canonical forms for time delay systems polynomial transformations are considered for linear systems with time delays a technique for state reduction is given as well as schemes for obtaining other useful canonical forms the results are achieved using a combination of module theoretic ideas polynomial ring and functional analysis

strong detectability and observers conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state the concepts of strong detectability and strong observability introduced before in the literature for discrete time systems only are defined and studied for continuous time systems it is shown that there are two different concepts of strong detectability which coincide for discrete time systems algebraic conditions for either concept are given it is shown that these concepts are intimately related to the existence of strong observers i e observers that only use the output of the plant

equivalence of linear time delay systems the question of characterizing those time delay systems which are equivalent up to bicausal transformations to a delay free system is a natural and fundamental problem which has been raised since the early 1980s surprisingly this problem remains largely open despite that some partial answers have been provided this technical note tackles this problem for linear systems with constant time delays and gives necessary and sufficient conditions to eliminate whenever is possible or to reduce the number of time delays and a constructive way to get the corresponding bicausal change of coordinates

on the observer design for descriptor systems for the descriptor system ex ax bu y cx du an observer of the order p rank e p sub 1 0

local automorphisms of finite dimensional simple lie algebras abstract let g be a finite dimensional simple lie algebra over an algebraically closed field k of characteristic 0 a linear map g g is called a local automorphism if for every x in g there is an automorphism x of g such that x x x we prove that a linear map g g is local automorphism if and only if it is an automorphism or an anti automorphism

design of observers for linear systems with unknown inputs with a straightforward treatment a design of reduced order observers is presented for linear systems with unknown inputs the observers are derived with a physical meaning some explanations are given within the framework of descriptor system observer design principles the conditions for the existence of the observers are presented some illustrative examples are included

observability of singular systems with commensurate time delays and neutral terms this paper deals with the observability problem of a sort of singular systems with commensurate time delays in the trajectories of the system in the time derivative of the trajectories neutral terms and in the output system by using a recursive algorithm sufficient conditions easy testable are proposed for guaranteeing the backward and the algebraic observability of the system this condition implies that the trajectories of the system can be reconstructed by using the actual and past values of the system output

observability of singular time delay systems with unknown inputs in this manuscript we give sufficient conditions guaranteeing the observability of singular linear systems with commensurable delays affected by unknown inputs appearing in both the state equation and the output equation these conditions allow for the reconstruction of the entire state vector using past and actual values of the system output the obtained conditions coincide with known necessary and sufficient conditions of singular linear systems without delays

brief analysis of nonlinear time delay systems using modules over non commutative rings the theory of non commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays the left ore ring of non commutative polynomials defined over the field of meromorphic function is suggested as the framework for such a study this approach is then generalized to a broader class of nonlinear systems with delays that are called generalized roesser systems finally the theory is applied to analyze nonlinear time delay systems a weak observability is defined and characterized generalizing the well known linear result properties of closed submodules are then developed to obtain a result on the accessibility of such systems

2 local automorphisms on finite dimensional lie algebras abstract we prove that every 2 local automorphism on a finite dimensional semi simple lie algebra l over an algebraically closed field of characteristic zero is an automorphism we also show that each finite dimensional nilpotent lie algebra l with dim l 2 admits a 2 local automorphism which is not an automorphism

on observation of time delay systems with unknown inputs causal and non causal observability are discussed in this technical note for nonlinear time delay systems with unknown inputs using the theory of non commutative rings and the algebraic framework introduced by xia the nonlinear time delay system is transformed into a suitable canonical form to solve the problem a necessary and sufficient condition is given to guarantee the existence of a change of coordinates leading to such a form

the pluricomplex poisson kernel for strongly convex domains let d be a bounded strongly convex domain in the complex space of dimension n for a fixed point p epsilon partial derivative d we consider the solution of a homogeneous complex monge ampere equation with a simple pole at p we prove that such a solution enjoys many properties of the classical poisson kernel in the unit disc and thus deserves to be called the pluricomplex poisson kernel of d with pole at p in particular we discuss extremality properties such as a generalization of the classical phragmen lindelof theorem relations with the pluricomplex green function of d uniqueness in terms of the associated foliation and boundary behaviors finally using such a kernel we obtain explicit reproducing formulas for plurisubharmonic functions

