dimensionally dependent tensor identities by double antisymmetrization some years ago lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure and could all be considered consequences in n dimensional space of a pair of fundamental identities involving trace free p p forms where 2p n we generalize lovelock s results and by using the fact that associated with any tensor in n dimensional space there is associated a fundamental tensor identity obtained by antisymmetrizing over n 1 indices we establish a very general master identity for all trace free k l forms we then show how various other special identities are direct and simple consequences of this master identity in particular we give direct application to maxwell lanczos ricci bel and bel robinson tensors and also demonstrate how relationships between scalar invariants of the riemann tensor can be investigated in a systematic manner

necessary and sufficient conditions for n dimensional conformal einstein spaces via dimensionally dependent identities listing has recently extended results of kozameh newman and tod for four dimensional space times and presented a set of necessary and sufficient conditions for a metric to be locally conformally equivalent to an einstein metric in all semi riemannian spaces of dimension n 4 subject to a nondegeneracy restriction on the weyl tensor by exploiting dimensionally dependent identities we demonstrate how to construct two alternative versions of these necessary and sufficient conditions which we believe will be useful in applications the four dimensional case is discussed in detail and examples are also given in five and six dimensions

stabilization of discrete time markovian jump linear systems via time delayed controllers this paper is concerned with the stabilization problem for a class of discrete time markovian jump linear systems with time delays both in the system state and in the mode signal the delay in the system state may be time varying the delay in the mode signal is manifested as a constant mismatch of the modes between the controller and the system we first show that the resulting closed loop system is a time varying delayed markovian jump linear system with extended state space then a sufficient condition is proposed for the design of a controller such that the closed loop system is stochastically stable finally numerical simulation is used to illustrate the developed theory

stability analysis for continuous systems with two additive time varying delay components this paper presents a new result of stability analysis for continuous systems with two additive time varying delay components which represent a general class of delay systems with strong application background in network based control systems this criterion is expressed as a set of linear matrix inequalities which can be readily tested by using standard numerical software a numerical example is provided to show the effectiveness and advantage of the proposed stability condition

new results on stability of discrete time systems with time varying state delay this note is concerned with the stability analysis of discrete time systems with time varying state delay by defining new lyapunov functions and by making use of novel techniques to achieve delay dependence several new conditions are obtained for the asymptotic stability of these systems the merit of the proposed conditions lies in their less conservativeness which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms sigmam k dk k 1 middot and sigma m k dm k 1 middot which is largely ignored in the existing literature these conditions are shown via several examples to be much less conservative than some existing result

on stabilization of uncertain linear systems with jump parameters in this paper we study the problem of robust stabilizability of the class of uncertain linear systems with markovian jumping parameters under the assumption of complete access to the continuous state the stochastic stabilizability of the nominal system and the boundedness of the system s uncertainties sufficient conditions which guarantee the robust stability of the uncertain systems are presented which are in terms of a set of coupled algebraic riccati equations a numerical example is given to illustrate the potential of the proposed technique

the lanczos potential for the weyl curvature tensor existence wave equation and algorithms in the last few years renewed interest in the 3 tensor potential l abc proposed by lanczos for the weyl curvature tensor has not only clarified and corrected lanczos9s original work but generalized the concept in a number of ways in this paper we first of all carefully summarize and extend some aspects of these results make some minor corrections and clarify some misunderstandings in the literature the following new results are also presented the computer checked complicated second order partial differential equation for the 3 potential in arbitrary gauge for weyl candidates satisfying bianchi type equations is given in those n dimensional spaces with arbitrary signature for which the potential exists this is easily specialized to lanczos potentials for the weyl curvature tensor it is found that it is only in four dimensional spaces with arbitrary signature that the nonlinear terms disappear and that certain awkward second order derivative terms cancel for four dimensional spacetimes with lorentz signature this remarkably simple form was originally found by illge using spinor methods it is also shown that for most four dimensional vacuum spacetimes any 3 potential in the lanczos gauges which satisfies a simple homogeneous wave equation must be a lanczos potential for the non zero weyl curvature tensor of the background vacuum spacetime this result is used to prove that the form of a possible lanczos potential recently proposed by dolan and kim for a class of vacuum spacetimes is in fact a genuine lanczos potential for these spacetimes

