde matrix approach is proposed in the design process by using the kronecker product operation and the matrix inequality techniques the desired quantized saturated controller gains are designed in terms of the solution to certain matrix inequalities finally a simulation example is exploited to verify the effectiveness of the proposed design approach

stability and stabilization of a class of stochastic switching systems with lower bound of sojourn time abstract this paper is concerned with the stability and stabilization issues for a family of discrete time stochastic switching systems with bounded sojourn time the stochastic switching systems are modeled by semi markov jump linear systems and the semi markov kernel approach is employed to handle the stability and stabilization problems the sojourn time of each system mode is considered to have both upper and lower bounds which is more general than the scenarios in previous literature that only consider the upper bound of sojourn time the concept of error mean square stability is put forward in a new form by taking into account the lower bounds of sojourn time for all system modes by virtue of a lyapunov function that not only depends on the current system mode but also on the elapsed time the system has been in the current mode together with certain techniques eliminating powers of matrices numerically testable stability and stabilization criteria in the sense of the proposed error mean square stability are obtained for the closed loop stochastic switching system finally a numerical example and a practical example of a dc motor are utilized to demonstrate the effectiveness of the proposed control strategy and the superiority of allowing for the lower bound of sojourn time

robust stability and stabilization of uncertain discrete time markovian jump linear systems this note deals with robust stability and control of uncertain discrete time linear systems with markovian jumping parameters systems with polytopic type parameter uncertainty in either the state space model matrices or in the transition probability matrix of the markov process are considered this note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty the design of both mode dependent and mode independent control laws is addressed the proposed methods are given in terms of linear matrix inequalities numerical examples are provided to demonstrate the effectiveness of the derived results

the dual iteration for fixed order control this paper proposes a new heuristic algorithm for fixed order control problems using linear matrix inequalities the authors call the algorithm the dual iteration because it is based on the iteration of two design steps state feedback and filtering which are dual to each other extensive numerical experiments show that the algorithm has a decent performance

finite time h control for t s fuzzy descriptor semi markov jump systems via static output feedback abstract this paper is concerned with the finite time static output feedback h controller design problem for a type of nonlinear continuous time descriptor semi markov jump systems s mjss via takagi sugeno t s fuzzy model where the transition rates are time varying and dependent on sojourn time firstly based on the stochastic lyapunov functional sufficient conditions on singular stochastic h finite time boundedness ss h ftb for continuous time t s fuzzy descriptor s mjss are given then in order to design the static output feedback controller easily the closed loop system is represented in an augmented form furthermore based on the lower and upper bounds of the time varying transition rates and by using the matrix inequality decoupling technique a novel linear matrix inequality lmi condition on ss h ftb of closed loop system is presented meanwhile the static output feedback controller is developed in terms of lmis the proposed design method doesn t impose any constraints on system matrices or slack variables which shows less conservative results lastly numerical examples are given to demonstrate the effectiveness of the obtained methods

output feedback negative imaginary synthesis under structural constraints the negative imaginary property is a property that many practical systems exhibit this paper is concerned with the negative imaginary synthesis problem for linear time invariant systems by output feedback control sufficient conditions are developed for the design of static output feedback controllers dynamic output feedback controllers and observer based feedback controllers based on the design conditions a numerical algorithm is suggested to find the desired controllers structural constraints can be imposed on the controllers to reflect the practical system constraints also the separation principle is shown to be valid for the observer based design finally three numerical examples are presented to illustrate the efficiency of the developed theory

on set valued kalman filtering and its application to event based state estimation motivated by challenges in state estimation with event based measurement updates the properties of the exact and approximate set valued kalman filters with multiple sensor measurements for linear time invariant systems are investigated in this work first we show that the exact and the proposed approximate set valued filters are independent of the fusion sequence at each time instant second the boundedness of the size of the set of estimation means is proved for the exact set valued filter for the approximate set valued filter if the closed loop matrix is contractive then the set of estimation means has a bounded size asymptotically otherwise a nonsingular linear transform is constructed such that the size of the set of estimation means for the transformed states is asymptotically bounded third the effect of set valued measurements on the size of the set of estimation means is analyzed and conditions for performance improvement in terms of smaller size of the set of estimation means are proposed finally the results are applied to event based estimation which allow the event triggering conditions to be designed by considering requirements on performance and communication rates the efficiency of the proposed results are illustrated by simulation examples and comparison with the approximate event based mmse estimator and the kalman filter with intermittent observations