exact state variable reconstruction of delay systems the problem of state variable reconstruction for a class of single input single output siso linear time delay system is considered a method for the exact reconstruction of state variables from the input and observed output of the system is presented

finite time and asymptotic left inversion of nonlinear time delay systems in this paper we investigate the left invertibility problem for a class of nonlinear time delay systems in both cases of time delay systems with and without internal dynamics the invertibility conditions are given a new approach based on the use of higher order sliding mode observer is developed for finite time left invertibility and for asymptotic left inversion causal and non causal estimations of the unknown inputs are respectively discussed the results are illustrated by numerical examples in order to show the efficiency of the method and its limits

2 local automorphisms of finite dimensional simple lie algebras abstract let f be an algebraically closed field of characteristic 0 l be a finite dimensional simple lie algebra of type a l l 1 d l l 4 e k k 6 7 8 over f a not necessarily linear map l l is called a 2 local automorphism if for every x y l there is an automorphism x y l l depending on x and y such that x x y x y x y y in this paper we prove that any 2 local automorphism of l is an automorphism

2 local derivations on finite dimensional lie algebras abstract we prove that every 2 local derivation on a finite dimensional semi simple lie algebra l over an algebraically closed field of characteristic zero is a derivation we also show that a finite dimensional nilpotent lie algebra l with dim l 2 admits a 2 local derivation which is not a derivation

unknown input observer for linear time delay systems this paper investigates an unknown input observer design for a large class of linear systems with unknown inputs and commensurate delays a luenberger like observer is proposed by involving only the past and actual values of the system output the required conditions for the proposed observer are considerably relaxed in the sense that they coincide with the necessary and sufficient conditions for the unknown input observer design of linear systems without delays

linear systems with commensurate time delays stability and stabilization independent of delay notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays constructive methods for determining a stabilizing feedback are also presented the last part of the paper deals with a standard type of observer and regulator with the requirement that the closed loop system be stable independent of delay

decoupling and arbitrary coefficient assignment in time delay systems this paper considers decoupling control of time delay systems we assume a new decoupling condition which is stronger than the one obtained until now and r controllability then a dynamic compensator to achieve decoupling and arbitrary coefficient assignment is presented

2 local derivations and automorphisms on b h abstract this paper is devoted to 2 local derivations and 2 local automorphisms on the algebra b h of all bounded linear operators on a hilbert space h we prove that every 2 local derivation on b h is a derivation a similar result is obtained for automorphisms

stability of stochastic functional differential systems using degenerate lyapunov functionals and applications motivated by the seminal work of dupire 2009 on functional ito formulas this work investigates asymptotic properties of systems represented by stochastic functional differential equations sfdes stability of general delay dependent sfdes is investigated using degenerate lyapunov functionals which are only positive semi definite rather than positive definite as used in the classical work this paper first establishes boundedness and regularity of sfdes by using degenerate lyapunov functionals then moment and almost sure exponential stabilities are obtained based on degenerate lyapunov functionals and the semi martingale convergence theorem as an application of the stability criteria consentability of stochastic multi agent systems with nonlinear dynamics is studied

on the design of observers for generalized state space systems using singular value decomposition in this paper a method is developed for the design of luenberger type observers for linear time invariant control systems whose state equation is of the form ex ax bu where e is a singular square matrix the method is based on the singular value decomposition of the matrix e and on the reduction of the equation ex ax bu to a system consisting of a differential equation of the form w1 f1w1 f2 w2 g1u and an algebraic equation of the form h1w1 h2w2 g1u 0 if w2 can be eliminated from the differential equation by the aid of the algebraic equation and the original output equation of the system the method yields a reduced order observer for the generalized state space system

text ad _ f g text ad _ f g and locally text ad _ f g invariant and controllability distributions in the study of nonlinear control systems the concepts of an invariant foliation and an invariant distribution play important roles in this paper we explore various forms of these concepts and show how they occur in the study of controllability observability and decoupling of nonlinear systems

