stability of a strongly stabilizing control for systems with a skew adjoint operator in hilbert space the stabilization problem of systems with a skew adjoint operator in a hilbert space is considered we prove that an one dimensional stabilizing feedback control allows a wide class of perturbations such that the system under consideration is strongly stabilizable with the aim of the perturbed controls

robust finite time h control of singular stochastic systems via static output feedback abstract this paper addresses the problem of robust finite time stabilization of singular stochastic systems via static output feedback firstly sufficient conditions of singular stochastic finite time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time varying norm bounded disturbance then the results are extended to singular stochastic h finite time boundedness for the class of singular stochastic systems designed algorithm for static output feedback controller is provided to guarantee that the underlying closed loop singular stochastic system is singular stochastic h finite time boundedness in terms of strict linear matrix equalities with a fixed parameter finally an illustrative example is presented to show the validity of the developed methodology

robust h control of descriptor discrete time markovian jump systems this paper considers the stochastic stability and the robust control of descriptor discrete time systems with markovian jumping parameters in terms of linear matrix inequalities a necessary and sufficient condition is proposed which ensures a discrete time descriptor markovian jump system to be regular causal and stochastically stable a robust admissibility condition and a robust bounded real lemma are also developed based on these a sufficient condition on the existence of a state feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique a robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities finally an example is provided to demonstrate the effectiveness of the proposed approach

stability analysis of neutral type systems in hilbert space the asymtoptic stability properties of neutral type systems are studied mainly in the critical case when the exponential stability is not possible we consider an operator model of the system in hilbert space and use recent results on the existence of a riesz basis of invariant finite dimensional subspaces in order to verify its dissipativity the main results concern the conditions of asymptotic non exponential stability we show that the property of asymptotic stability is not determinated only by the spectrum of the system but essentially depends on the geometric spectral characteristic of its main neutral term moreover we present an example of two systems of neutral type which have both the same spectrum in the open left half plane and the main neutral term but one of them is asymptotically stable while the other is unstable

tauberian theorems and stability of one parameter semigroups the main result is the following stability theorem let t t t tzo be a bounded co semigroup on a reflexive space x denote by a the generator of t and by a a the spectrum of a if a a n ir is countable and no eigenvalue of a lies on the imaginary axis then limt boo t t x o for all x e x

on properties not inherited by monoids from their schutzenberger groups we give an example of a monoid with finitely many left and right ideals all of whose schutzenberger groups are presentable by finite complete rewriting systems and so each have finite derivation type but such that the monoid itself does not have finite derivation type and therefore does not admit a presentation by a finite complete rewriting system the example also serves as a counterexample to several other natural questions regarding complete rewriting systems and finite derivation type specifically it allows us to construct two finitely generated monoids m and n with isometric cayley graphs where n has finite derivation type respectively admits a presentation by a finite complete rewriting system but m does not this contrasts with the case of finitely generated groups for which finite derivation type is known to be a quasi isometry invariant the same example is also used to show that neither of these two properties is preserved under finite green index extensions

a finiteness condition for rewriting systems abstract we present a purely combinatorial approach to the question of whether or not a finitely presented monoid has a finite canonical presentation our approach is based on the notion of finite derivation type which is a combinatorial condition satisfied by certain rewriting systems our main result states that if a monoid m has a finite canonical presentation then all finite presentations of m have finite derivation type by proving that a certain monoid s1 does not have finite derivation type we show in addition that the homological finiteness condition fp is not sufficient to guarantee that a finitely presented monoid with a decidable word problem has a finite canonical presentation

on the lyapunov theorem for singular systems in this paper we revisit the lyapunov theory for singular systems there are basically two well known generalized lyapunov equations used to characterize stability for singular systems we start with the lyapunov theorem of the work by lewis we show that the lyapunov equation of that theorem can lead to incorrect conclusion about stability some cases where that equation can be used are clarified we also show that an attempt to correct that theorem with a generalized lyapunov equation similar to the original one leads naturally to the generalized equation of takaba et al

on stabilization by state feedback for neutral differential difference equations in this paper we consider a class of feedback operators for a linear differential difference equation of the neutral type we show that if a system has unstable neutral root chains any stabilizing feedback operator in this class must contain a derivative of the delayed state component under the assumption of exact controllability we construct a stabilizing feedback operator