h and h 2 filtering for linear systems with uncertain markov transitions this paper is concerned with h and h 2 filtering for markovian jump linear systems with uncertain transition probabilities motivated by the fact that the existing results either impose severe restrictions on some key matrices or introduce some unnecessary matrix variables this paper is focused on developing a new approach to systematically relax these restrictions for filter design by applying a novel technique to eliminate the product terms between the lyapunov matrices and the filter parameters an improved condition is first obtained for analyzing the h performance of the filtering error system then sufficient conditions in terms of linear matrix inequalities are presented for designing filters with a guaranteed h filtering performance level the proposed method is further extended to h 2 filtering theoretical analyses followed by a few numerical examples show that the proposed filter design method outperforms some existing results with respect to reduction of conservatism or variables needed for computation the filter design problems for both continuous time and discrete time markovian jump linear systems are addressed in a unified framework

distributed event triggered coordination for average consensus on weight balanced digraphs this paper proposes a novel distributed event triggered algorithmic solution to the multi agent average consensus problem for networks whose communication topology is described by weight balanced strongly connected digraphs the proposed event triggered communication and control strategy does not rely on individual agents having continuous or periodic access to information about the state of their neighbors in addition it does not require the agents to have a priori knowledge of any global parameter to execute the algorithm we show that under the proposed law events cannot be triggered an infinite number of times in any finite period i e no zeno behavior and that the resulting network executions provably converge to the average of the initial agents states exponentially fast we also provide weaker conditions on connectivity under which convergence is guaranteed when the communication topology is switching finally we also propose and analyze a periodic implementation of our algorithm where the relevant triggering functions do not need to be evaluated continuously simulations illustrate our results and provide comparisons with other existing algorithms

dynamic output feedback control of discrete time markov jump linear systems through linear matrix inequalities this paper addresses the cal h 2 and cal h infty dynamic output feedback control design problems of discrete time markov jump linear systems under the mode dependent assumption which means that the markov parameters are available for feedback the main contribution is the complete characterization of all full order proper markov jump linear controllers such that the cal h 2 or cal h infty norm of the closed loop system remains bounded by a given prespecified level yielding the global solution to the corresponding mode dependent optimal control design problem expressed in terms of pure linear matrix inequalities some academic examples are solved for illustration and comparison as a more consequent practical application the networked control of a vehicle platoon using measurement signals transmitted in a markov channel as initially proposed in p seiler and r sengupta ieee trans automat control 50 2005 pp 356 364 is considered

second order consensus in time delayed networks based on periodic edge event driven control abstract the second order consensus problems in multi agent systems with undirected topologies and time invariant delays are considered in this paper the time delay robustness of a consensus protocol based on periodic edge event driven control is investigated and the studied protocol can largely reduce the communication and controller updating costs the relationship between time delays and event detecting period is characterized by lyapunov methods it is shown that the protocol can solve state consensus problems when the interaction topology is connected and the system does not exhibit zeno behavior finally simulations are given to demonstrate the effectiveness of our theoretical results

cluster synchronization of complex networks via event triggered strategy under stochastic sampling abstract this paper is concerned with the issue of mean square cluster synchronization of non identical nodes connected by a directed network suppose that the nodes possess nonlinear dynamics and split into several clusters then an event triggered control scheme is proposed for synchronization based on the information from stochastic sampling meanwhile an equilibrium is considered to be the synchronization state or the virtual leader for each cluster which can apply pinning control to the following nodes assume that a spanning tree exists in the subgraph consisting of the nodes belonging to the same cluster and the corresponding virtual leader and the instants for updating controllers are determined by the given event triggered strategy then some sufficient conditions for cluster synchronization are presented according to the lyapunov stability theory and linear matrix inequality technique finally a specific numerical example is shown to demonstrate the effectiveness of the theoretical results