2 bilocal derivations abstract let x be a banach space and a be a unital subalgebra of b x containing all finite rank operators in b x a map a b x is called a 2 bilocal derivation if for a b a x x there exists a derivation a b x such that a a b x a x and b x a b x b x in this paper we show that each 2 bilocal derivation on a is a derivation

observers for descriptor systems for a singular non causal descriptor system of order n a p k lh order observer is proposed where p n q q is the number of infinite non dynamic modes of the system and k is the rank of a matrix obtained from a transformed system derived by using the singular value decomposition some useful results are given which establish the existence of this observer and which resolve problems encountered with pth order observers proposed in the literature robustness is achieved by choosing optimum gain matrices which reduce the sensitivity of observer performance to perturbations

detectability of linear systems over a principal ideal domain with unknown inputs abstract observability and detectability conditions are obtained for a sort of linear time invariant systems affected by unknown inputs it is assumed that the system can be described using matrices whose elements are within a principal ideal domain pid it is shown that under suitable hypothesis the obtained conditions are necessary and sufficient the analysis is carried out by making use of the smith normal form of matrices over a pid the obtained conditions are a generalization of known conditions for particular sorts of systems which are included in those considered here

design of observers for descriptor systems in this note simple and straightforward methods to design full and reduced order observers for linear time invariant descriptor systems are presented the approach for the reduced order observer design is based on the generalized sylvester equation sufficient conditions for the existence of the observers are given an illustrative example is included

observability and related structural results for linear hereditary systems new results on the theory of observability and deterministic observers for linear time invariant systems with delays are presented the results have been established only for the case of point delays which are commensurable however most of the results can be generalized to the situation with distributed delays and to the ease with non commensurate delays

observability and observers for a class of linear systems with delays a brief description of observability detectability and spectral observability concepts for time delay systems is given and some results on relations between these concepts are presented another result of this correspondence is the derivation of constructive design procedures for dynamic observers for a large class of linear autonomous systems with time delays this class includes systems with arbitrary output measurement delays where the procedure is based on well known methods of spectrum assignment for a pair of real matrices it is also shown that the observer problem for general systems with delays can be reformulated so as to get an easier case without output delays

observability of linear systems with commensurate delays and unknown inputs this paper investigates the observability analysis for linear time systems whose outputs are affected by unknown inputs three different definitions of observability are proposed by introducing the smith form and comparing the invariant factors a sufficient condition is deduced for each proposed definition observability several examples are given for the purpose of highlighting the effectiveness of the proposed approach

monge ampere equations and moduli spaces of manifolds of circular type abstract a bounded manifold of circular type is a complex manifold m of dimension n admitting a bounded exhaustive real function u defined on m minus a point x o so that a it is a smooth solution on m x o to the monge ampere equation d d c u n 0 b x o is a singular point for u of logarithmic type and e u extends smoothly on the blow up of m at x o c d d c e u 0 at any point of m x o this class of manifolds naturally includes all smoothly bounded strictly linearly convex domains and all smoothly bounded strongly pseudoconvex circular domains of c n a set of modular parameters for bounded manifolds of circular type is considered in particular for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form it is also shown that the class of normalizing maps for an n dimensional manifold m is a new holomorphic invariant with the following property it is parameterized by the points of a finite dimensional real manifold of dimension n 2 when m is a non convex circular domain while it is of dimension n 2 2 n when m is a strictly linearly convex domain new characterizations of the circular domains and of the unit ball are also obtained

smith forms over r z_ 1 z_ 2 relationships between a polynomial matrix and its smith forms are explored it is shown for example that a matrix over r z 1 z 2 is equivalent to its smith form over r z 1 z 2 if and only if a certain system of linear polynomial equations has a solution

