some new simple stability criteria of linear neutral systems with a single delay this article mainly considers the linear neutral delay differential systems with a single delay using the characteristic equation of the system new simple delay independent asymptotic and exponential stability criteria are derived in terms of the matrix measure the spectral norm and the spectral radius of the corresponding matrices numerical examples demonstrate that our criteria are less conservative than those of previous corresponding results l m li stability of linear neutral delay differential systems bull aust math soc 38 1988 339 344 g d hu g d hu some simple criteria for stability of neutral delay differential systems appl math comput 80 1996 257 271 d q cao ping he sufficient conditions for stability of linear neutral systems with a single delay appl math lett 17 2004 139 144 g d hu g d hu b cahlon algebraic criteria for stability of linear neutral systems with a single delay j comput appl math 135 2001 125 130

h 2 optimization for systems with adobe input delays a loop shifting approach this paper studies the h 2 optimization problem for systems with adobe input delay these are systems having only two possibly vector input channels one is delay free and the other is delayed we present a solution based on the reduction of the problem to an equivalent delay free problem via simple loop shifting arguments this results in a solution based on two standard algebraic riccati equations which are associated with the delay free version of the problem the optimal controller is in the dead time compensator form we also derive an explicit and transparent expression for the cost of delay and in the case when the problem is solvable without the delayed channel a numerically stable form of the optimal solution which includes exponentials of hurwitz matrices only the approach is readily extendible to more general multiple input output delay cases

delay independent stability test for systems with multiple time delays delay independent stability dis of a general class of linear time invariant lti multiple time delay system mtds is investigated in the entire delay parameter space stability of such systems may be lost only if their spectrum lies on the imaginary axis for some delays we build an analytical approach that requires the inspection of the roots of finite number of single variable polynomials in order to detect if the spectrum ever lies on the imaginary axis for some delays excluding infinite delays the approach enables to test the necessary and sufficient conditions of dis of lti mtds technically known as weak dis as well as the robust stability of single delay systems against all variations in delay ratios the proposed approach which does not require any parameter sweeping and graphical display becomes possible by establishing a link between the infinite spectrum and algebraic geometry case studies are provided to show the effectiveness of the approach

formulas on preview and delayed h infty control a generalized hinfin control problem which covers preview and delayed control strategies is discussed based on a state space approach by introducing a hamiltonian matrix which is associated with a delay free generalized plant the analytic solution to the corresponding operator riccati equation is newly established based on the result obtained here the hinfin control problem is solved and for typical control problems e g hinfin and linear quadratic lq control for multiple input delay systems hinfin preview control some interpretations are provided on the resulting control system

complete quadratic lyapunov functionals for distributed delay systems this paper is concerned with the stability analysis of distributed delay systems using complete lyapunov functionals numerous articles aim at approximating their parameters thanks to a discretization method or polynomial modeling the interest of such approximations is the design of tractable sufficient stability conditions in the present article we provide an alternative method based on polynomial approximation which takes advantages of the legendre polynomials and their properties the resulting stability conditions are scalable with respect to the maximum degree of the polynomials and are expressed in terms of tractable linear matrix inequalities several examples of delayed systems are tested to show the effectiveness of the method

easily testable necessary and sufficient algebraic criteria for delay independent stability of a class of neutral differential systems this paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems and establishes the relationship between the eigenvalue distribution and delay independent stability of neutral differential systems by using the complete discrimination system for polynomials easily testable necessary and sufficient algebraic criteria for delay independent stability of a class of neutral differential systems are established the algebraic criteria generalize and unify the relevant results in the literature moreover the maximal delay bound guaranteeing stability can be determined if the systems are not delay independent stable some numerical examples are provided to illustrate the effectiveness of our results c 2007 elsevier b v all rights reserved

designing parametric linear quadratic regulators for parametric lti systems via lmis this paper addresses the problem of determining parametric linear quadratic regulators lqrs for continuous time linear time invariant systems affected by parameters through rational functions th