lebesgue approximation model of continuous time nonlinear dynamic systems traditional model based approaches are based on periodic iterations where the continuous time model is discretized with a fixed period despite the easiness in analysis and design such periodic approximation model may be undesirable from the computation efficiency point of view this paper presents the lebesgue approximation model lam of continuous time nonlinear systems where the iteration is activated on an as needed basis but not periodically we show that the proposed lam behaves exactly the same as a specific event triggered feedback system through which the properties of the lam can be studied we provide a sufficient condition to ensure asymptotic stability of the lam and derive theoretical bounds on the difference between the states of the lam and the original continuous time system the lam is then integrated in the particle filtering approach for fault prognosis simulation results show that the lam can dramatically reduce the number of iterations in prognosis without sacrificing accuracy and precision

a bounded real lemma for jump systems this note presents a bounded real lemma for discrete time markovian jump linear systems mjlss we show that the linear matrix inequality in the bounded real lemma is both necessary and sufficient for this class of systems for the case of one plant mode this condition reduces to the standard necessary and sufficient condition for discrete time systems we envision this lemma being used to construct necessary and sufficient analysis and synthesis conditions for mjlss

brief paper a controller design based on a functional h filter for descriptor systems the time and frequency domain cases in this paper we investigate the time and frequency domain designs of a controller based on a functional filter for both continuous time and discrete time multivariable descriptor systems the order of this controller is equal to the dimension of the state to be estimated and the control gain is designed using h techniques the time procedure is based on the unbiasedness of the estimation error using a sylvester equation then a new method for avoiding the derivative of the disturbance vector in the observation error dynamics is proposed this problem is solved by means of linear matrix inequalities lmis the frequency domain procedure design is derived from time domain results where we propose some suitable matrix fraction descriptions mfds and most importantly the factorization approach permits us to give a polynomial parameterization of the functional h filter based controller

brief paper parameterization of all stabilizing h static state feedback gains application to output feedback design this paper presents a simplified parameterization of all h static state feedback controllers in terms of a single algebraic riccati equation and a free parameter matrix as a special case necessary and sufficient conditions for the existence of an static output feedback gain are given an efficient computational algorithm is given and its correctness proven no initial stabilizing output feedback gain is needed the technique is used to design an h lateral directional command augmentation system for the f 16 aircraft

duality in vector pade hermite approximation problems abstract the article defines a class of dual vector pade hermite problems it describes dual basis matrices for the solution spaces of such problems and proves their properties we show how degree restrictions can be imposed on vector pade hermite problems and what the effect is on the dual basis matrices we also show that the classical duality between pade hermite problems of type i and type ii is a special case of vector pade hermite duality this is proved without the classical restrictive assumption of normality the article proposes an algorithm that solves two dual vector pade hermite problems at the same time returning dual basis matrices of the respective solution spaces

generalised nonlinear l 2 l filtering of discrete time markov jump descriptor systems this paper is devoted to the l2 l filter design problem for nonlinear discrete time markov jump descriptor systems subject to partially unknown transition probabilities the partially unknown transition probabilities are modelled via the polytopic uncertainties the objective is to propose a generalised nonlinear full order filter design method such that the resulting filtering error system is regular casual and stochastically stable and a prescribed l2 l attenuation level is satisfied for the autonomous discrete time descriptor system subject to lipschitz nonlinear condition by introducing some slack matrix variables a mode dependent stability criterion is established it cannot only ensure the regularity casuality and stochastic stability of system but also guarantee the considered system has a unique solution based on this obtained criterion a sufficient condition in terms of linear matrix inequalities lmis is derived such that the resulting filtering error system is regular casual s

event detection and control co design of sampled data systems this paper proposes event detector and controller co design criteria for sampled data systems in which static or dynamic output feedback controllers are used the resulting criteria provide sufficient conditions to ensure the asymptotic stability of the closed loop system with reduced communication rates among sensors controllers and actuators the transmissions are mediated by event detectors at both sensor and controller nodes for static output feedback control the sufficient condition is given in terms of the feasibility of bilinear matrix inequalities bmis the bmi feasibility problem is converted into a nonlinear optimisation problem involving linear matrix inequalities lmis which is solved via the complementarity linearisation algorithm for dynamic output feedback control the sufficient condition is formulated into an lmi feasibility problem which is readily solved with existing tools numerical examples are included to show the effectiveness of the proposed methods