observers for descriptor systems abstract the design of observers is investigated for the estimation of the descriptor vector x t of descriptor systems of the form ex t ax t bu t y t cx t such systems are divided into two categories non causal impulsive systems and causal impulse free systems for non causal systems an observer of order rank e is proposed and termed a full order observer since the dynamical order of a descriptor system is regarded as rank e for causal systems it is shown that the number of independent outputs m does not exceed rank e and an observer of order rank e m is introduced and termed a minimal order observer the approach is based on the transformation of the system into particular design coordinates via a singular value decomposition of the matrix e illustrative examples are included

a geometric approach to dynamic feedback cyclization over commutative rings a different geometric point of view is introduced in the study of dynamic feedback cyclization over rings this considerably simplifies the theory in the free case in the sense that the main results can now be obtained by simple proofs the non free case remains to be examined

decoupling and coefficient assignment for a b c d time delay systems using v as the time delay operator a linear invariant time delay system is expressed by a quadruple a b c v d v with the matrices over a polynomial ring in v this paper studies the decoupling and coefficient assignment of such a system for a class of time delay systems non controllable over the polynomial ring in v but controllable over the field of rational functions in v we present sufficient conditions under which the system characteristic polynomial may be determined arbitrarily by feasible control laws two examples are investigated to illustrate the theory

observers for linear systems with unknown inputs a direct design procedure of a full order observer for a linear system with unknown inputs is presented using straightforward matrix calculations some examples are given in these examples a reduced order observer is also derived it is shown that this may restrict the rate of convergence of some state estimates

linear functional observers for systems with delays in state variables this paper is concerned with the design of linear functional state observers for systems with delays in state variables in particular the necessary and sufficient conditions for the existence of the rth order observers are given sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear matrix in equality formulation a systematic design method of these observers is presented numerical examples are given to illustrate this method

observer design for linear singular time delay systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state and its derivatives the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantees the existence of a luenberger like observer for the general system

weak 2 local symmetric maps on c algebras abstract we introduce and study weak 2 local symmetric maps between c algebras a and b as not necessarily linear nor continuous maps a b such that for each a b a and b there exists a symmetric linear map t a b a b depending on a b and satisfying a t a b a and b t a b b we prove that every weak 2 local symmetric map between c algebras is a linear map among the consequences we show that every weak 2 local derivation on a general c algebra is a linear derivation we also establish a 2 local version of the kowalski slodkowski theorem for general c algebras by proving that every 2 local homomorphism between c algebras is a linear homomorphism

technical communique an improved result for complete stability of delayed cellular neural networks this paper provides a new sufficient condition for the complete stability of the delayed cellular neural networks this condition imposes constraints on the parameters of the networks and the size of time delay the linear matrix inequality approach plays an important role in the proof our result recovers the known results in the earlier literature as special cases finally we give an example to illustrate the applicability of our main result

linear systems with delayed controls a reduction linear systems with delayed control action are transformed into systems without delays under an absolute continuity condition the new system is an ordinary differential control equation in the general case the new system is a measure differential control system it is shown how the controllability stabilization and various optimization problems can be analyzed via the reduced systems

identification of the delay parameter for nonlinear time delay systems with unknown inputs using the theory of non commutative rings this paper studies the delay identification of nonlinear time delay systems with unknown inputs a sufficient condition is given in order to deduce an output delay equation from the studied system then necessary and sufficient conditions are proposed to judge whether the deduced output delay equation can be used to identify delay involved in this equation two different cases are discussed for the dependent and independent outputs respectively the presented result is applied to identify delay in a biological system

local derivations on finite dimensional lie algebras abstract we prove that every local derivation on a finite dimensional semisimple lie algebra over an algebraically closed field of characteristic zero is a derivation we also give examples of finite dimensional nilpotent lie algebras l with dim l 3 which admit local derivations which are not derivations

unknown input functional observability of descriptor systems with neutral and distributed delay effects in this paper a general class of linear systems with time delays is considered which includes linear classical systems linear systems with commensurate delays neutral systems and singular systems with delays after given a formal definition of functional backward observability bo an easily testable condition is found the fulfillment of the obtained condition allows for the reconstruction of the trajectories of the system under consideration using the actual and past values of the system output and some of its derivatives the methodology we follow consists in an iterative algorithm based upon the classical silverman algorithm used for inversion of linear systems by using basic module theory we manage to prove that the proposed algorithm is convergent a direct application of studying functional observability is that a condition can be derived for systems with distributed delays also we do this as a case of study the obtained results are illustrated by two examples one is merely academic but illustrates clearly the kind of systems which the proposed methodology works for and the other is a practical system with distributed delays

