survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

covariance controllers for linear continuous time systems abstract necessary and sufficient conditions are given for the existence of a controller of specified order n c which will assign a specified matrix value x to the covariance of the closed loop system if a solution exists the entire set of stabilizing controllers that assign x are parameterized by a certain skew symmetric matrix

design of robust static output feedback for large scale systems the design of static output feedback is of fundamental importance in control theory in this note we propose a new approach to this problem based on linear matrix inequalities a distinguishing feature of the method is its ability to handle large scale problems with additive nonlinearities the resulting control is robust with respect to uncertainties and can incorporate several types of information structure constraints the effectiveness of the proposed strategy is demonstrated by application to a practical large scale system

simultaneous stabilization via static output feedback and state feedback in this paper the simultaneous stabilization problem is considered using the matrix inequality approach some necessary and sufficient conditions for simultaneous stabilizability of strictly proper multi input multi output mimo plants via static output feedback and state feedback are obtained in the form of coupled algebraic riccati inequalities it is shown that any such stabilizing feedback gain is the solution of some coupled linear quadratic control problems where every cost functional has a suitable cross term a heuristic iterative algorithm based on the linear matrix inequality technique is presented to solve the coupled matrix inequalities the effectiveness of the approach is illustrated by numerical examples

impact of critical mass on the evolution of cooperation in spatial public goods games we study the evolution of cooperation under the assumption that the collective benefits of group membership can only be harvested if the fraction of cooperators within the group i e their critical mass exceeds a threshold value considering structured populations we show that a moderate fraction of cooperators can prevail even at very low multiplication factors if the critical mass is minimal for larger multiplication factors however the level of cooperation is highest at an intermediate value of the critical mass the latter is robust to variations of the group size and the interaction network topology applying the optimal critical mass threshold we show that the fraction of cooperators in public goods games is significantly larger than in the traditional linear model where the produced public good is proportional to the fraction of cooperators within the group

a linear programming approach to the synthesis of fixed structure controllers this paper describes a new approach to the synthesis of fixed structure and fixed order controllers such controllers are required in many practical applications a broad class of fixed structure controller synthesis problems can be reduced to the determination of a real controller parameter vector or simply a controller k k 1 k 2 k t so that a given set of real or complex polynomials of the form p s k po s k 1 p 1 s k t p t s is hurwitz the stability of the closed loop system requires a real characteristic polynomial to be hurwitz while several performance criteria can be satisfied by ensuring that a family of complex polynomials is hurwitz a novel feature of this paper is the exploitation of the interlacing property ip of hurwitz polynomials to construct arbitrarily tight approximations of the set of stabilizing controllers this is done by systematically constructing sets of linear inequalities in k the union of the feasible sets of linear inequalities provides an approximation of the set of all controllers k which render p s k hurwitz as the number of sets of linear inequalities increases and approaches infinity we show that the union of the feasible sets approaches the set of all stabilizing controllers of the desired structure the main tools that are used in the construction of the sets of linear inequalities are the hermite biehler theorem descartes rule of signs and its generalization we provide examples of the applicability of the proposed methodology to the synthesis of fixed order stabilizing controllers

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

partial model matching via static feedback the multivariable case the problem of partial model matching is studied for the case of multi input multi output mimo linear time invariant systems using a regular static state feedback law the necessary and sufficient conditions for the problem to have a solution are established the general analytic expressions of the controller matrices are derived for the case of single input single output systems sufficient conditions are derived for the solution of the partial model matching problem with simultaneous stabilizability for the same type of systems the necessary and sufficient conditions for the solution of the partial model matching problem with simultaneous regulation of the free response of the closed loop system are established finally the problem of partial model matching via regular static measurement output feedback is solved for the case of mimo systems

optimization of static output feedback using substitutive lmi formulation this note proposes a new design tool for optimizing static output feedback using a linear matrix inequality lmi formula called substitutive lmi a matrix inequality derived from static output feedback is not usually linear adding a positive definite term including auxiliary variables the matrix inequality is transformed into an lmi with respect to the positive definite matrix and the static output feedback gain an iterative calculation algorithm is given to solve the substitutive lmi in this note designs of the static output feedback gain are shown in the frame of h sub spl infin and h sub 2 syntheses a numerical example is shown to demonstrate the effectiveness of the proposed technique

stabilization of discrete time linear systems by static output feedback this note proposes a systematic approach for the static output feedback control design for discrete time linear systems it is shown that if the open loop system satisfies some particular structural conditions a static output feedback gain can be calculated easily using a formula only involving the original system matrices among the conditions the system has to satisfy the stronger relies on a minimum phase argument square and nonsquare systems are considered

static output feedback and guaranteed cost control of a class of discrete time nonlinear systems with partial state measurements abstract in this paper both the static output feedback issue and the observer based control of a class of discrete time nonlinear systems are considered thanks to a newly developed linearization lemma it is shown that the solution of the discrete time output feedback problem is conditioned by a set of simple convex optimization conditions that are numerically tractable and free from any equality constraint an illustrative example is provided to show the usefulness of the proposed control designs

nonnull asymptotic distributions of three classic criteria in generalised linear models summary this paper develops simple formulae for the asymptotic expansions up to order n of the distributions of the likelihood ratio wald and score statistics in generalised linear models under a sequence of pitman alternatives the powers of all three criteria which are equivalent to first order are compared under specific conditions based on second order approximations the asymptotic distributions of all three statistics are obtained for testing a subset of linear parameters when the dispersion parameter is known for testing the dispersion parameter and for testing the whole set of linear parameters assuming that the dispersion parameter is unknown the formulae derived are simple enough to be used analytically to obtain closed form expressions for these expansions in special models with a fisher information matrix in closed form