uniform stabilization of discrete time switched and markovian jump linear systems the uniform stability of discrete time switched linear systems possibly with a strongly connected switching path constraint and the existence of finite path dependent dynamic output feedback controllers uniformly stabilizing such a system are both shown to be characterized by the existence of a finite dimensional feasible system of linear matrix inequalities this characterization is based on the observation that a linear time varying system is uniformly stable only if there exists a finite path dependent quadratic lyapunov function the synthesis of a uniformly stabilizing controller is done without conservatism by solving any feasible system of linear matrix inequalities among an increasing family of systems of linear matrix inequalities the result carries over to the almost sure uniform stabilization of markovian jump linear systems

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

integral based event triggering controller design for stochastic lti systems via convex optimisation abstractthe presence of measurement noise in the event based systems can lower system efficiency both in terms of data exchange rate and performance in this paper an integral based event triggering control system is proposed for lti systems with stochastic measurement noise we show that the new mechanism is robust against noise and effectively reduces the flow of communication between plant and controller and also improves output performance using a lyapunov approach stability in the mean square sense is proved a simulated example illustrates the properties of our approach

passivity as a design tool for group coordination we pursue a group coordination problem where the objective is to steer the differences between output variables of the group members to a prescribed compact set to stabilize this set we study a class of feedback rules that are implementable with local information available to each member when the information flow between neighboring members is bidirectional we show that the closed loop system exhibits a special interconnection structure which inherits the passivity properties of its components by exploiting this structure we develop a passivity based design framework which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature the passivity approach offers additional design flexibility compared to these special cases and systematically constructs a lurie type lyapunov function for the closed loop system we further study the robustness of these feedback laws in the presence of a time varying communication topology and present a persistency of excitation condition which allows the interconnection graph to lose connectivity pointwise in time as long as it is established in an integral sense

distributed event triggered cooperative attitude control of multiple groups of rigid bodies on manifold so 3 in this note the distributed event triggered cooperative attitude control of multiple groups of rigid bodies evolved on nonlinear manifold so 3 is investigated the distributed event triggered mechanism is introduced into the controller design to reduce the communication pressure it is verified that the orientations of rigid bodies in each group converge to a common value with zero angular velocities and these common values in all groups achieve an anti consensus configuration under the proposed intra and inter group cooperative control law simulation results show the effectiveness of the proposed method

h sub spl infin compensator design with minimal order observers a method based on a bounded real lemma is presented in the form of sufficient conditions for designing observer based proper reduced order h sub spl infin compensators the proposed compensators are shown to include the strictly proper full order central h sub spl infin compensators as a special class a compensator design algorithm is included to illustrate the use of the proposed compensator design equations

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

robust and non fragile finite time h control for uncertain markovian jump nonlinear systems this paper investigates the non fragile and robust finite time h control problem for a class of uncertain markovian jump nonlinear systems with bounded parametric uncertainties and norm bounded disturbance by employing stochastic analysis and linear matrix inequality techniques sufficient criteria of stochastic finite time boundedness and stochastic h finite time boundedness are first provided for the class of stochastic jump systems then a controller is designed such that the class of stochastic nonlinear dynamics are stochastically finite time bounded and have an h attention performance level by utilizing matrix decomposition approach furthermore the analysis and design of non fragile and robust finite time controller are provided to guarantee that the class of uncertain stochastic systems are stochastically finite time boundeded with a prescribed attention index by using non fragile control technique in addition we also deal with the analysis and design of stochastic finite time stability and stochastic finite time stabilization all criterions can be characterized in terms of linear matrix inequalities finally two examples are also given to illustrate the effectiveness of obtained results

event based agreement protocols for multi agent networks abstract this paper considers an average consensus problem for multiple integrators over fixed or switching undirected and connected network topologies event based control is used on each agent to drive the state to their initial average eventually an event triggering scheme is designed based on a quadratic lyapunov function the derivative of the lyapunov function is made negative by an appropriate choice of the event condition for each agent the event condition is sampled data and distributed in the sense that the event detector uses only neighbor information and local computation at discrete sampling instants the event based protocol design is illustrated with simulations