2 local derivations on associative and jordan matrix rings over commutative rings abstract in the present paper we prove that every 2 local inner derivation on the matrix ring over a commutative ring is an inner derivation and every derivation on an associative ring has an extension to a derivation on the matrix ring over this associative ring we also develop a jordan analog of the above method and prove that every 2 local inner derivation on the jordan matrix ring over a commutative ring is a derivation

a reduced order observer for descriptor systems abstract in this paper a reducer order observer is analyzed for so called generalized state space or descriptor systems based on the staircase form for generalized state space models a recursive algorithm is presented to construct a reduced order observer for a given observable descriptor system in the algorithm only the eigenfrequencies of the observer have to be specified

reduced order observer construction by generalized matrix inverse a procedure is presented to construct a reduced order observer for a linear time invariant system defined by a state space description the construction procedure makes use of the concept of a generalized matrix inverse and does not presuppose the observer structure illustrative examples arc included

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

stabilization of generalized linear systems via the algebraic riccati equation abstract this paper presents results from a study to examine the stabilization properties of linear time delay systems and systems depending on a parameter using techniques associated with the algebraic riccati equation are these classes of systems can be viewed as members of a broader class of systems called generalized linear systems gls techniques of spectral factorization for the gls play an essential role in the methods for performing this stabilization necessary and sufficient conditions for the existence of a polynomial solution to the generalized are are derived numerical examples are given in order to illustrate and clarify the results

an observer design for linear time delay systems an observer design is proposed for linear systems with time delays the key to the design is to find a generalized coordinate change such that in the new coordinates all the time delay terms are injected by the system s output the existence of such a coordinate change is guaranteed by a rank condition on the observability matrix the novelty of the proposed design is clearly reflected in the multiple output case where a dimensional expansion in the coordinate change could become necessary and hence is allowed

observers for discrete singular systems the author considers the design of observers for the discrete singular system ex k 1 ax k bu k y k cx k placing special emphasis on the problems of state reconstruction and minimal time state reconstruction it is shown that for a singular system finite poles can be moved to infinity by state feedback and the state can be reconstructed by causal observers

design of a minimal order observer for singular systems this paper considers the design of an observer for generalized state space systems using the concept of generalized inverses in contrast to the luenberger observer theory a new method is proposed which does not presuppose the observer structure it is shown that under certain conditions it is possible to construct a minimal order observer for this class of systems illustrative examples are included

the disturbance decoupling problem for time delay nonlinear systems in this paper the disturbance decoupling problem ddp for a class of siso nonlinear systems with multiple delays in the input and the state is studied a pioneering mathematical approach is introduced for this class of systems and is claimed to be the cornerstone of the problem necessary and sufficient conditions are given for the existence of a bicausal feedback that solves the ddp sufficient conditions for the existence of a solution within other classes of compensators are included as well

regulation of split linear systems over rings coefficient assignment and observers a theory of regulators is developed for finite free split linear systems over a commutative ring k this is achieved by developing a theory of coefficient assignment and observers it is shown that the problem of coefficient assignment can be solved for reachable systems by using dynamic state feedback for strongly observable systems it is shown that observers with arbitrary dynamics can be constructed internal stability of observer and state feedback configuration is considered explicitly some examples are given to illustrate these techniques

monge ampere foliations with singularities at the boundary of strongly convex domains let d c n be a bounded strongly convex domain with smooth boundary we consider a monge ampere type equation in d with a simple pole at the boundary using the lempert foliation of d in extremal discs we construct a solution u whose level sets are bound aries of horospheres among other things we show that the biholomorphisms between strongly convex domains are exactly those maps which preserves our solution