stabilization of linear systems with distributed input delay and input saturation this paper is concerned with stabilization of a linear system with distributed input delay and input saturation both constant and time varying delays are considered in the case that the input delay is constant under the stabilizability assumption on an auxiliary system it is shown that the system can be stabilized by state feedback for an arbitrarily large delay as long as the open loop system is not exponentially unstable in the case that the input delay is time varying but bounded it is shown that the system can be stabilized by state feedback if the non asymptotically stable poles of the open loop system are all located at the origin in both cases stabilizing controllers are explicitly constructed by utilizing the parametric lyapunov equation based low gain design approach we recently developed it is also shown that in the presence of actuator saturation and under the same assumptions on the system these controllers achieve semi global stabilization some discussions on the assumptions we impose on the system are given a numerical example illustrates the effectiveness of the proposed stabilization approach

optimum linear causal coding schemes for gaussian stochastic processes in the presence of correlated jamming the complete solution is obtained to the following problem a gaussian stochastic process theta sub t t in 0 t sub f satisfying a certain stochastic differential equation is to be transmitted through a stochastic channel to a receiver under minimum mean squared error distortion measure the channel is to be used for exactly t sub f seconds and in addition to white gaussian noise with a given energy level the channel is corrupted by another source whose output may be correlated with the input to the channel and which satisfied a given power constraint there is an input power constraint to the channel and noiseless feedback is allowed between the receiver decoder and the transmitter encoder the authors determine the linear causal encoder and decoder structures that function optimally under the worst admissible noise inputs to the channel the least favorable probability distribution for this unknown noise is found to be gaussian and is correlated with the transmitted signal also included is a comparative study of these results with earlier ones that addressed a similar problem without a causality restriction imposed on the transmitter

discretized lyapunov functional for systems with distributed delay and piecewise constant coefficients the stability problem for systems with distributed delay is considered using discretized lyapunov functional the coefficients associated with the distributed delay are assumed to be piecewise constant and the discretization mesh may be non uniform the resulting stability criteria are written in the form of linear matrix inequality numerical examples are also provided to illustrate the effectiveness of the method the basic idea can be extended to a more general setting with more involved formulation

linear quadratic regulation for linear time varying systems with multiple input delays this paper studies the classic linear quadratic regulation lqr problem for both continuous time and discrete time systems with multiple input delays for discrete time systems the lqr problem for systems with single input delay has been studied in existing literature whereas a solution to the multiple input delay case is not known to our knowledge for continuous time systems with multiple input delays the lqr problem has been tackled via an infinite dimensional system theory approach and a frequency time domain approach the objective of the present paper is to give an explicit solution to the lqr problem via a simple and intuitive approach the main contributions of the paper include a fundamental result of duality between the lqr problem for systems with multiple input delays and a smoothing problem for an associated backward stochastic system the duality allows us to obtain a solution to the lqr problem via standard projection in linear space the lqr controller is simply constructed by the solution of one backward riccati difference for the discrete time case or differential for the continuous time case equation of the same order as the plant ignoring the delays

on the linear quadratic problem for systems with time reversed markov jump parameters and the duality with filtering of markov jump linear systems we study a class of systems whose parameters are driven by a markov chain in reverse time a recursive characterization for the second moment matrix and the formulas for optimal control are given our results are determining the answer for the question is it possible to extend the classical duality between filtering and control of linear systems whose matrices are transposed in the dual problem by simply adding the jump variable of a markov jump linear system the answer is positive provided the jump process is reversed in time

relaxed cal h _ infty stabilization conditions for discrete time fuzzy systems with interval time varying delays to derive less conservative delay and range dependent h infin stabilization conditions for discrete time takagi sugeno t s fuzzy systems with interval time varying delays the use of a fuzzy weighting dependent lyapunov krasovskii functional fwlkf in which all variables are set to be affinely or quadratically dependent on fuzzy weighting functions is proposed subsequently parameterized linear matrix inequality plmi based h infin stabilization conditions are derived by following the free weighting matrix approach to fully exploit the convexity of fuzzy weighting functions the derived plmis are sequentially replaced by a finite set of lmis by considering all possible conditions associated with fuzzy weighting functions

observer with evolutionary programming based optimal digital tracker for analog neutral multiple time delay systems abstract in this paper the finite time optimal hybrid tracking control problem for analog neutral systems with multiple discrete and distributed time delays is formulated and studied a novel approach that combining the evolutionary programming ep algorithm and the high gain property for analog neutral multiple time delay systems is proposed to achieve the best tracking performance for the first time first the newton center interpolation formula and the linear interpolation formula together with a modified rectangular rule and an augmented state vector are utilized to construct the equivalent digital linear models next according to the separation principle the control gains of the digital tracker and the digital observer are designed separately by the discrete time optimal control theory and prediction based digital redesign method and then combined together to form an observer based optimal time varying digital tracker eventually the process is to combine the high gain property with ep algorithm to search the optimal weighting matrices in the performance index to form an observer with ep based low gain digital tracker to achieve the objective of optimal tracking control an example is given for illustrating the effectiveness of the new tracker design method