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

technical communique new bounded real lemma for discrete time singular systems in this paper the problem of bounded real lemma for discrete time singular system with strict matrix inequalities is investigated it is proved that the bounded real lemma for discrete singular system can be described by a strict matrix inequality the results lead to more tractable and reliable computation when applying them to design control systems

higher dimensional normalisation strategies for acyclicity we introduce acyclic polygraphs a notion of complete categorical cellular model for small categories containing generators relations and higher dimensional globular syzygies we give a rewriting method to construct explicit acyclic polygraphs from convergent presentations for that we introduce higher dimensional normalisation strategies defined as homotopically coherent ways to relate each cell of a polygraph to its normal form then we prove that acyclicity is equivalent to the existence of a normalisation strategy using acyclic polygraphs we define a higher dimensional homotopical finiteness condition for higher categories which extends squier s finite derivation type for monoids we relate this homotopical property to a new homological finiteness condition that we introduce here

the closure of the generalised eigenspace of a class of infinitesimal generators in this paper we study the fine geometric structure of a class of strongly continuous semigroups that satisfy the following property the resolvent of the infinitesimal generator can be represented as the quotient of entire functions of finite exponential type this class includes the solution map for functional differential equations and certain partial differential equations in particular we present necessary and sufficient conditions for one to oneness of the solution map and for completeness of the system of generalised eigenfunctions of the generator

on strong regular stabilizability for linear neutral type systems the problem of strong stabilizability of linear systems of neutral type is investigated we are interested in the case when the system has an infinite sequence of eigenvalues with vanishing real parts this is the case when the main part of the neutral equation is not assumed to be stable in the classical sense we discuss the notion of regular strong stabilizability and present an approach to stabilize the system by regular linear controls the method covers the case of multivariable control and is essentially based on the idea of infinite dimensional pole assignment proposed in g m sklyar a v rezounenko a theorem on the strong asymptotic stability and determination of stabilizing controls c r acad sci paris ser i math 333 8 2001 807 812 our approach is based on the recent results on the riesz basis of invariant finitedimensional subspaces and strong stability for neutral type systems presented in r rabah g m sklyar a v rezounenko stability analysis of neutral type systems in hilbert space j differential equations 214 2 2005 391 428

finite time control of discrete time linear systems in this note we consider the finite time stabilization of discrete time linear systems subject to disturbances generated by an exosystem finite time stability can be used in all those applications where large values of the state should not be attained for instance in the presence of saturations the main result provided in the note is a sufficient condition for finite time stabilization via state feedback this result is then used to find some sufficient conditions for the existence of an output feedback controller guaranteeing finite time stability all the conditions are then reduced to feasibility problems involving linear matrix inequalities lmis some numerical examples are presented to illustrate the proposed methodology

reliable finite time h filtering for discrete time delay systems with markovian jump and randomly occurring nonlinearities this paper is concerned with the problem of reliable finite time h filtering for discrete time varying delay systems with markovian jump and randomly occurring nonlinearities rons rons are introduced to model a class of sector like nonlinearities that occur in a probabilistic way according to a two dimensional discrete random variables joint distribution the failures of sensors are quantified by a variable varying in a given interval the time varying delay is unknown with given lower and upper bounds firstly the filtering errr dynamic system is constructed based on an h filter sufficient criteria are provided to guarantee that the resulting filtering error system is stochastic finite time boundedness and stochastic finite time h filtering in both normal and fault cases the gain matrices of the controller and filter are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter respectively finally numerical examples are given to demonstrate the effectiveness of the proposed design approach

technical communique finite time control of linear systems subject to parametric uncertainties and disturbances in this paper we consider finite time control problems for linear systems subject to time varying parametric uncertainties and to exogenous constant disturbances the main result provided is a sufficient condition for robust finite time stabilization via state feedback it can be applied to problems with both non zero initial conditions and unknown constant disturbances this condition is then reduced to a feasibility problem involving linear matrix inequalities lmis a detailed example is presented to illustrate the proposed methodology

