on a solvable system of difference equations of kth order it is shown that the next system of k difference equationsx n j a n j x n k j b n j i 1 kx n i s j i 1 c n j n n 0 j 1 k where a n j b n j c n j

on continuous solutions of a class of systems of nonlinear functional difference equations with deviating argument abstract bounded continuous solutions on r of a class of systems of nonlinear functional difference equations with a complicated nonlinear deviation of the argument that depends on unknown functions are studied here

solutions of a system of functional differential equations in a right neighborhood of zero abstract we give some sufficient conditions for the system of nonlinear functional differential equations x qt x t f t x t x 1 qt x 2 qt x k qt x qt x g t where q 0 1 and functions f 0 t r n r n r n r n j 0 t r n 0 t j 1 k and g 0 t 0 t are continuous for the unique existence of continuously differentiable solutions x t on the interval 0 t 0 t satisfying the condition x 0 0

asynchronous control for 2 d switched systems with mode dependent average dwell time abstract this work is concerned with asynchronous control for a class of two dimensional switched systems with mode dependent average dwell time the systems are formulated by the famous fornasini marchesini local state space model and the switching signal of the switched controller involves time delays which lead to the asynchronism between controllers and subsystems by extending mode dependent average dwell time with the switched quadratic lyapunov functional approach the stabilization condition is established for 2 d asynchronously switched systems based on the stabilization result mode dependent state feedback controllers are designed to guarantee h performance and asymptotic stability of the corresponding closed loop system finally two examples are provided to illustrate the effectiveness of the proposed design scheme

positive real control of two dimensional systems roesser models and linear repetitive processes this paper considers the problem of positive real control for two dimensional 2 d discrete systems described by the roesser model and also discrete linear repetitive processes which are another distinct sub class of 2 d linear systems of both systems theoretic and applications interest the purpose of this paper is to design a dynamic output feedback controller such that the resulting closed loop system is asymptotically stable and the closed loop system transfer function from the disturbance to the controlled output is extended strictly positive real we first establish a version of positive realness for 2 d discrete systems described by the roesser state space model then a sufficient condition for the existence of the desired output feedback controllers is obtained in terms of four lmis when these lmis are feasible an explicit parameterization of the desired output feedback controllers is given we then apply a similar approach to discrete linear repetitive processes represented in their equivalent 1 d state space form finally we provide numerical examples to demonstrate the applicability of the approach

a linear programming oriented procedure for quadratic stabilization of uncertain systems abstract this paper gives a new necessary and sufficient condition for linear quadratic stabilization of linear uncertain systems when both the dynamic as well as the control matrix are subject to uncertainty a constructive numerical procedure is defined to check the condition and it furthermore provides a stabilizing linear feedback gain some experiments are presented

h _ infty filtering for discrete time state delayed systems with finite frequency specifications this article researches the problem of finite frequency ff h filtering for linear discrete time state delayed systems the disturbance is assumed to reside in low middle high frequency ranges to reduce the conservatism of the results delay partitioning idea is used to derive a new ff bounded real lemma brl by applying the generalized kalman yakubovich popov lemma two equivalent approaches to the proof of the proposed ff brl are given respectively starting from transfer function and lyapunov krasovskii functional a new ff h filter design method is proposed in terms of solving a set of linear matrix inequalities finally a numerical example clearly demonstrates the merits and effectiveness of the proposed method

dynamical system design from a control perspective finite frequency positive realness approach nonminimum phase zeros are well known to limit the best achievable control performance when the control gain is allowed to be arbitrarily high on the other hand the phase crossover appears to be a limiting factor for performance when high gain controllers are not allowed in particular the positive realness in a finite frequency range seems crucial for achieving good performance in the presence of control constraints this paper will first give multiple reasons to support this conjecture and then develop a systematic method for designing mechanical systems to achieve the finite frequency positive real ffpr property specifically we present a state space characterization of the ffpr property by generalizing the well known kalman yakubovich popov lemma to deal with a class of frequency domain inequalities that are required to hold within a finite frequency interval the result is further extended for uncertain systems to give a sufficient condition for satisfaction of a robust ffpr property the nominal ffpr result is interpreted in the time domain in terms of input output signals finally we show that certain sensor actuator placement problems to achieve the ffpr property can be reduced to finite dimensional convex problems involving linear matrix inequalities the method is applied to the shape design of a swing arm for magnetic storage devices with the objective of maximizing the control bandwidth achievable with a limited actuator power