memoryless approach to the lq and lqg problems with variable input delay this note studies the lq and lqg problems for linear time invariant systems with a single time varying input delay and instantaneous memoryless state feedback we extend the memoryless state feedback solution proposed in 1 in two directions we prove that in the deterministic case a memoryless state feedback can be in general optimal only up to a certain delay for which we provide a sufficient and sometimes strict bound moreover we show that this memoryless control is optimal also in the case of time varying delays and that the quadratic cost functional has the same value as in the case without delay for time varying delays the control law requires that the relationship between time points in which the input is generated and applied is known and invertible even if the delay function needs not to be differentiable or even continuous finally we prove that the cost functional is bounded also in the stochastic case for the same delay interval as in the deterministic case but with a larger cost than the delay less lqg solution

on the design of observer based controller of linear neutral delay differential systems in this note the observer based control problem for a class of linear delay differential systems of neutral type is investigated using the lyapunov method a criterion for asymptotic stability is derived in terms of matrix inequalities which solved by convex optimization algorithms a numerical example is given to illustrate the proposed method

technical communique a closed form optimal control for linear systems with equal state and input delays this paper presents the optimal regulator for a linear system with equal delays in state and input and a quadratic criterion the optimal regulator equations are obtained using the maximum principle performance of the obtained optimal regulator is verified in the illustrative example against the best linear regulators available for the linear system without delays and for a rational approximation of the original time delay system simulation graphs demonstrating better performance of the obtained optimal regulator are included

on delay dependent stability under model transformations of some neutral linear systems this paper focuses on the stability analysis of a class of neutral linear systems some sufficient delay dependent stability conditions are derived in terms of an appropriate model transformation of the original system transformation similar to the one used in the retarded case the analysis makes use of an appropriate construction of a degenerate lyapunov krasovskii functional several computational schemes and frequency domain interpretations as well as an example are also presented

h2 optimal control of systems with multiple i o delays time domain approach in this paper the h 2 optimal control problem of systems with multiple i o delays is presented the problem is first converted to an equivalent h 2 regulator problem with multiple delays the idea is to view the regulator problem in time domain as a linear quadratic regulator problem with multiple input delays it is shown that the rational part of the optimal controller has the same dimension as the plant and the non rational part may be chosen to have finite impulse response furthermore the regulator problem solution is also used to solve the h 2 filtering problem with multiple measurement delays

stability of discrete delay systems boundary criteria this paper deals with the stability of linear discrete delay systems two stability criteria that are described by evaluating a corresponding harmonic function on the boundary of a torus region are presented testing these criteria can be proved to be much easier than those reported in the literature

congestion control as a stochastic control problem with action delays we consider the design of explicit rate based congestion control for high speed communication networks and show that this can be formulated as a stochastic control problem where the controls of different users enter the system dynamics with different delays we discuss the existence derivation and the structure of the optimal controller as well as of suboptimal controllers of the certainty equivalent type a terminology that is precisely defined in the paper for the specific context of the congestion control problem considered we consider in particular two certainty equivalent controllers which are easy to implement and show that they are stabilizing i e they lead to bounded infinite horizon average cost and stable queue dynamics further these controllers perform well in simulations

analysis of an on off jamming situation as a dynamic game the process of communication jamming can be modeled as a two person zero sum noncooperative dynamic game played between a communicator a transmitter receiver pair and a jammer we consider a one way time slotted packet radio communication link in the presence of a jammer where the data rate is fixed and 1 in each slot the communicator and jammer choose their respective power levels in a random fashion from a zero and a positive value 2 both players are subject to temporal energy constraints which account for protection of the communicating and jamming transmitters from overheating the payoff function is the time average of the mean payoff per slot the game is solved for certain ranges of the players transmitter parameters structures of steady state solutions to the game are also investigated the general behavior of the players strategies and payoff increment is found to depend on a parameter related to the payoff matrix which me call the payoff parameter and the transmitters parameters when the payoff parameter is lower than a threshold the optimal steady state strategies are mixed and the payoff increment constant over time whereas when it is greater than the threshold the strategies are pure and the payoff increment exhibits oscillatory behavior