optimal sampling and performance comparison of periodic and event based impulse control in this technical note several issues of periodic and event based impulse control for a class of second order stochastic systems are considered including the optimal sampling and performance comparison the procedures are provided to design the optimal sampling period for periodic sampling and optimal threshold for event based sampling it is demonstrated that event based impulse control outperforms periodic impulse control in terms of mean square state variations while both having the same average control rate

a newton like method for solving rank constrained linear matrix inequalities this paper presents a newton like algorithm for solving systems of rank constrained linear matrix inequalities though local quadratic convergence of the algorithm is not a priori guaranteed or observed in all cases numerical experiments including application to an output feedback stabilization problem show the effectiveness of the algorithm

stability of kalman filtering with markovian packet losses we consider kalman filtering in a network with packet losses and use a two state markov chain to describe the normal operating condition of packet delivery and transmission failure based on the sojourn time of each visit to the failure or successful packet reception state we analyze the behavior of the estimation error covariance matrix and introduce the notion of peak covariance as an estimate of filtering deterioration caused by packet losses which describes the upper envelope of the sequence of error covariance matrices p t t 1 for the case of an unstable scalar model we give sufficient conditions for the stability of the peak covariance process in the general vector case and obtain a sufficient and necessary condition for the scalar case finally the relationship between two different types of stability notions is discussed

angular dynamical spectra a new method for determining frequencies weak chaos and cantori we define the invariant spectra of rotation angles and twist angles angular dynamical spectra and study the properties of their moments angular moments in a model two dimensional map the angular moments give the main frequencies of the orbits a main frequency is defined both for a regular and chaotic orbit for kam curves around a centre this frequency corresponds to the rotation number inside islands of stability we obtain both the main frequency rotation number and the epicyclic frequency a fast detection of thin chaotic layers is obtained on the basis of the behaviour of the frequency curve we explore the resonant structure near a last kam boundary the secondary islands of various multiplicities forming farey sequences and the noble tori between them are located we find a criterion to determine whether various resonant chaotic zones communicate or are separated by invariant tori

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

phase length distributions in intermittent band switching the distribution of phase lengths t for intermittent band switching is investigated its form is observed to deviate from a exponential function a minimal phase length is seen to exist and the probabilities for the first few occuring phase lengths are often strongly enhanced or suppressed these deviations are analyzed and described explicitly in terms of the parameters of a model map

robust h2 control for discrete time markovian jump linear systems this paper deals with the robust h2 control of discrete time markovian jump linear systems it is assumed that both the state and jump variables are available to the controller uncertainties satisfying some norm bounded conditions are considered on the parameters of the system an upper bound for the h2 control problem is derived in terms of a linear matrix inequality lmi optimization problem for the case in which there are no uncertainties we show that the convex formulation is equivalent to the existence of the mean square stabilizing solution for the set of coupled algebraic riccati equations arising on the quadratic optimal control problem of discrete time markovian jump linear systems therefore for the case with no uncertainties the convex formulation considered in this paper imposes no extra conditions than those in the usual dynamic programming approach finally some numerical examples are presented to illustrate the technique

optimal unbiased reduced order filtering for discrete time descriptor systems via lmi abstract in this paper the reduced order unbiased optimal h filtering problem for discrete time descriptor linear systems is considered necessary and sufficient conditions for the existence of unbiased causal time invariant filters are obtained solutions of the filtering problems are given in terms of linear matrix inequalities lmis parametrization of all optimal causal unbiased filters is provided the proposed method generalizes the existing results in the standard case

static output feedback stabilization with h sub spl infin performance for linear discrete time systems this note presents a new sufficient condition for the static output feedback stabilization of linear discrete time systems this new condition is expressed as a linear matrix inequality feasibility problem and hence easily tractable numerically an extension of this condition is given in order to incorporate h sub spl infin performance objectives the applicability of the proposed approach is shown through numerical examples and compared to some recent methods