on a system of two nonlinear difference equations abstract in this paper we study the oscillatory behavior the boundedness of the solutions and the global asymptotic stability of the positive equilibrium of the system of two nonlinear difference equationsxn 1 a yn xn p yn 1 a xn yn q n 0 1 p qare positive integers

passivity preserving model reduction with finite frequency h approximation performance this paper is concerned with model reduction for passive systems for a given linear time invariant system that is stable and positive real pr our goal is to find a pr reduced order model to approximate it and our attention is focused on reducing the error with respect to a finite frequency h performance which is the most remarkable difference between the proposed approach and the existing ones first by applying multiplier expansion new conditions in terms of linear matrix inequalities are derived for characterizing the positive realness of the reduced order model and the finite frequency h performance of the error system a necessary and sufficient condition is then established for parameterizing a pr reduced order model with finite frequency h approximation performance based on which an iterative algorithm is constructed for numerically exploring such a reduced order model particularly a partial multiplier expansion treatment is introduced which greatly reduces the decision variables but does not cause conservatism to the derived conditions the proposed method is also extended to robust passivity reserving model reduction with polytopic uncertainty finally we provide two numerical examples about rlc circuits to show the effectiveness and advantages of the proposed model reduction method

on some solvable systems of difference equations abstract we show that the following systems of difference equations x n 1 u n 1 v n y n 1 w n 1 s n n n 0 where u n v n w n s n are some of the sequences x n or y n with real initial values x 0 and y 0 are solvable in fourteen out of sixteen possible cases two cases are left unsolved probably the most interesting is the result in the case u n x n v n x n w n x n s n y n where a fascinating formula is obtained in an elegant way by using some ad hoc ideas

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

on some linear difference equations and inequalities with continuous argument abstract we study some properties of solutions of linear difference equations and inequalities with continuous argument in terms of the location of the zeroes of the characteristic polynomial of the associated homogeneous linear difference equation with constant coefficients

domains of undefinable solutions of some equations and systems of difference equations for some classes of difference equations and systems of difference equations we find the sets of initial values for which solutions of these equations and systems are not well defined so called domains of undefinable solutions

bounded solutions of some systems of nonlinear functional differential equations with iterated deviating argument abstract for a class of systems of nonlinear functional differential equations with iterated deviating arguments dependent of unknown functions are given some conditions for the existence of bounded solutions on the real line satisfying some additional conditions

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

power series everywhere convergent on r and all qp power series are introduced that are simultaneously convergent for all real and all p adic numbers our expansions are in some aspects similar to those of exponential trigonometric and hyperbolic functions starting from these series and using their factorial structure new and summable series with rational sums are obtained for arguments x q adeles of series are constructed possible applications at the planck scale are also considered

asymptotically convergent solutions of a system of nonlinear functional differential equations of neutral type with iterated deviating arguments some conditions that guarantee the existence of a family of solutions converging to zero of a system of nonlinear functional differential equations with iterated deviating arguments are given

unique existence of bounded continuous solutions on the real line of a class of nonlinear functional equations with complicated deviations abstract the existence and uniqueness of bounded continuous solutions on the real line of a general class of nonlinear functional equations with quite complicated deviations dependent of unknown functions are established in this paper

robust filtering for 2 d state delayed systems with nft uncertainties this paper is concerned with the robust filtering problem for two dimensional 2 d state delayed systems with uncertainties represented by nonlinear fraction transformation the authors first establish the stability h sub spl infin performance and generalized h sub 2 performance criteria for the system based on the results the authors propose efficient methods to solve the robust h sub spl infin filtering generalized h sub 2 filtering and mixed generalized h sub 2 h sub spl infin filtering problems by using a parameter dependent lyapunov function approach the methods involve solving linear matrix inequalities two examples are given to show the effectiveness of the proposed approach