linear quadratic regulation for discrete time systems with input delay and colored multiplicative noise abstract this paper is concerned with the linear quadratic regulation lqr problem for discrete time systems involving input delay and colored multiplicative noise due to the correlation of the adjoining state this problem will be more complicated than the case of white noise in this paper the necessary and sufficient condition for the solvability of optimal control problem is presented by solving the forward and backward stochastic difference equations fbsdes moreover the optimal lqr controller is given in terms of the coupled difference equations developed in this paper

on robust stabilization for neutral delay differential systems with parametric uncertainties and its application this paper considers the problem of robust stabilization for uncertain neutral delay differential systems based on the lyapunov method a delay dependent criterion for determining the stability of systems is obtained in terms of matrix inequalities which can be easily solved by efficient convex optimization algorithms then the method presented is extended to systems with controller gain variations that is the design problem for the nonfragile controller is considered a numerical example is included to illustrate the design procedure of the proposed method

on asymptotic stability of delay difference systems in this paper we obtain some criteria for determining the asymptotic stability of the zero solution for some classes of delay difference systems by using a discrete version of the second lyapunov method our results can be well suited for computational purposes

new stability analysis for uncertain neutral system with time varying delay in this paper a class of uncertain neutral system with time varying delay is studied based on lyapunov functional approach and linear matrix inequality technology the stability criteria are given numerical examples show the effectiveness of our theoretical results and the influence of uncertainties to the stability of the neutral system

delay range stability of a class of distributed time delay systems this paper is dedicated to the stability analysis of a class of uncertain distributed delay systems the kernel of which can be modeled as a polynomial function of the delay the results are constructed by rewriting the system as an uncertain interconnected model appropriate robust control tools i e quadratic separation are then used to address the stability issue to this end some relations that highlight relevant characteristics of the delayed term are added to the interconnected model leading then to the conservatism reduction finally numerical examples show the effectiveness of the proposed method

on novel stability criterion of neutral system with time varying delay this article studies the neutral system with time varying delay and uncertainties novel stability criteria of the neutral system are derived by using lyapunov method and linear matrix inequality technology which can be easily solved by efficient convex optimization algorithms some numerical examples are given to illustrate our theoretical results

lq control for ito type stochastic systems with input delays this paper considers the linear quadratic lq control problem for the ito type stochastic system with input delays due to simultaneous appearances of diffusion terms dependent on the state and the control as well as delays in the dynamic system the problem is very involved and remains to be solved we not only provide the solvable condition of the problem but also the explicit expression of the causal and adapted controller for a kind of lq problems all of these are based on a stochastic riccati equation the key technique is to pursue the explicit cost value of the lq problem by fbsde and derive the analytical controller via the interplay between the original problem and its equivalent abstract description

delay dependent guaranteed cost stabilization criterion for neutral delay differential systems matrix inequality approach abstract in this paper we address the problem of the guaranteed cost stabilization for a class of neutral delay differential systems with a given quadratic cost function based on the lyapunov method delay dependent criteria which are expressed in terms of matrix inequalities are proposed to guarantee the asymptotic stability of the system the matrix inequalities can be easily solved by various efficient optimization algorithms

some sufficient conditions for exponential stability of linear neutral functional differential equations abstract in this paper we give some sufficient conditions for exponential stability of linear neutral functional differential equations the obtained results are extensions of the recent results in d q cao p he stability criteria of linear neutral systems with a single delay appl math comput 148 2004 135 143 d q cao p he sufficient conditions for stability of linear neutral systems with a single delay appl math lett 17 2004 139 144 g d hu g d hu x f zou stability of linear neutral systems with multiple delays boundary criteria appl math comput 148 2004 707 715 j h park s won a note on stability of neutral delay differential systems j franklin inst 336 1999 1 9 to linear neutral functional differential equations

on h control for linear systems with interval time varying delay this paper deals with the problem of delay dependent robust h control for linear time delay systems with norm bounded and possibly time varying uncertainty the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available and no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function based on an integral inequality which is introduced in this paper and lyapunov krasovskii functional approach a delay dependent bounded real lemma brl is first established without using model transformation and bounding techniques on the related cross product terms then employing the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop systems for all admissible uncertainties is proposed in terms of a linear matrix inequality lmi a numerical example is also given to illustrate the effectiveness of the proposed method