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

robust controller design for uncertain systems with time delays lmi approach we present a robust output feedback controller design method for linear systems with norm bounded time varying parameter uncertainties and time varying delays in both states and controls and sufficient conditions for the existence of the robust output feedback controller of any order are given in terms of three linear matrix inequalities lmis furthermore we provide a parameterization of all robust controllers from the positive definite solutions of the lmis

the identities of the algebraic invariants of the four dimensional riemann tensor this paper extends the investigation of the invariants of the riemann tensor to include the invariants that are of odd degree in the trace free ricci tensor it is shown that these invariants can be expressed in terms of 15 such invariants that are irreducible as a consequence it is possible to write down a complete set of invariants of the riemann tensor several syzygies for these invariants have been found and examples of these are given these syzygies suggest there may be several new syzygies of invariants with even degree in the trace free ricci tensor a large number of these have also been found and are discussed in the paper

linear independence of renormalization counterterms in curved space times of arbitrary dimensionality the counterterms in the lagrangian of a renormalizable quantum field theory that involve the riemann curvature tensor are considered it is proved that for six or fewer dimensions the counterterms not containing derivatives of the riemann tensor are linearly independent it is shown that there appears to be a maximum space time dimension for which identities can exist among invariants involving the product of n riemann tensors without derivatives acting on them space times that would require these products as counterterms for a renormalizable theory have a dimensionality which is one higher than this maximum dimension this makes it plausible that the required set of counterterms not involving derivatives of the riemann tensor is linearly independent in arbitrary dimensions in the appendix a relation cubic in the weyl tensor which relates invariants cubic in the riemann tensor in five dimensions is proved

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

brief paper new results on stabilization of markovian jump systems with time delay this paper studies the problem of stochastic stabilization for a class of markovian jump systems with time delay a new delay dependent stochastic stability criterion on the stochastic stability of the system is derived based on a novel lyapunov krasovskii functional lkf approach the equivalence and superiority to existing results are demonstrated then a state feedback controller which guarantees the stochastic stability of the closed loop system is designed illustrative examples are provided to show the reduced conservatism and effectiveness of the proposed techniques

practical stability controllability and optimal control of stochastic markovian jump systems with time delays the notions of the practical stability in probability and in the pth mean and the practical controllability in probability and in the pth mean are introduced for some stochastic systems with markovian jump parameters and time varying delays sufficient conditions on such practical properties are obtained by using the comparison principle and the lyapunov function methods besides for a class of stochastic nonlinear systems with markovian jump parameters and time varying delays existence conditions of optimal control are discussed particularly for linear systems optimal control and the corresponding index value are presented for a class of quadratic performance indices with jumping weighted parameters

on effective constraints for the riemann lanczos system of equations there have been conflicting points of view concerning the riemann lanczos problem in three and four dimensions using direct differentiation on the defining partial differential equations massa and pagani in four dimensions and edgar in dimensions n 3 have argued that there are effective constraints so that not all riemann tensors can have lanczos potentials using cartan s criteria of integrability of ideals of differential forms bampi and caviglia have argued that there are no such constraints in dimensions n 4 and that in these dimensions all riemann tensors can have lanczos potentials in this article we give a simple direct derivation of a constraint equation confirm explicitly that known exact solutions of the riemann lanczos problem satisfy it and argue that the bampi and caviglia conclusion must therefore be flawed in support of this we refer to the recent work of dolan and gerber on the three dimensional problem by a method closely related to that of bampi and caviglia they have fou

convergence criteria for attracting cycles of newton s method let f be a one dimensional real or complex analytic map it is well known that newton s method may fail to find a zero of f if the initial guess x 0 lies near a nonfixed periodic orbit of the newton dynamical system x n 1 x n f x n f x n for each period r ge 2 this paper identifies such initial guesses by stating sufficient conditions for newton s method beginning at x 0 to converge toward an attracting periodic orbit of period r criteria for convergence toward such an orbit are obtained for the dynamical system defined by any map which is specified as a quotient of analytic functions

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

identities of the scalars of the four dimensional riemannian manifold a general algorithm is presented for the calculation of identities relating scalars constructed from appropriate contractions of the riemann tensor ricci tensor and curvature scalar the algorithm is applied to determining the identities among the quartic scalars

old and new results for superenergy tensors from dimensionally dependent tensor identities it is known that some results for spinors and in particular for superenergy spinors are much less transparent and require a lot more effort to establish when considered from the tensor viewpoint in this paper we demonstrate how the use of dimensionally dependent tensor identities enables us to derive a number of 4 dimensional identities by straightforward tensor methods in a signature independent manner in particular we consider the quadratic identity for the bel robinson tensor tabcxtabcy xy tabcdtabcd 4 and also the new conservation law for the chevreton tensor both of which have been obtained by spinor means both of these results are rederived by tensor means for 4 dimensional spaces of any signature using dimensionally dependent identities and moreover we are able to conclude that there are no direct higher dimensional analogs in addition we demonstrate a simple way to show the nonexistense of such identities via counter examples in particular we show that there is no nontrivial bel ten

robust h sub spl infin control of uncertain markovian jump systems with time delay this paper is concerned with the robust stochastic stabilizability and robust h sub spl infin disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters the transition of the jumping parameters is governed by a finite state markov process sufficient conditions on the existence of a robust stochastic stabilizing and spl gamma suboptimal h sub spl infin state feedback controller are presented using the lyapunov functional approach it is shown that a robust stochastically stabilizing h sub spl infin state feedback controller can be constructed through the numerical solution of a set of coupled linear matrix inequalities