finite frequency model reduction of two dimensional digital filters this technical note is concerned with the model reduction problem of two dimensional 2 d digital filters over finite frequency ranges the 2 d digital filter is described by the fornasini marchesini local state space fm lss model with the aid of the generalized kalman yakubovich popov gkyp lemma for 2 d systems sufficient conditions for the finite frequency model reduction problem are derived compared with full frequency methods the proposed finite frequency method can get a better approximation performance over finite frequency ranges an example is given to demonstrate the effectiveness of the proposed method

passivity analysis and passification for uncertain signal processing systems the problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers decision feedback equalizers and digital and analog filters equally important is the problem of passification where a compensator needs to be designed for a given system to become passive this paper considers these two problems for a large class of systems that involve uncertain parameters time delays quantization errors and unmodeled high order dynamics by characterizing these and many other types of uncertainty using a general tool called integral quadratic constraints iqcs we present solutions to the problems of robust passivity analysis and robust passification more specifically for the analysis problem we determine if a given uncertain system is passive for all admissible uncertainty satisfying the iqcs similarly for the problem of robust passification we are concerned with finding a loop transformation such that a particular part of the uncertain signal processing system becomes passive for all admissible uncertainty the solutions are given in terms of the feasibility of one or more linear matrix inequalities lmis which can be solved efficiently

global stability of some symmetric difference equations suppose r 0 1 m n and 1 k1 k2 k2m 1 and let s2m 1 1 2 2m 1 we show that every positive solution to the difference equation yn p2m 12m 1 yn k1r yn k2r yn k2m 1r p2m2m 1 yn k1r yn k2r yn k2m 1r n n0 where p2m 12m 1 x1 x2 x2m 1 r 1rodd2m 1 t1 t2 tr s2m 1t1 t2 trxt1xt2 xtr and p2m2m 1 x1 x2 x2m 1 1 r 2reven2m t1 t2 tr s2m 1t1 t2 trxt1xt2 xtr converges to one this result confirms a quite recent conjecture posed by liu and yang 2010 in 10 we also prove another result regarding a related equation

on some systems of difference equations abstract in this note we show that the following systems of difference equations u n 1 v n 1 v n v n 1 u n 1 u n u n 1 v n 1 u n v n 1 u n 1 v n u n 1 u n 1 v n v n 1 v n 1 u n with n n 0 and complex initial values u 0 and v 0 are solvable explicitly by means of riccati equations and based on the formulae for the general solutions we present the behaviour of their solutions as n while the result is natural for the first system it is a bit surprising for the other two systems

brief paper robust finite frequency h filtering for uncertain 2 d roesser systems this paper investigates the problem of robust finite frequency ff h filtering for two dimensional 2 d roesser models with polytopic uncertainties our attention is focused on designing filters guaranteeing the robustly asymptotic stability and ff h disturbance attenuation level of the filtering error system by the parameter dependent idea and the generalized kalman yakubovich popov lemma for 2 d roesser models the existence conditions of robust ff h filters are obtained in terms of solving an optimization problem which is more general than the existing results an example is given to validate the proposed methods the contribution of the paper is twofold 1 systematic methods are proposed for designing ff h filters for roesser models 2 an improved strategy has been presented to deal with the robust h filter design for roesser models

on a system of difference equations of odd order solvable in closed form it is shown that the next system of difference equationsx n c ny n 2 k 1 a n b ny n 2 k 1 i 1 k 1y n 2 i 1 x n 2 i y email protected nx n 2 k 1 a email protected nx n 2 k 1 i 1 k 1x n 2 i 1 y n 2 email protected n 0 where a n b n c n a n b n c n email protected n 0 and initial values x i y i email protected 1 2 2k 1 are real numbers is solved in closed form and the behavior of its well defined solutions when all the coefficients in the system are constant is described

