improved linear matrix inequality approach to stability analysis of linear systems with interval time varying delays this paper investigates the problem of stability analysis for a class of linear systems with interval time varying delay in order to develop a less conservative stability condition a lyapunov krasovskii functional comprising novel integral terms is introduced convex combination idea is utilized to derive a stability criterion in terms of linear matrix inequalities lmis without any additional free weighting matrices which increase drastically the computational burden of the stability test numerical examples are presented to illustrate the superiority of the proposed approach compared to some existing ones in the literature

delay dependent robust h control for t s fuzzy system with interval time varying delay this paper is concerned with the problem of robust h control for uncertain t s fuzzy systems with interval time varying delay that is the delay is assumed to be a time varying function belonging to an interval by defining new lyapunov functions and making use of novel techniques to achieve delay dependence new conditions for the existence of robust h controller are obtained based on the parallel distributed compensation pdc method in this article all the conditions are shown in terms of linear matrix inequalities lmis which can be solved efficiently by using the lmi optimization techniques two numerical examples are given to illustrate the less conservatism of the proposed method

a less conservative robust stability test for linear uncertain time delay systems this note concerns with the robust stability of linear uncertain systems with state delay the uncertainty is assumed to be of polytopic type a less conservative delay dependent linear matrix inequality lmi method is presented based on a new lyapunov krasovskii functional the present method incorporates a relaxed parameter dependent technique combined with a recently proposed idea of introducing free weighting matrices when confined to delay free case the present result is also less conservative than existing stability tests using parameter dependent methods numerical examples are given to show the less conservativeness of the results

a note on relationship between two classes of integral inequalities this technical note firstly introduces two classes of integral inequalities with and without free matrices respectively and points out that they although in different forms are actually equivalent in the sense of conservatism i e the two corresponding ones produce the same tight upper bounds secondly the relationship between the method of integral inequalities with free matrices and the free weighting matrix technique is intensively investigated it is shown that these two different methods are actually equivalent in assessing the stability of time delay systems

the two stage iteration algorithms based on the shortest distance for low rank matrix completion abstract despite matrix completion requiring the global solution of a non convex objective there are many computational efficient algorithms which are effective for a broad class of matrices based on these algorithms for matrix completion with given rank problem we propose a class of two stage iteration algorithms for general matrix completion in this paper the inner iteration is the scaled alternating steepest descent algorithm for the fixed rank matrix completion problem presented by tanner and wei 2016 the outer iteration is used two iteration criterions the gradient norm and the distance between the feasible part with the corresponding part of reconstructed low rank matrix the feasibility of the two stage algorithms are proved finally the numerical experiments show the two stage algorithms with shorting the distance are more effective than other algorithms

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

toeplitz matrix completion via smoothing augmented lagrange multiplier algorithm abstract toplitz matrix completion tmc is to fill a low rank toeplitz matrix from a small subset of its entries based on the augmented lagrange multiplier alm algorithm for matrix completion in this paper we propose a new algorithm for the tmc problem using the smoothing technique of the approximation matrices the completion matrices generated by the new algorithm are of toeplitz structure throughout iteration which save computational cost of the singular value decomposition svd and approximate well the solution convergence results of the new algorithm are proved finally the numerical experiments show that the augmented lagrange multiplier algorithm with smoothing is more effective than the original alm and the accelerated proximal gradient apg algorithms

low rank matrix completion by riemannian optimization the matrix completion problem consists of finding or approximating a low rank matrix based on a few samples of this matrix we propose a new algorithm for matrix completion that minimizes the least square distance on the sampling set over the riemannian manifold of fixed rank matrices the algorithm is an adaptation of classical nonlinear conjugate gradients developed within the framework of retraction based optimization on manifolds we describe all the necessary objects from differential geometry necessary to perform optimization over this low rank matrix manifold seen as a submanifold embedded in the space of matrices in particular we describe how metric projection can be used as retraction and how vector transport lets us obtain the conjugate search directions finally we prove convergence of a regularized version of our algorithm under the assumption that the restricted isometry property holds for incoherent matrices throughout the iterations the numerical experiments indicate that our approach