the linear quadratic optimal control problem with delays in state and control variables a state space approach this paper generalizes the results of vinter and kwong to a control operator with a more general delay structure than the one in a ichikawa and to delay systems with both finite and infinite memories the linear quadratic optimal control problem over both finite and infinite time horizons is treated several forms of associated abstract riccati differential and algebraic equations are presented the properties of the kernel of the solution are studied and a coupled set of matrix ordinary and partial differential equations is obtained

linear quadratic regulation and stabilization of discrete time systems with delay and multiplicative noise this paper is concerned with the long standing problems of linear quadratic regulation lqr control and stabilization for a class of discrete time stochastic systems involving multiplicative noises and input delay these fundamental problems have attracted resurgent interests due to development of networked control systems an explicit analytical expression is given for the optimal lqr controller more specifically the optimal lqr controller is shown to be a linear function of the conditional expectation of the state with the feedback gain based on a riccati zxl difference equation it is also shown that the system is stabilizable in the mean square sense if and only if an algebraic riccati zxl equation has a particular solution these results are based on a new technical tool which establishes a non homogeneous relationship between the state and the costate of this class of systems and the introduction of a new lyapunov function for the finite horizon optimal control design

stability of neutral delay differential systems boundary criteria this paper deals with the delay dependent stability of linear invariant neutral delay differential systems with a positive constant delay six criteria that are described by evaluating a corresponding harmonic function on the boundary of a certain rectangular region are presented

a complete characterization of minimax and maximin encoder decoder policies for communication channels with incomplete statistical description the problem is considered of transmitting a sequence of independent and identically distributed gaussian random variables over a channel whose statistical description is incomplete the channel is modeled as one that is conditionally gaussian with the unknown part being controlled by a so called jammer who may have access to the input to the encoder and operates under a given power constraint by adopting a game theoretic approach a complete set of solutions is obtained encoder and decoder mappings and least favorable distributions for the channel noise for this statistical decision problem under two different sets of conditions depending on whether the encoder mapping is deterministic or stochastic in the latter case existence of a mixed saddle point solution can be verified when a side channel of a specific nature is available between the transmitter and the receiver in the former case however only minimax and maximin solutions can be derived

on computing the maximum time delay bound for stability of linear neutral systems this note is concerned with the stability problem of linear delay differential systems of neutral type a discretized lyapunov functional approach is developed the resulting stability criterion is formulated in the form of a linear matrix inequality for nominal systems the analytical results can be approached with fine discretization numerical examples show significant improvement over approaches in the literature

algebraic criteria for stability of linear neutral systems with a single delay abstract the stability of linear neutral delay differential systems with a single delay via routh hurwitz and schur cohn criteria is investigated some algebraic criteria for delay independent stability are presented these criteria may complement those reported in the literature finally two examples illustrate the criteria

a new delay dependent criterion for neural systems with multiple delays in this paper the problem of the stability analysis for neutral systems with multiple delays is investigated using lyapunov method we present a new delay dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities lmis which can be easily solved by various convex optimization algorithms a numerical example is given to illustrate the effectiveness of the proposed method

stability of linear neutral systems with multiple delays boundary criteria the stability of linear neutral delay differential systems with multiple delays is investigated the delay dependent stability criteria are presented through the evaluation of the corresponding harmonic functions on the boundary of a certain half circular region and such criteria are extensions of some results in literature an example is given to illustrate the stability criteria

on delay dependent robust stability of uncertain neutral systems with interval time varying delays in this paper the problem of a new delay dependent robust stability criterion for neutral systems is investigated the considered system has time varying structured uncertainties and interval time varying delays based on the lyapunov method a delay dependent criterion for asymptotic stability is established in terms of lmi linear matrix inequality numerical examples are carried out to support the effectiveness of our results

some simple criteria for stability of neutral delay differential systems this paper deals with the stability of linear neutral delay differential systems some simple criteria for delay independent stability of this class of problems which are described by evaluating the measure and norm of corresponding matrices are presented the main results proposed in this study are sharper than those reported in the literature