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

on the difference equation xn xn 2 bn cnxn 1xn 2 abstract we prove that the difference equation x n x n 2 b n c n x n 1 x n 2 n n 0 where b n n n 0 and c n n n 0 are sequences periodic with period two and the initial values x 2 x 1 are real numbers can be solved explicitly some applications of obtained formulae are given

on the system of two difference equations xn 1 i 0kai yn ipi yn 1 i 0kbi xn iqi abstract in this paper we study the system of two difference equations of the form x n 1 i 0 k a i y n i p i y n 1 i 0 k b i x n i q i where a i b i i 0 1 k x i y i i k k 1 0 are positive numbers and p i q i i 0 k are positive constants more precisely we investigate the boundedness the persistence of the positive solutions the existence of a unique positive equilibrium and the global asymptotic stability of the positive equilibrium of the above system finally we find solutions of the system which do not oscillate about the positive equilibrium

global stability of a difference equation with maximum we prove that every positive solution to the difference equationx n maxa 1x n 1 a 1 a 2x n 2 a 2 a kx n k a k email protected n 0 where email protected n a i 0 a email protected 0 1 i 1 k converges to the following quantity maxa 1 1 a 1 1 a k 1 a k 1 confirming a quite recent conjecture of interest we also prove another result on global convergence which concerns some cases when not all a i i 1 k belong to the interval 0 1

global stability and asymptotics of some classes of rational difference equations in this note we prove that the positive solutions of some classes of rational difference equations are globally asymptotically stable using a berg s result we also find asymptotics of some solutions of these equations

eventual periodicity of some systems of max type difference equations the periodicity of the next system of max type difference equations xn 1 max1 i1 m1f1i1xn ki1 1 1 1 xn ki1 2 1 2 xn ki1 l 1 l n xn t1s 1 xn 2 max1 i2 m2f2i2xn ki2 1 2 1 xn ki2 2 2 2 xn ki2 l 2 l n xn t2s 2 xn l max1 il mlflilxn kil 1 l 1 xn kil 2 l 2 xn kil l l l n xn tls l n n0n n0 where s l mj tj kij h j n j h 1 l j h 1 l 1 2 l 1 2 l is a permutation of 1 2 l 1 2 l and fjij 0 l n0 0 fjij 0 l n0 0 j 1 l j 1 l ij 1 mj ij 1 mj is studied it is shown that under some conditions posed on functions fjijfjij all positive solutions of the system are eventually periodic with period ts for some t nt n

asymptotic behavior of the positive solutions of an exponential type system of difference equations in this paper we study the existence of a unique positive equilibrium the boundedness persistence and global attractivity of the positive solutions of a system of the following two difference equations x n 1 ax n by n 1 e x n y n 1 cy n dx n 1 e y n n 0 1 where a b c d are positive constants and the initial values x 1 x 0 y 1 y 0 are positive numbers

existence of bounded solutions of a class of neutral systems of functional differential equations some results on the existence of bounded solutions together with their first derivatives of a class of neutral systems of functional differential equations with complicated deviations which extend and unify numerous results in the literature are proved

on difference equations with powers as solutions and their connection with invariant curves abstract we look for nonlinear systems of difference equations which have power functions as solutions and we find a connection to the theory of invariant curves and to self reversed polynomials in particular we construct algebraic solutions of a special equation of invariant curves

on a solvable system of difference equations of fourth order it is shown that the next system of k difference equationsx n j a n j x n k j b n j i 1 kx n i s j i 1 c n j n n 0 j 1 k where a n j b n j c n j n n 0 j 1 k and initial values x i j i j 1 k are real numbers and where s n 1 k is defined by s km j j 1 j 1 k 1 s km k 1 m n 0 can be solved in closed form in an elegant way some applications of obtained formulas for the case when the sequences a n j b n j and c n j are k periodic are also given

robust stability and performance analysis of 2d mixed continuous discrete time systems with uncertainty this paper investigates 2d mixed continuous discrete time systems whose coefficients are polynomial functions of an uncertain vector constrained into a semialgebraic set it is shown that a nonconservative linear matrix inequality lmi condition for ensuring robust stability can be obtained by introducing complex lyapunov functions depending polynomially on the uncertain vector and a frequency moreover it is shown that nonconservative lmi conditions for establishing upper bounds of the robust h and h 2 norms can be obtained by introducing analogous lyapunov functions depending rationally on the frequency some numerical examples illustrate the proposed methodology