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

brief paper output feedback sampled data polynomial controller for nonlinear systems this paper presents the stability analysis and control synthesis for a sampled data control system which consists of a nonlinear plant and an output feedback sampled data polynomial controller connected in a closed loop the output feedback sampled data polynomial controller which can be implemented by a microcontroller or a digital computer is proposed to stabilize the nonlinear plant based on the lyapunov stability theory stability conditions in terms of sum of squares are obtained to guarantee the stability and to aid the design of a polynomial controller a simulation example is given to demonstrate the effectiveness of the proposed control approach

a new gradient projection method for matrix completion in this paper a new gradient projection method is proposed which generates a feasible matrix sequences the decent property of this method is proved based on the decent property the convergence of the new method is discussed moreover a sufficient and necessary condition for the optimal matrix is obtained finally numerical experiments show the new method is effective in precision

an lmi approach to stability of systems with severe time delay this note describes the stability problems of uncertain systems with arbitrarily time varying and severe time delay using new lyapunov krasovskii functionals less conservative stability conditions are obtained for such systems the results are illustrated using the numerical examples based on simple linear matrix inequalities

new results on h filtering for fuzzy systems with interval time varying delays this paper investigates the problem of h filtering for continuous takagi sugeno t s fuzzy systems with an interval time varying delay in the state based on the delay partitioning idea a new approach is proposed for solving this problem which can achieve much less conservative feasibility conditions the attention is focused on the design of an h filter via the parallel distributed compensation scheme such that the filter error system is asymptotically stable and the h attenuation level from disturbance to estimation error is below a prescribed scalar the constructed lyapunov krasovskii functional by applying the delay partitioning method can potentially guarantee the obtained delay dependent conditions to be less conservative than those in the literature the obtained results are formulated in the form of linear matrix inequalities lmis which can be readily solved via standard numerical software finally an example is illustrated to show the reduction in conservatism of the proposed filter design method

non fragile asynchronous h control for uncertain stochastic memory systems with bernoulli distribution abstract this study constructs and investigates the non fragile asynchronous h control for uncertain stochastic memory systems with bernoulli distribution the system not only contains the randomly occurring uncertainties of all parameters rouaps and stochastic disturbances in the system model but also includes randomly gain perturbations in the controller by introducing the stochastic variables a new model structure is built obeying bernoulli distribution to describe the system and the controller moreover a modified lyapunov krasovskii function lkf is constructed combining ito s differential formula and free weighting matrix method less conservative results are presented in terms of the linear matrix inequality lmi furthermore an observer based non fragile asynchronous h controller is designed without any limits on the system parameters finally three numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed results

robust stability and stabilization methods for a class of nonlinear discrete time delay systems this paper establishes new robust delay dependent stability and stabilization methods for a class of nonlinear discrete time systems with time varying delays the parameter uncertainties are convex bounded and the unknown nonlinearities are time varying perturbations satisfying lipschitz conditions in the state and delayed state an appropriate lyapunov functional is constructed to exhibit the delay dependent dynamics and compensate for the enlarged time span the developed methods for stability and stabilization eliminate the need for over bounding and utilize smaller number of lmi decision variables new and less conservative solutions to the stability and stabilization problems of nonlinear discrete time system are provided in terms of feasibility testing of new parametrized linear matrix inequalities lmis robust feedback stabilization methods are provided based on state measurements and by using observer based output feedback so as to guarantee that the corresponding closed loop system enjoys the delay dependent robust stability with an l 2 gain smaller that a prescribed constant level all the developed results are expressed in terms of convex optimization over lmis and tested on representative examples

delay dependent robust stabilization of uncertain systems with multiple state delays this paper deals with the problem of robust stabilization for uncertain systems with multiple state delays the parameter uncertainties are time varying and unknown but are norm bounded and the delays are time varying a new method for achieving robust stabilization is presented for a class of uncertain time delay systems via linear memoryless state feedback control the results depend on the size of the delays and are given in terms of several linear matrix inequalities

further results on stability analysis of discrete time systems with time varying delays via the use of novel convex combination coefficients this paper focuses on deriving an improved stability criterion for discrete time delay systems via a lyapunov krasovskii functional approach that takes advantage of triple summation terms to this end novel convex combination coefficients coupled with second order time varying delay terms are introduced and the corresponding reciprocally convex approach is established with the use of the minimal number of slack matrix variables finally three numerical examples are provided to illustrate the effectiveness of the proposed method with particular regard to robustness and h performance

delay dependent stability analysis for a class of dynamical systems with leakage delay and nonlinear perturbations this paper studies the stability problem for a class of dynamical systems with leakage delay and nonlinear perturbations based on linear matrix inequality lmi approach some sufficient conditions which are dependent on the leakage delay are derived to ensure the global asymptotic stability by using lyapunov krasovskii functional method and free weighting matrix technique two examples and their simulations are given to show the effectiveness and advantage of the present results