periodic solutions for a class of neutral functional differential equations with infinite delay abstract in this paper we study the existence and uniqueness of periodic solutions of the nonlinear neutral functional differential equation with infinite delay of the form d d t x t 0 g s x t s d s a t x t x t f t x t in the process we use the fundamental matrix solution of x t a t u t x t and construct appropriate mappings where u c r r n is an periodic function then we employ matrix measure and the leray schauder fixed point theorem to show the existence of periodic solutions of this neutral differential equation in the special case where g s u 0 and a t x a t some sufficient conditions which ensure the uniform stability and global attractivity of a unique periodic solution are derived

a filtered repetitive controller for a class of nonlinear systems in this note a filtered repetitive controller frc is designed to compensate for periodic disturbances in a class of nonlinear systems first a new model of periodic disturbances is proposed by this model the frc is designed and the resulting closed loop error dynamics are analyzed with the help of a lyapunov krasovskii functional finally the method is applied to periodic disturbance rejection in a class of robotic manipulators compared with repetitive controllers the frc provides the flexibility to choose filter parameters to achieve a tradeoff between tracking performance and stability more importantly frc can deal with small input delay while the corresponding rc cannot

spectral assignment for neutral type systems and moment problems for a large class of linear neutral type systems the problem of assigning eigenvalues and eigenvectors is investigated i e finding the system that has the given spectrum and in some sense allmost all eigenvectors the solution of this problem enables vector moment problems to be considered using the construction of a neutral type system the exact controllability property of the system obtained gives the solution of the vector moment problem

analysis and design for discrete time linear systems subject to actuator saturation we present a method to estimate the domain of attraction for a discrete time linear system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis the following surprising result is revealed for systems with single input suppose that an ellipsoid is made invariant with a linear feedback then it is invariant under the saturated linear feedback if and only if there exists a saturated nonlinear feedback which makes the ellipsoid invariant finally the set invariance condition is extended to determine invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements

on energy to peak filtering for nonuniformly sampled nonlinear systems a markovian jump system approach this paper focuses on the filter design for nonuniformly sampled nonlinear systems which can be approximated by takagi sugeno t s fuzzy systems the sampling periods of the measurements are time varying and the nonuniform observations of the outputs are modeled by a homogenous markov chain a mode dependent estimator with a fast sampling frequency is proposed such that the estimation can track the signal to be estimated with the nonuniformly sampled outputs the nonlinear systems are discretized with the fast sampling period by using an augmentation technique the corresponding stochastic estimation error system is obtained by studying the stochastic stability and the energy to peak performance of the estimation error system we derive the linear matrix inequality based sufficient conditions the parameters of the mode dependent estimator can be calculated by using the proposed iterative algorithm two examples are used to demonstrate the design procedure and the efficacy of the proposed design method

extended dissipative state estimation for markov jump neural networks with unreliable links this paper is concerned with the problem of extended dissipativity based state estimation for discrete time markov jump neural networks nns where the variation of the piecewise time varying transition probabilities of markov chain is subject to a set of switching signals satisfying an average dwell time property the communication links between the nns and the estimator are assumed to be imperfect where the phenomena of signal quantization and data packet dropouts occur simultaneously the aim of this paper is to contribute with a markov switching estimator design method which ensures that the resulting error system is extended stochastically dissipative in the simultaneous presences of packet dropouts and signal quantization stemmed from unreliable communication links sufficient conditions for the solvability of such a problem are established based on the derived conditions an explicit expression of the desired markov switching estimator is presented finally two illustrated examples are given to show the effectiveness of the proposed design method

the analysis of exact controllability of neutral type systems by the moment problem approach the problem of exact null controllability is considered for a wide class of linear neutral type systems with distributed delay the main tool of the analysis is the application of the moment problem approach and the theory of the basis property of exponential families a complete characterization of this problem is given the minimal time of controllability is specified the results are based on the analysis of the riesz basis property of eigenspaces of the neutral type systems in hilbert space