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

on the system of difference equations x n x n 1 y n 2 a y n 2 b y n 1 y n y n 1 x n 2 c x n 2 d x n 1 we show that the following system of difference equations x n x n 1 y n 2 a y n 2 b y n 1 y n y n 1 x n 2 c x n 2 d x n 1 n n 0 where parameters a b c d as well as initial values x 2 x 1 y 2 y 1 are real numbers is solvable in closed form and by using obtained formulas we give some results on the long term behavior of their solutions we also give natural explanations and considerably extend some recent results in the literature

local existence of lipschitz continuous solutions of systems of nonlinear functional equations with iterated deviations abstract some conditions which guarantee the local existence of lipschitz continuous solutions of some systems of nonlinear functional equations with complicated deviations dependent of unknown functions are presented

generalized kalman yakubovich popov lemma for 2 d fm lss model this paper is concerned with the generalized kalman yakubovich popov kyp lemma for 2 d fornasini marchesini local state space fm lss systems by carefully analyzing the feature of the states in 2 d fm lss models a linear matrix inequality lmi characterization for a rectangular finite frequency region is constructed and then by combining this characterization with s procedure a generalized kyp lemma is proposed for 2 d fm lss models as applications of the developed kyp lemma new conditions are further derived for designing controllers guaranteeing finite frequency positive realness of the closed loop systems where both state feedback and dynamic output feedback control laws are considered finally two illustrative examples clearly show the effectiveness of the proposed results the main contribution of the paper is trifold 1 a novel characterization for a finite frequency region has been developed 2 a generalized kyp lemma has been proposed including the existing bounded realness and positive realness results as special cases and 3 systematic methods for finite frequency positive real control of 2 d systems have been presented

solutions of a max type system of difference equations we show in an elegant way that the general solution to the following max type system of difference equations xn 1 maxaxn ynxn yn 1 maxayn xnyn n n0 for the case y0 x0 a 0 y0 x0 max a 1 a is given by xn afk n 1 n x0fk n y0fk n 1 n n n y1 x0 y0 and yn y0fk n 1 1afk n 1 n 1x0fk n 1 1 1 n n 2 where k n n for n even k n n 1 for n odd n n0 n n mod2 for n n0 and where the sequence fn n n is the fibonacci sequence correcting and giving a proof of a wrong result in the paper d simsek b demir c cinar on the solutions of the system of difference equations xn 1 max a xn yn xn yn 1 max a yn xn yn discrete dyn nat soc 2009 2009 11 pp article id 325296

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

brief paper a generalized kyp lemma based approach for disturbance rejection in data storage systems this paper is concerned with disturbance rejection for data storage systems which applies microactuator to expand its servo bandwidth an approach based on the generalized kalman yakubovic popov kyp lemma together with the youla parameterization is proposed which allows us to suppress disturbances of particular frequencies within or beyond the servo bandwidth via convex optimization the rejection of narrowband high frequency disturbances is achieved by using this approach simulation together with implementation results demonstrate the simplicity and effectiveness of the design method as compared with the traditional frequency weighting method

on a symmetric system of max type difference equations we study behavior of positive solutions of the following max type system of difference equationsx n 1 maxc y n px n 1 p y n 1 maxc x n py n 1 p email protected n 0 where p email protected 0 extending some results in the literature among other results we prove that if p email protected 0 1 then every positive solution of the system converges to 1 1

positive real control for 2 d discrete delayed systems via output feedback controllers this paper considers the problem of positive real control for two dimensional 2 d discrete delayed systems in the fornasini marchesini second local state space model attention is focused on the design of dynamic output feedback controllers which guarantee that the closed loop system is asymptotically stable and the closed loop transfer function is extended strictly positive real we first present a sufficient condition for extended strictly positive realness of 2 d discrete delayed systems based on this a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality lmi when the lmi is feasible an explicit parametrization of a desired output feedback controller is presented finally we provide a numerical example to demonstrate the application of the proposed method

on a system of difference equations which can be solved in closed form we present an elegant method for solving the system of difference equationsx n 1 1x email protected n y n email protected n 1y n email protected n 0 where parameters a and b and the initial values x 0 and y 0 are positive numbers and by using obtained formulae we show that every solution of the system converges to a two periodic solution