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

recursiveness in matrix rational interpolation problems abstract we consider the problem of computing solutions to a variety of matrix rational interpolation problems these include the partial realization problem for matrix power series and newton pade hermite pade simultaneous pade m pade and multipoint pade approximation problems along with their matrix generalizations a general recurrence relation is given for solving these problems unlike other previous recursive methods our recurrence works along arbitrary computational paths when restricted to specific paths the recurrence relation generalizes previous work of antoulas cabay and labahn beckermann van barel and bultheel and gutknecht along with others our results rely on the concept of extended m pade approximation introduced in this paper this is a natural generalization of the two point pade approximation problem extended to multiple interpolation points including infinity and matrix laurent and newton series by using module theoretic techniques we determine complete parameterizations of all solutions to this problem our recurrence relation then efficiently computes these parameterizations this recursion requires no conditions on the input data we also discuss the concept of duality which was shown to be of particular interest for a stable computation of those approximants finally we show the invariance of our approximation problem under linear transformations of the extended complex plane

event based pulse modulated control of linear stochastic systems in this technical note event based pulse modulated control is studied for linear stochastic systems with an average quadratic performance over an infinite horizon from the probabilistic representation of solutions to differential equations an analytic expression of the quadratic performance is provided for stable and critically stable first order systems the schemes for seeking optimal parameters are given in the unstable case the stabilization problem is discussed unstable systems first order or higher order with white noises cannot be stabilized with probability 1 except that the noises are known to be bounded

distributed algorithms for reaching consensus on general functions this paper presents analysis and design results for distributed consensus algorithms in multi agent networks we consider continuous consensus functions of the initial state of the network agents under mild smoothness assumptions we obtain necessary and sufficient conditions characterizing any algorithm that asymptotically achieves consensus this characterization is the building block to obtain various design results for networks with weighted directed interconnection topologies we first identify a class of smooth functions for which one can synthesize in a systematic way distributed algorithms that achieve consensus we apply this result to the family of weighted power mean functions and characterize the exponential convergence properties of the resulting algorithms we establish the validity of these results for scenarios with switching interconnection topologies finally we conclude with two discontinuous distributed algorithms that achieve respectively max and min consensus in finite time

event triggered consensus tracking of multi agent systems with lur e nonlinear dynamics abstractin this paper distributed consensus tracking problem for networked lur e systems is investigated based on event triggered information interactions an event triggered control algorithm is designed with the advantages of reducing controller update frequency and sensor energy consumption by using tools of s procedure and lyapunov functional method some sufficient conditions are derived to guarantee that consensus tracking is achieved under a directed communication topology meanwhile it is shown that zeno behaviour of triggering time sequences is excluded for the proposed event triggered rule finally some numerical simulations on coupled chua s circuits are performed to illustrate the effectiveness of the theoretical algorithms

brief paper static output feedback stabilization of discrete time markovian jump linear systems a system augmentation approach this paper studies the static output feedback sof stabilization problem for discrete time markovian jump systems from a novel perspective the closed loop system is represented in a system augmentation form in which input and gain output matrices are separated by virtue of the system augmentation a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities which possess a monotonic structure for a linearized computation and a convergent iteration algorithm is given to solve such inequalities in addition a special property of the feasible solutions enables one to further improve the solvability via a simple d k type optimization on the initial values an extension to mode independent sof stabilization is provided as well compared with some existing approaches to sof synthesis the proposed one has several advantages that make it specific for markovian jump systems the effectiveness and merit of the theoretical results are shown through some numerical examples

discrete time markovian jump linear quadratic optimal control this paper is concerned with the optimal control of discrete time linear systems that possess randomly jumping parameters described by finite state markov processes for problems having quadratic costs and perfect observations the optimal control laws and expected costs to go can be precomputed from a set of coupled riccati like matrix difference equations necessary and sufficient conditions are derived for the existence of optimal constant control laws which stabilize the controlled system as the time horizon becomes infinite with finite optimal expected cost

transition probability bounds for the stochastic stability robustness of continuous and discrete time markovian jump linear systems this paper considers the robustness of stochastic stability of markovian jump linear systems in continuous and discrete time with respect to their transition rates and probabilities respectively the continuous time discrete time system is described via a continuous valued state vector and a discrete valued mode which varies according to a markov process chain by using stochastic lyapunov function approach and kronecker product transformation techniques sufficient conditions are obtained for the robust stochastic stability of the underlying systems which are in terms of upper bounds on the perturbed transition rates and probabilities analytical expressions are derived for scalar systems which are straightforward to use numerical examples are presented to show the potential of the proposed techniques