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

analysis and design of singular linear systems under actuator saturation and l2 l disturbances abstract this paper carries out an analysis of the l 2 gain and l performance for singular linear systems under actuator saturation the notion of bounded state stability bss with respect to the influence of l 2 or l disturbances is introduced and conditions under which a system is bounded state stable are established in terms of linear matrix inequalities lmis the disturbance tolerance capability of the system is then measured as the bound on the l 2 or l norm of the disturbances under which the system remains bounded state stable and the disturbance rejection capability is measured by the restricted l 2 gain from the disturbance to the system output or l norm of the system output based on the bss conditions assessment of the disturbance tolerance and rejection capabilities of the system under a given state feedback law is formulated and solved as lmi constrained optimization problems by viewing the feedback gain as an additional variable these optimization problems can be readily adapted for control design our analysis and design reduce to the existing results for regular linear systems in the degenerate case where the singular linear system reduces to a regular system and to the existing results for singular systems in the absence of actuator saturation or when the disturbance is weak enough to not cause saturation

finite time h control for a class of discrete time switched singular time delay systems subject to actuator saturation this paper concerns with the finite time h control problem for a class of discrete time switched singular time delay with actuator saturation not only linear matrix inequality conditions for the systems but also average dwell time of switching signal is given to guarantee regular causal and finite time boundedness for the discrete time switched singular time delay system moreover sufficient conditions are presented to ensure the h disturbance attenuation level and the design method of h controller is developed by solving linear matrix inequalities lmi optimization problem without any decompositions of system matrices and equivalent transformation furthermore the function in the proof procedure belongs to multiple lyapunov like functions whose advantage lies in their flexibility finally numerical examples are employed to verify the effectiveness of the proposed methods and to illustrate the significant improvement on the conservativeness of some reported results in the literature

robust finite time h control for discrete time singular markovian jump systems with time varying delay and actuator saturation in this paper the problem of robust finite time h control for discrete time singular markovian jump systems with time varying delay and actuator saturation is studied first sufficient conditions that guarantee the systems singular stochastic finite time boundedness are derived via constructing a delay dependent lyapunov krasonskii functional and linear matrix inequalities lmi approaches then the results are extended to singular stochastic finite time h boundedness furthermore with these conditions and convex optimization arithmetic the design method of h controller and conditions that ensure the h disturbance attenuation level are obtained finally some numerical examples are presented to illustrate the validity and efficiency of the proposed methods

exponential mean square stability of time delay singular systems with markovian switching and nonlinear perturbations abstract this paper considers exponential stability in mean square of singular markovian jump systems the systems under consideration involve nonlinear perturbation and time varying delays by using the lyapunov krasovskii functional delay dependent stability conditions in terms of linear matrix inequality lmi are addressed which guarantee exponential mean square stability and a prescribed h performance index for the considered systems two numerical examples are given to illustrate the effectiveness of the proposed main results

asymptotic stability of a class of neutral delay neuron system in a critical case in this brief the asymptotic stability properties of a neutral delay neuron system are studied mainly in a critical case when the exponential stability is not possible if a critical value of the coefficient in the neutral delay neuron system is considered then the difficulty for our investigation is caused by the fact that the spectrum of the linear operator is asymptotically approximated to the imaginary axis it is obvious that in such a case the equation is not exponentially stable and one needs more subtle methods in order to characterize this type of asymptotic stability hence first the local asymptotic stability for the neutral delay neuron system is studied and the main tools involved are the asymptotic expansions of characteristic roots laplace transforms and function series and a complete analysis of the stability diagram is also presented then based on the energy method the globally asymptotic stability results for the neutral delay neuron system are derived

for finitely presented monoids the homological finiteness conditions fht and bi fp3 coincide abstract fht is a homological finiteness condition of monoids that was introduced by pride and wang for finitely presented groups this property is equivalent to the homological finiteness condition fp 3 but for finitely presented monoids in general it is strictly stronger than the conditions left fp 3 and right fp 3 together here we define the notion of bi fp n for monoids using bimodules instead of left or right modules and by establishing an exact sequence involving the relation bimodule of a monoid we prove that for finitely presented monoids the property fht is equivalent to the finiteness condition bi fp 3

composite nonlinear feedback control for linear singular systems with input saturation abstract this paper investigates the composite nonlinear feedback cnf control technique for linear singular systems with input saturation first a linear feedback control law is designed for the step tracking control problem of linear singular systems subject to input saturation then based on this linear feedback gain a cnf control law is constructed to improve the transient performance of the closed loop system by introducing a generalized lyapunov equation this paper develops a design procedure for constructing the cnf control law for linear singular systems with input saturation after decomposing the closed loop system into fast subsystem and slow subsystem it can be shown that the nonlinear part of the cnf control law only relies on slow subsystem the improvement of transient performance by the proposed design method is demonstrated by an illustrative example