on a solvable rational system of difference equations abstract we show that the system of difference equations x n 1 x n y n k y n k 1 a n b n x n y n k y n 1 y n x n k x n k 1 c n d n y n x n k n n 0 where k n the sequences a n b n c n d n n n 0 and initial values x i y i i 0 k are real numbers can be solved in closed form by using obtained formulae we investigate asymptotic behavior of well defined solutions of the system for the case when all the sequences a n b n c n and d n are constant

on the system of difference equations xn cnyn 3 an bnyn 1xn 2y n 3 yn γnxn 3 αn βnxn 1yn 2 xn 3 we show that the system of difference equationsx n c ny n 3a n b ny n 1x n 2y n 3 y email protected nx n email protected email protected nx n 1y n 2x n 3 email protected n 0 where the sequences a n b n c n a n b n c n email protected n 0 and initial values x i y i email protected 1 2 3 are real numbers such that c n 0 c n 0 email protected n 0 can be solved in closed form and for the case when all the sequences a n b n c n a n b n and c n are constant we describe the asymptotic behavior of well defined solutions of the system

finite frequency model reduction of takagi sugeno fuzzy systems this paper considers the model reduction problem for continuous time takagi sugeno t s fuzzy systems different from existing full frequency methods a finite frequency model reduction method is proposed in this paper the proposed method can get a better approximation performance when input signals belong to a finite frequency domain to this end a finite frequency h infty performance index is first defined then a sufficient finite frequency performance analysis condition is derived by the aid of parseval s theorem and quadratic functions based on this condition and projection lemma three model reduction algorithms for t s fuzzy systems with input signals in low frequency middle frequency and high frequency domain are obtained respectively finally an example is given to illustrate the effectiveness of the proposed method

on stabilization of 2d roesser models this note is devoted to the stabilization of 2d roesser models which are discrete continuous or mixed continuous discrete a recent linear matrix inequalities lmis necessary and sufficient condition for stability of such models is used to derive a quasi non conservative technique for state feedback stabilization

difference equations and nonexistence of solutions of an integral equation abstract by using difference equations we give some easily applicable sufficient conditions for the non existence of nonnegative solutions satisfying some additional conditions of the integral equation f x x a x t b x t f t p d t where p 1 and x is a measurable space with probability measure

globally bounded solutions of a system of nonlinear functional differential equations with iterated deviating argument abstract some sufficient conditions which guarantee the existence of a bounded solution together with its first derivative on the whole real line of a system of nonlinear functional differential equations with an iterated deviating argument dependent of unknown function are given

on a nonlinear generalized max type difference equation abstract the boundedness character of positive solutions of the following max type difference equation x n max a x n 1 p x n k r n n 0 where k n 1 the parameters a and r are positive and p is a nonnegative real number is studied in this paper our main results considerably improve results appearing in the literature

on a system of difference equations abstract we show that the system of difference equations x n 1 ax n 1 by n x n 1 c y n 1 y n 1 x n y n 1 n n 0 where the parameters a b c and initial values x 1 x 0 y 1 y 0 are real numbers can be solved considerably improving the results in the literature

global stability of a max type difference equation we show that every positive solution to the difference equationx n maxa 1x n p 1 a 1 a 2x n p 2 a 2 a kx n p k a k n n 0 where p i i 1 k are natural numbers such that 1 0 a i 1 1 i 1 k converges to max 1 i ka i 1 a i 1 this result improves and complements the main result in our recent note s stevic global stability of a difference equation with maximum appl math comput 210 2009 525 529 since it also considers the case when a i 1 0 i 1 k

on the recursive sequencexn 1 α xn 1 xn abstract we study the global stability the boundedness character and the periodic nature of the positive solutions of the difference equationxn 1 xn 1 xn where 0 and where the initial conditionsx 1andx0are arbitrary positive real numbers

trichotomy of a system of two difference equations abstract in this paper we study the boundedness and the asymptotic behavior of the positive solutions of the system of difference equations x n 1 a i 1 k a i x n p i j 1 m b j y n q j y n 1 b i 1 k c i y n p i j 1 m d j x n q j where k m 1 2 a b ai ci bj dj i 1 k j 1 m are positive constants pi qj i 1 k j 1 m are positive integers such that p1

generalized kyp lemma unified frequency domain inequalities with design applications the celebrated kalman yakubovic spl caron popov kyp lemma establishes the equivalence between a frequency domain inequality fdi and a linear matrix inequality and has played one of the most fundamental roles in systems and control theory this paper first develops a necessary and sufficient condition for an s procedure to be lossless and uses the result to generalize the kyp lemma in two aspects the frequency range and the class of systems and to unify various existing versions by a single theorem in particular our result covers fdis in finite frequency intervals for both continuous discrete time settings as opposed to the standard infinite frequency range the class of systems for which fdis are considered is no longer constrained to be proper and nonproper transfer functions including polynomials can also be treated we study implications of this generalization and develop a proper interface between the basic result and various engineering applications specifically it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain phase properties in several frequency ranges the method is illustrated by numerical design examples of digital filters and proportional integral derivative controllers

improved results on h model reduction for continuous time linear systems over finite frequency ranges this paper revisits the h model reduction problem for continuous time linear systems over finite frequency ranges given an asymptotically stable system our goal is to find a stable reduced order system in such a way that the error of the transfer functions between the original system and the reduced order one is bounded over a finite frequency range by virtue of the generalized kalman yakubovich popov gkyp lemma we first establish necessary and sufficient characterizations for this problem in terms of linear matrix inequalities lmis for the low and mid frequency cases through introducing a non conservative multiplier and resorting to the projection lemma the reduced order system matrices are decoupled with the matrix variables from the gkyp lemma then by introducing a new diagonal matrix variable and based on congruence transformation the reduced order system matrices are further decoupled with the matrix variable induced by the projection lemma and can be parameterized by a new matrix variable the results are extended to the high frequency case without the use of projection lemma to reduce the conservatism moreover an iterative convex optimization algorithm is developed to solve the conditions finally we demonstrate via numerical examples that our method can achieve much smaller approximation error than existing results

periodicity of a class of nonautonomous max type difference equations abstract in this note we prove several general and easily applicable results regarding the periodicity of positive solutions of the following difference equations x n max f 1 x n k 1 n f m x n k m n x n s n n 0 and x n min f 1 x n k 1 n f m x n k m n x n s n n 0 where 1 k 1 k m m s n and where the functions f i 0 n 0 0 1 i m satisfy some additional conditions these results considerably extend and unify numerous results on max type difference equations existing in the literature

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

l gain performance analysis for two dimensional roesser systems with persistent bounded disturbance and saturation nonlinearity the l gain approach has been an essential tool in one dimensional system theory however limited results have been presented in the literature for the two dimensional 2 d l gain approach this paper investigates the l gain performance for 2 d systems in the roesser model with persistent bounded disturbance input and saturation nonlinearity a linear matrix inequality lmi based condition is established to reduce the effect of persistent bounded disturbance input on 2 d systems within a given disturbance attenuation level based on the discrete jensen inequality lower bounds lemma and diagonally dominant matrices we apply the obtained results to the l gain performance analysis for 2 d digital filters with saturation arithmetic

long term behavior of positive solutions of a system of max type difference equations abstract some sufficient conditions which guaranty the attractivity of all positive solutions of the next system of difference equations x n max a y n 1 p j 2 k x n j q j y n max a x n 1 p j 2 k y n j q j n n 0 where a p 0 and q j j 2 k are nonnegative numbers are given the boundedness character of positive solutions of the system is also studied

unbiased minimum variance fault and state estimation for linear discrete time varying two dimensional systems the fault and state estimation problem is addressed for a class of linear discrete time varying two dimensional systems subject to state and measurement noises two estimators are proposed to compute the estimation of the system state and or fault recursively both of which are unbiased with minimum variance through formulating the estimation problem as the solvability problem of the corresponding matrix equations of estimator gains and system constraint the necessary and sufficient condition of the existence and the solution for the proposed estimators are given an example is used to demonstrate the effectiveness of the proposed estimators