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

new results on dissipativity analysis of singular systems with time varying delay abstract this paper focuses on the dissipativity analysis of singular systems with time varying delay the objective is to obtain a less conservative criterion with less computational demand based on the state decomposition method singular systems are rewritten as differential subsystems and algebraic ones first of all the components of state vectors are applied to design a novel lyapunov krasovskii functional lkf for the differential subsystems then in the derivative of the lkf the algebraic ones are introduced and the wirtinger based integral inequality together with the extended reciprocally convex matrix inequality is adopted to estimate the single integral term therefore a new dissipativity criterion is obtained which realizes both less conservativeness and less computational demand finally two numerical examples are given to verify the superiority of the proposed method

mixed time delays dependent exponential stability for uncertain stochastic high order neural networks this paper presents a discrete and distributed time delays dependent simultaneous approach to deterministic and uncertain stochastic high order neural networks new results are proposed in terms of linear matrix inequality lmi by exploiting a novel lyapunov krasovskii functional and by making use of novel techniques for time delay systems some constraints of systems are removed and new results cover some recently published works two numerical examples are given to show the usefulness of presented approach

delay dependent stabilization of linear systems with time varying state and input delays the integral inequality method is a new way of tackling the delay dependent stabilization problem for a linear system with time varying state and input delays email protected t ax t a 1x t h 1 t b 1u t b 2u t h 2 t in this paper a new integral inequality for quadratic terms is first established then it is used to obtain a new state and input delay dependent criterion that ensures the stability of the closed loop system with a memoryless state feedback controller finally some numerical examples are presented to demonstrate that control systems designed based on the criterion are effective even though neither a b 1 nor a a 1 b 1 is stabilizable

a novel result on stability analysis for uncertain neutral stochastic time varying delay systems generalized finsler lemma is applied to deduce delay dependent stability conditions the case is considered that the discrete delay is different from the neutral delay model transformation cross terms estimation and free weighting matrices are avoided the conditions show less conservatism and involves fewer computational variables numerical examples show that the proposed approach improves some existing ones this paper is concerned with the mean square exponential stability analysis for uncertain neutral linear stochastic time varying delay systems by lyapunov krasovskii theory and linear matrix inequality method under the generalized finsler lemma gfl framework delay dependent mean square exponential stability criteria are established without involving model transformation cross terms bounding technique or additional free weighting matrix moreover gfl is also employed to obtain stability criteria for a class of uncertain linear stochastic neutral systems with different discrete and neutral delays numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing results

h control of switched delayed systems with average dwell time this paper considers the problems of stability analysis and h controller design of time delay switched systems with average dwell time in order to obtain less conservative results than what is seen in the literature a tighter bound for the state delay term is estimated based on the scaled small gain theorem and the model transformation method an improved exponential stability criterion for time delay switched systems with average dwell time is formulated in the form of convex matrix inequalities the aim of the proposed approach is to reduce the minimal average dwell time of the systems which is made possible by a new lyapunov krasovskii functional combined with the scaled small gain theorem it is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature moreover the exponential h controller can be constructed by solving a set of conditions which is developed on the basis of th

relaxed stability criteria for neural networks with time varying delay using extended secondary delay partitioning and equivalent reciprocal convex combination techniques this article investigates global asymptotic stability for neural networks nns with time varying delay which is differentiable and uniformly bounded and the delay derivative exists and is upper bounded first we propose the extended secondary delay partitioning technique to construct the novel lyapunov krasovskii functional where both single integral and double integral state variables are considered while the single integral ones are only solved by the traditional secondary delay partitioning second a novel free weight matrix equality fwme is presented to resolve the reciprocal convex combination problem equivalently and directly without schur complement which eliminates the need of positive definite matrices and is less conservative and restrictive compared with various improved reciprocal convex inequalities furthermore by the present extended secondary delay partitioning equivalent reciprocal convex combination technique and bessel legendre inequality two different relaxed sufficient conditions ensuring global asymptotic stability for nns are obtained for time varying delays respectively with unknown and known lower bounds of the delay derivative finally two examples are given to illustrate the superiority and effectiveness of the presented method

stability analysis and controller synthesis for discrete time delayed fuzzy systems via small gain theorem this paper investigates the problems of stability analysis and controller synthesis of discrete time takagi sugeno t s fuzzy systems with time varying delay via an input output approach the original system is reformulated as a feedback subsystem and a forward subsystem with two constant time delays and a delay uncertainty satisfying the scaled small gain theorem the lifting method is employed to convert the forward subsystem to a delay free system where the main result concerning the stability analysis of the system is obtained based on the scaled small gain theorem the merit of the new stability condition lies in its reduced conservatism which is made possible by a more precise estimation of the time varying delay additionally a state feedback controller is designed through the lyapunov krasovskii functional approach combined with the utilization of the scaled small gain theorem two illustrative examples are given to demonstrate the less conservatism of the stability condition and the effectiveness of the controller design method

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

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

module tensor product of subnormal modules need not be subnormal let d d c d d c be a diagonal positive definite kernel and let h h denote the associated reproducing kernel hilbert space of holomorphic functions on the open unit disc dd assume that zf hzf h whenever f hf h then hh is a hilbert module over the polynomial ring c z c z with module action p f pfp f pf we say that h h is a subnormal hilbert module if the operator mzmz of multiplication by the coordinate function z on h h is subnormal n salinas 1988 11 asked whether the module tensor product h 1 c z h 2h 1 c z h 2 of subnormal hilbert modules h 1h 1 and h 2h 2 is again subnormal in this regard we describe all subnormal module tensor products la2 d ws1 c z la2 d ws2 where la2 d ws denotes the weighted bergman hilbert module with radial weight ws z 1s z 2 1 s s z d s 0 in particular the module tensor product la2 d ws c z la2 d ws is never subnormal for any s 6s 6 thus the answer to this question is no

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

robust stabilization of uncertain t s fuzzy time delay systems with exponential estimates this paper deals with the problem of robust stabilization for uncertain takagi sugeno t s fuzzy systems with constant time delays the purpose is to design a state feedback fuzzy controller such that the closed loop system is robustly exponentially stable with a prescribed decay rate sufficient conditions for the solvability of this problem are presented in terms of linear matrix inequalities lmis by using feasible solutions of these lmis desired fuzzy controllers are designed and their corresponding exponential estimates are given in addition the main results of this paper are explicitly dependent on the decay rate this enables one to design fuzzy controllers by freely selecting decay rates according to different practical conditions two numerical examples are provided finally to demonstrate the effectiveness of the proposed design methods

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

accelerated low rank matrix approximate algorithms for matrix completion abstract in this paper we propose two accelerated algorithms for the low rank approximate method in wang et al 0000 for matrix completion the main idea is to use the successive over relaxation technique based on the successive over relaxation method for the feasible matrices or projection matrices the low rank matrix approximate method is modified and accelerated meanwhile we discuss the convergence of the over relaxation algorithm for the feasible matrix finally the numerical experiments show them to be effective

shape and motion from image streams under orthography a factorization method inferring scene geometry and camera motion from a stream of images is possible in principle but is an ill conditioned problem when the objects are distant with respect to their size we have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step an image stream can be represented by the 2fxp measurement matrix of the image coordinates of p points tracked through f frames we show that under orthographic projection this matrix is of rank 3 based on this observation the factorization method uses the singular value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively two of the three translation components are computed in a preprocessing stage the method can also handle and obtain a full solution from a partially filled in measurement matrix that may result from occlusions or tracking failures the method gives accurate results and does not introduce smoothing in either shape or motion we demonstrate this with a series of experiments on laboratory and outdoor image streams with and without occlusions

new results on a delay derivative dependent fuzzy h infty filter design for t s fuzzy systems this paper focuses on the fuzzy h filter design problem for takagi sugeno t s fuzzy systems with interval time varying delays two cases of the time varying delays are considered 1 the delays are differentiable and have both the lower and upper bounds of the delay derivatives and 2 the delays are bounded but not necessary to be differentiable since we employ a new fuzzy lyapunov krasovskii functional lkf and estimate a tighter upper bound of its derivative the proposed delay derivative dependent bound real lemma brl condition has advantages over some previous results in that it enlarges the application scope but has less conservatism which is established theoretically the brl condition that depends on both the upper and lower bounds of the delay derivatives is derived then based on the aforesaid brl a new fuzzy h filter scheme is proposed and a sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities lmis finally some numerical examples and an application to the truck trailer system are utilized to demonstrate the effectiveness and reduced conservatism of our results

stability analysis for delayed neural networks considering both conservativeness and complexity this paper investigates delay dependent stability for continuous neural networks with a time varying delay this paper aims at deriving a new stability criterion considering tradeoff between conservativeness and calculation complexity a new lyapunov krasovskii functional with simple augmented terms and delay dependent terms is constructed and its derivative is estimated by several techniques including free weighting matrix and inequality estimation methods then the influence of the techniques used on the conservativeness and the complexity is analyzed one by one moreover useful guidelines for improving criterion and future work are briefly discussed finally the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples

improved delay dependent robust stability criteria for uncertain time delay systems abstract this paper deals with the robust stability analysis for uncertain systems with time varying delay new delay dependent robust stability criteria of uncertain time delay systems are proposed by exploiting appropriate lyapunov functional candidate these developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism due to the introduction of a method to estimate the upper bound of the derivative of lyapunov functional candidate without ignoring the additional useful terms numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

robust stability of delay dependence for linear uncertain systems a sufficient condition for the stability of the linear uncertain time delay systems is presented the result obtained can include information on the size of the delay and therefore can be a delay dependent stability condition the lyapunov method is employed to investigate the problem the result is demonstrated by an illustrative example

stability analysis for linear delayed systems via an optimally dividing delay interval approach this paper addresses the problem of stability for linear systems with time varying delay a novel augmented lyapunov krasovskii functional is constructed by using the idea of optimally dividing the delay interval 0 t into some variable sub intervals and line integral technology using the novel augmented functional the new delay dependent stability criteria are proposed for linear systems with time varying delay the gain is that this stability criterion can lead to much less conservative stability results compared to other methods for linear systems with delay two numerical examples are provided to verify the effectiveness of the proposed criteria

absolute stability criteria for a class of nonlinear singular systems with time delay abstract this paper deals with the problem of absolute stability for a class of time delay singular systems with sector bounded nonlinearity both delay independent and delay dependent criteria are presented and formulated in the form of linear matrix inequalities lmis neither model transformation nor a bounding technique for cross terms nor a slack variable method is involved in obtaining the stability criteria numerical examples are given to show the effectiveness and improvements over some existing results

notes on stability of time delay systems bounding inequalities and augmented lyapunov krasovskii functionals the bounding inequalities and the lyapunov krasovskii functionals lkfs are important for the stability analysis of time delay systems much attention has been paid to develop tighter inequalities for improving stability criteria while the contribution of the lkfs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria this note is concerned with this issue firstly it is proved that when a simple lkf is applied the stability criteria obtained by the wirtinger based inequality and the jensen inequality are equivalent although the wirtinger based inequality is tighter it means that the tighter inequality does not always lead to a less conservative criterion secondly it is found that a suitable augmented lkf with necessary integral vectors in its derivative is required to achieve the advantage of the wirtinger based inequality based on this observation two delay product type terms are introduced into the lkf to establish new stability criteria finally a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria

on the rank minimization problem over a positive semidefinite linear matrix inequality we consider the problem of minimizing the rank of a positive semidefinite matrix subject to the constraint that an affine transformation of it is also positive semidefinite our method for solving this problem employs ideas from the ordered linear complementarity theory and the notion of the least element in a vector lattice this problem is of importance in many contexts for example in feedback synthesis problems and such an example is also provided

exponential stability of descriptor systems with large delay period based on a switching method this paper addresses the problem of exponential stability for a class of descriptor systems with interval time varying delays the time varying delays contain a large delay period ldp which is often present in practical control systems such descriptor system with ldp has been modeled as a switched descriptor system with delay which may include an unstable subsystem caused by large delay bound by adopting the switching technique and constructing a novel lyapunov krasovskii functional stability criteria are proposed under the restriction frequency and the rate of ldp to ensure that the descriptor system is regular impulse free and exponentially stable finally an integrated circuit example and a numerical simulation are given to illustrate the effectiveness and applicability of the proposed method