event triggered control of multiagent systems for fixed and time varying network topologies a decentralized controller that uses event triggered communication scheduling is developed for the leader follower consensus problem under fixed and switching communication topologies to eliminate continuous interagent communication state estimates of neighboring agents are designed for control feedback and are updated via communication to reset growing estimate errors the communication times are based on an event triggered approach and are adapted based on the trade off between the control system performance and the desire to minimize the amount of communication an important aspect of the developed event trigger strategy is that communication is not required to determine when a state update is needed since the control strategy produces switched dynamics analysis is provided to show that zeno behavior is avoided by developing a positive constant lower bound on the minimum inter event interval a lyapunov based convergence analysis is also provided to indicate bounded convergence of the developed control methodology

stabilization of markovian systems via probability rate synthesis and output feedback this technical note is concerned with the stabilization problem of markovian jump linear systems via designing switching probability rate matrices and static output feedback gains a novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of markovian jump linear systems based on this a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices extensions to the polytopic uncertain case are also provided all the conditions are formulated in terms of linear matrix inequalities with some equality constraints which can be solved by two modified cone complementarity linearization algorithms examples are given to show the effectiveness of the proposed method

inversion components of block hankel like matrices abstract the inversion problem for square matrices having the structure of a block hankel like matrix is studied examples of such matrices include hankel striped hankel layered and vector hankel matrices it is shown that the components that both determine nonsingularity and construct the inverse of such matrices are closely related to certain matrix polynomials these matrix polynomials are multidimensional generalizations of pade hermite and simultaneous pade approximants the notions of matrix pade hermite and matrix simultaneous pade systems are also introduced these are shown to provide a second set of inverse components for block hankel like matrices a recurrence relation is presented that allows for efficient computation of matrix pade hermite and matrix simultaneous pade systems as a result it is shown that the inverse components can be computed via either the matrix euclidean algorithm or a matrix berlekamp massey algorithm applied to an associated matrix power series an alternative algorithm based on this recurrence relation is also presented for a block hankel like matrix of type n 0 n 1 n k this algorithm is shown to compute the inverse components with a complexity of o k n 0 n k 2 block matrix operations although this can be higher in some pathological cases this is the same complexity as with existing algorithms this algorithm has the significant advantage however that no extra conditions are required on the input matrix other block algorithms require that certain submatrices be nonsingular similar results hold in the case of block toeplitz like matrices

passivity analysis and passification of uncertain markovian jump systems with partially known transition rates and mode dependent interval time varying delays in this paper the problem of delay dependent robust passivity analysis and robust passification of uncertain markovian jump linear systems mjlss with partially known transition rates and mode dependent time varying delays are investigated in the deterministic model the time varying delay is in a given range and the uncertainties are assumed to be norm bounded by constructing an appropriate lyapunov krapunov functional lkf combining with jensen s inequality and the free weighting matrix method delay dependent passification conditions are obtained in term of linear matrix inequalities lmis for the robust passification problem desired passification controllers are designed which guarantee that the closed loop mjls is passive finally a numerical example is given to illustrate the effectiveness of the proposed approach

on exponential almost sure stability of random jump systems this paper is concerned with a class of random jump systems represented by transition operators which includes switched linear systems with strictly stationary switching signals in infinite modes space as its special case a series of necessary and sufficient conditions are established for almost sure stability of this class of random jump systems under different scenarios the stability criteria obtained are further extended to markov jump linear systems with infinite states and hence a unified approach to describing the almost sure stability of mjlss is addressed under this context all the results in the work are developed for both the continuous and discrete time systems

indefinite quadratic with linear costs optimal control of markov jump with multiplicative noise systems in this paper we consider the stochastic optimal control problem of discrete time markov jump with multiplicative noise linear systems the performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables the weighting matrices of the state and control for the quadratic part are allowed to be indefinite we present a necessary and sufficient condition under which the problem is well posed and a state feedback solution can be derived from a set of coupled generalized riccati difference equations interconnected with a set of coupled linear recursive equations for the case in which the quadratic term matrices are non negative this necessary and sufficient condition can be written in a more explicit way the results are applied to a problem of portfolio optimization

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper