affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

algebraic characterization of the wess zumino consistency conditions in gauge theories a new way of solving the descent equations corresponding to the wess zumino consistency conditions is presented the method relies on the introduction of an operator which allows to decompose the exterior space time derivatived as a brs commutator the case of the yang mills theories is treated in detail

brief paper root mean square gain of discrete time switched linear systems under dwell time constraints this paper deals with discrete time switched linear systems and considers the problem of computing an upper bound to the dwell time ensuring a pre specified root mean square rms gain as a natural consequence of treating general systems of this class in terms of the order and the number of subsystems only sufficient conditions are worked out they depend on the complete separation of the stabilizing and anti stabilizing solutions of the algebraic riccati equation associated to each subsystem moreover as positive features it is shown that the dwell time preserving the specification can be calculated through linear matrix inequalities lmis and line search being thus numerically solvable in polynomial time and this allows the treatment of stable switched linear systems which do not admit a common lyapunov function the case of a guaranteed rms gain for arbitrary switching signals is also addressed a simple academic example constituted by three subsystems of third order is included for illustration

simulation of the three dimensional ising model on the creutz cellular automaton abstract the three dimensional ising model is simulated on the creutz cellular automaton the values computed for the critical temperature and the static critical exponents within the framework of the finite size scaling theory are in agreement with their values obtained by different methods

computation of contractive polyhedra for discrete time linear systems with saturating controls this paper deals with computational aspects of characterization and construction of polyhedral u contractive sets with respect to discrete time linear systems with saturating feedback control inputs using a piecewise affine model of the saturating closed loop system new necessary and sufficient algebraic condition for convex closed polyhedra be u contractive is derived based on linear programming formulation of this condition an effective procedure is proposed for construction of as large as possible u contractive convex polyhedra for estimation of the region of asymptotic stability of origin the procedure starts with a u contractive polyhedron possibly contained in the region of linear control and progressively expands it non homothetically over the region of non linear saturated control the proposed approach is less conservative and computationally much more efficient than previously published ones

sufficient lmi conditions for output feedback control problems the authors present linear matrix inequality lmi conditions for output feedback control problems the results are based on sufficient conditions because they are dependent on the particular state space representation used for describing the system nevertheless the conditions are not sensitive to a certain class of state space transformations and if the control problem is feasible then there exists some state space transformation leading the conditions to be necessary and sufficient for the problem the authors approach can be used for designing decentralized controllers and is easily extended to h sub 2 h sub spl infin and mixed h sub 2 h sub spl infin problems via standard lmi techniques the continuous and discrete time cases are considered and numerical examples are given to illustrate the results

critical slowing down in ising model for creutz algorithm abstract dynamical critical exponents for the two dimensional ising model are computed on a cellular automaton from the relaxations of the time displaced correlation and auto correlation functions for the order parameter and the internal energy at the critical temperatures and from the nonlinear relaxation time for the order parameter near the critical temperature the analysis of the data within the frame of the dynamical finite size scaling hypothesis gives z m z e 2 20 and z a m 1 91 and z a e 0 19 for the linear dynamical exponents corresponding respectively to the relaxations of the correlation and the autocorrelation functions for the order parameter and the internal energy and nl m 2 07 for the nonlinear dynamical exponent for the order parameter these values verify the scaling relations between the dynamical exponents

computation of critical exponents for two dimensional ising model on a cellular automaton static critical exponents for the two dimensional ising model are computed on a cellular automaton the analysis of the data within the framework of the finite size scaling theory reproduces their well established values

becchi rouet stora cohomology of zero curvature systems ii the noncomplete ladder case the yang mills type theories and their brs cohomologies are analyzed within the zero curvature formalism

a new realization for the d 2 topological algebra we derive topological algebras for two dimensional models admitting a d b decomposition with b the brst operator in general the topological algebra we obtain is not derived from the twisting of an n 2 supersymmetry algebra we show for the particular case of an abelian model described by a ladder of matter how to derive n 2 supersymmetry generators from the odd generators of the topological algebra

critical behavior of the two dimensional ising model with next nearest neighbor antiferromagnetic interaction on the creutz cellular automaton the two dimensional ising model with nearest and next nearest neighbor antiferromagnetic interactions of ratio r is simulated on the creutz cellular automaton the values of the critical temperature and the critical exponents for o r are estimated within the framework of the finite size scaling theory the dependence of tc on r agrees with the crossover scaling theory for 1 75 the results for 0 r are compatible with ising critical behavior

brief paper stability results for linear parameter varying and switching systems in this paper stabilizability problems for discrete and continuous time linear systems with switching or polytopic uncertainties are dealt with both state feedback and full information controllers are considered possibly with an integral action several cases will be analyzed depending on the control the uncertainty and the presence of uncertainties in the input matrix a complete overview of the stabilizability implications among these different cases will be given

parameter dependent lyapunov functions and the discrete time popov criterion for robust analysis abstract parameter dependent lyapunov functions are developed for discrete time systems with constant real parameter uncertainty this construction of a family of lyapunov functions is then used to analyze robust stability with h 2 performance bounds for state space systems a special case of these results generalizes the classical discrete time popov criterion

stochastic stabilization of a class of nonhomogeneous markovian jump linear systems this paper deals with the problem of stochastic stability analysis and control synthesis of a class of markovian jump linear systems mjls with time varying transition probabilities tps in the discrete time domain the time varying character is considered to be in a polytopic sense the approach followed in this note is based on the use of a parameter dependent stochastic lyapunov function we give a stability condition in terms of a linear matrix inequality lmi feasibility problem the obtained results are illustrated in a numerical example

a new class of universal lyapunov functions for the control of uncertain linear systems the authors analyze the problem of synthesizing a state feedback control for the class of uncertain continuous time linear systems affected by time varying memoryless parametric uncertainties they consider as candidate lyapunov functions the elements of the class spl sigma sub p sup z which is formed by special homogeneous positive definite functions they show that this class is universal in the sense that a lyapunov function exists if and only if there exists a lyapunov function in spl sigma sub p sup z they prove this result in a constructive way showing that such a lyapunov function can always be obtained by smoothing a polyhedral function for which construction algorithms are available the authors show that unlike the polyhedral lyapunov functions these functions allow us to derive explicit formulas for the stabilizing controller

the effect of the increase of linear dimensions on exponents obtained by finite size scaling relations for the six dimensional ising model on the creutz cellular automaton the six dimensional ising model is simulated on the creutz cellular automaton using the finite size lattices with the linear dimension 4

a new iterative approach for multi objective fault detection observer design and its application to a hypersonic vehicle abstractthis paper addresses the multi objective fault detection observer design problems for a hypersonic vehicle owing to the fact that parameters variations modelling errors and disturbances are inevitable in practical situations system uncertainty is considered in this study by fully utilising the orthogonal space information of output matrix some new understandings are proposed for the construction of lyapunov matrix sufficient conditions for the existence of observers to guarantee the fault sensitivity and disturbance robustness in infinite frequency domain are presented in order to further relax the conservativeness slack matrices are introduced to fully decouple the observer gain with the lyapunov matrices in finite frequency range iterative linear matrix inequality algorithms are proposed to obtain the solutions the simulation examples which contain a monte carlo campaign illustrate that the new methods can effectively reduce the design conservativeness compared with the existing methods

on strict positive real systems design guaranteed cost and robustness issues this paper deals with unbounded nonlinear real uncertainty and proposes a solution to the strict positive real control problem by dynamic output feedback besides a guaranteed cost problem solved by lmi optimization combined with line search is introduced in order to provide robust performance

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

the estimation of a ktc p j p phase diagram for a two dimensional site diluted ising model using a microcanonical algorithm abstract the site diluted ising model has been investigated using an improved microcanonical algorithm from creutz cellular automaton for a microcanonical algorithm the basic problem is to estimate the correct temperatures using average values of the kinetic energy in the simulations of site diluted ising model in this study the average kinetic energy has been re described with an expression dependent on dilution x 1 p the values of the temperature have been calculated using the new expression and the critical temperatures have been estimated from the peaks of specific heat for each value of dilution x the obtained phase transition line k t c p j p is in good agreement with functional prediction for the site diluted ising model the simulations were carried out on a square lattice with periodic boundary conditions

the test of the finite size scaling relations for the six dimensional ising model on the creutz cellular automaton the six dimensional ising model is simulated on the creutz cellular automaton using the finite size lattices with the linear dimension 4 l 10 the exponents in the finite size scaling relations for the magnetic susceptibility and the order parameter at the infinite lattice critical temperature are computed to be 3 00 12 and 1 47 10 using 6 l 10 respectively which are in very good agreement with the theoretical predictions of and the critical temperature for the infinite lattice is found to be 10 835 5 using 4 l 10 which is also in very good agreement with the precise results the finite size scaling relation for the magnetic susceptibility at the infinite lattice critical temperature is also valid for the maxima of the magnetic susceptibilities of the finite size lattices the finite size scaling plots of the magnetic susceptibility and the order parameter verify the finite size scaling relations about the infinite lattice critical temperature

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

computation of correlation functions of the two dimensional ising model abstract the spin spin and energy energy correlation functions of the two dimensional ising model are computer on the creutz cellular automaton from the data for the spin spin correlation functions the values of the critical exponents and are obtained they are in agreement with their theoretical values

parameter dependent lyapunov functions for discrete time systems with time varying parametric uncertainties abstract in this paper we consider discrete time systems with polytopic time varying uncertainty we look for a class of parameter dependent lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter we show that extending the new discrete time stability condition proposed by de oliveira et al systems control lett 36 1999 135 to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a lyapunov function this allows to check asymptotic stability of the system under study the obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem

convex liftings based robust control design this paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties this method hinges on so called convex liftings which emulate control lyapunov function by providing a constructive framework for optimization based control implementation it will be shown that this method can guarantee the recursive feasibility and robust stability finally a numerical example will be presented to illustrate this method