technical communique indefinite linear quadratic optimal control problem for singular discrete time system with multiple input delays an indefinite linear quadratic ilq optimal control problem is discussed for singular discrete time varying linear systems with multiple input delays the problem is transformed to the one for standard systems by normalizability decomposition an explicit controller is obtained by computing the gain of the smoothing estimation of dual systems necessary and sufficient conditions guaranteeing the existence of unique solution are given simultaneously a numerical example illustrates the presented method

robust h_ infty control for uncertain takagi sugeno fuzzy systems with interval time varying delay this paper is concerned with the problem of robust hinfin control for a class of uncertain time delay fuzzy systems the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function the takagi sugeno t s uncertain fuzzy model with interval time varying delay is adopted based on the lyapunov krasovskii functional approach some delay dependent conditions for the existence of robust hinfin controller are formulated in the form of linear matrix inequalities lmis when these lmis are feasible an hinfin controller is presented a numerical example is given to demonstrate the effectiveness of the proposed method

an innovation approach to h prediction for continuous time systems with application to systems with delayed measurements this paper studies the problem of h prediction for linear continuous time systems by developing a new method of characterizing the innovation process and applying a novel innovation analysis approach in krein space a necessary and sufficient condition for the existence of a finite horizon h predictor is derived the solution to the h prediction is given in terms of solutions of riccati and matrix differential equations we further extend our study to give a necessary and sufficient condition for the h filtering of linear continuous time systems with both instantaneous and delayed measurements

stabilization of discrete time systems with multiplicative noise and multiple delays in the control variable this paper focuses on the stabilization problem of discrete time systems with multiplicative noise and multiple delays in the control variable first a transformation is constructed to convert the original system into a delay free system with its input matrix containing future noise next the finite horizon linear quadratic regulation problem for the delay free system subject to a constraint on the control is investigated we provide the necessary and sufficient condition for the problem having a unique solution and the optimal feedback control using riccati type difference equations finally we show that the original system can be stabilized in the mean square sense if and only if the set of solutions to the riccati type difference equations is convergent this further yields the fact that the system under consideration can be stabilized if and only if the algebraic riccati type equations have a unique solution such that a specific matrix is positive definite

stability criteria of linear neutral systems with a single delay this article studies the asymptotic stability of linear neutral delay differential systems using the characteristic equation of the system new simple delay independent stability criteria are derived in terms of the spectral radius of modulus matrices numerical examples are given to demonstrate the validity of our main criteria

stability analysis for delay differential equations with multidelays and numerical examples in this paper we are concerned with the asymptotic stability of the delay differential equation x t a 0 x t a k x t k where a 0 a k c d d are constant complex matrices and x t k x 1 t k1 x 2 t k2 x d t kd t kl 0 stand for n x d constant delays k 1 n i 1 d we obtain two criteria for stability through the evaluation of a harmonic function on the boundary of a certain region we also get similar results for the neutral delay differential equation x t lx t m i x t i n j x t j where l m i and nj e c d d are constant complex matrices and i j 0 stands for constant delays i 1 m j 1 n numerical examples on various circumstances are shown to check our results which are more general than those already reported

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

optimal control of linear systems with large and variable input delays abstract this paper proposes an optimal control law for linear systems affected by input delays specifically we prove that when the delay functions are known it is possible to generate the optimal control for arbitrarily large delay values by using a dde without distributed terms the solution can be seen as a chain of predictors whose size depends on the maximum delay

brief paper stochastic linear quadratic regulation for discrete time linear systems with input delay this paper considers the stochastic lqr problem for systems with input delay and stochastic parameter uncertainties in the state and input matrices the problem is known to be difficult due to the presence of interactions among the delayed input channels and the stochastic parameter uncertainties in the channels the key to our approach is to convert the lqr control problem into an optimization one in a hilbert space for an associated backward stochastic model and then obtain the optimal solution to the stochastic lqr problem by exploiting the dynamic programming approach our solution is given in terms of two generalized riccati difference equations rdes of the same dimension as that of the plant

on stability criteria for uncertain delay differential systems of neutral type with time varying delays in this paper we propose a new stability criterion for uncertain neutral systems the considered system has time varying structured uncertainties and time varying delay based on the lyapunov method a delay dependent criterion for asymptotic stability is derived in terms of lmi linear matrix inequality numerical examples are given to show the effectiveness of our results