a test for stabilizability by constant output feedback an elementary test is developed to check the stabilizability of linear time invariant single input single output plants using static output feedback the test is applied to the plant s transfer function and requires finding roots of certain polynomials

role separating ordering in social dilemmas controlled by topological frustration three is a crowd is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models accordingly social relations within a triangle deserve special attention with this motivation we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice this topology provides an irreconcilable frustration which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game by using different strategy updating protocols we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb like organization which helps to minimize the negative consequence of the topological frustration we relate the emergence of these patterns to the microscopic dynamics of the evolutionary process both by means of mean field approximations and monte carlo simulations for comparison we also consider the same evolutionary dynamics on the square lattice where of course the topological frustration is absent however with the deletion of diagonal links of the triangular lattice we can gradually bridge the gap to the square lattice interestingly in this case the level of cooperation in the system is a direct indicator of the level of topological frustration thus providing a method to determine frustration levels in an arbitrary interaction network

static output feedback control synthesis for linear systems with time invariant parametric uncertainties this technical note is concerned with the problem of designing robust static output feedback controllers for linear discrete and continuous time systems with time invariant polytopic uncertainties sufficient conditions for static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities furthermore the results are also extended to h2 static output feedback controller designs numerical examples are given to illustrate the effectiveness of the proposed design methods

improved likelihood ratio statistics for exponential family nonlinear models summary this paper gives a general formula for the expected likelihood ratio statistic for exponential family nonlinear models corrected up to order n 1 where n is the sample size this result generalizes previous work by cordeiro 1983 various general bartlett adjustment formulae are given to some special models and improved likelihood ratio tests are discussed

improved likelihood ratio statistics for generalized linear models summary this paper gives a general formula for the expected value of the likelihood ratio statistic for generalized linear models corrected up to terms of order n 1 where n is the size of the sample the application of this formula to some models is illustrated

comments on stabilization via static output feedback in the above paper trofino neto and kucera 1993 the proof given for theorem 3 1 is inconsistent in this note a modified proof is suggested

brief paper parameterization of all stabilizing h static state feedback gains application to output feedback design this paper presents a simplified parameterization of all h static state feedback controllers in terms of a single algebraic riccati equation and a free parameter matrix as a special case necessary and sufficient conditions for the existence of an static output feedback gain are given an efficient computational algorithm is given and its correctness proven no initial stabilizing output feedback gain is needed the technique is used to design an h lateral directional command augmentation system for the f 16 aircraft

output feedback controllers of suboptimality degree beta a misconception in a recent paper by d z zheng 1989 about suboptimal feedback control is highlighted a novel synthesis method for designing output feedback controllers of suboptimality degree beta is developed these controllers yield a cost value equal to or less than a scalar multiple beta times the cost value obtained by optimal linear quadratic state feedback control the output feedback control gains are explicit in terms of the standard riccati equation when certain conditions are satisfied

stabilization via static output feedback necessary and sufficient conditions for the existence of a stabilizing static output feedback gain matrix are presented it is shown that any such gain matrix is the solution of some linear quadratic control problem where the cost functional has a suitable cross term

brief robust stabilization and guaranteed cost control for discrete time linear systems by static output feedback this paper proposes a systematic approach for the static output feedback control design for discrete time uncertain linear systems it is shown that if the open loop system satisfies some particular structural conditions and the uncertainty has a specific structure a static output feedback gain can be calculated easily using a formula only involving the original system matrices among the conditions the system has to satisfy the strongest one relies on a minimum phase argument square and nonsquare systems are considered the performance problem through a quadratic criterion is also discussed guaranteed cost control

group formation in the spatial public goods game with continuous strategies abstract we study group formation in the spatial public goods game with continuous strategies an active group will become inactive with high low probability if the collective contribution is below above a threshold value meanwhile an inactive group recovers to be active with some probability we have found that the cooperation level and the average payoff of players are maximized at moderate values of the threshold and the recovery rate spatial distributions of strategies and active groups are plotted to understand the evolution of cooperation

an improved ilmi method for static output feedback control with application to multivariable pid control an improved iterative linear matrix inequality ilmi algorithm for static output feedback sof stabilization problem without introducing any additional variables is proposed in this note the proposed ilmi algorithm is also extended to solve the sof hinfin controller design problem they are applied to the multivariable pid controllers numerical examples show that the proposed algorithms yield better results and faster convergence than the existing ones

minimum entropy static output feedback control with an h sub spl infin norm performance bound the problem of designing static output feedback controllers is considered the controller is required to minimize the closed loop entropy at s spl infin and to satisfy a prescribed h sub spl infin norm bound the design equations consist of a modified riccati equation and a lyapunov equation that are coupled via a projection these equations are solved using a homotopy algorithm the design procedure is illustrated by two examples the first one is a classical example that was solved in the literature using convex optimization techniques the second example is one of designing a gain scheduled normal acceleration loop for an air launched unmanned air vehicle

a necessary and sufficient condition for output feedback stabilizability a necessary and sufficient condition for a linear system to be stabilizable via static output feedback is presented it makes an appeal to the linear quadratic regulator theory

a convergent algorithm for computing stabilizing static output feedback gains we revisit the approach by cao et al that uses a fixed structure control law to find stabilizing static output feedback gains for linear time invariant systems by performing singular value decomposition on the output matrix together with similarity transformations we present a new stabilization method unlike their results that involve a difficult modified riccati equation whose solution is coupled with other two intermediate matrices that are difficult to find we obtain lyapunov equations we present a convergent algorithm to solve the new design equations for the gains we will show that our new approach like theirs is a dual optimal output feedback linear quadratic regulator theory numerical examples are given to illustrate the effectiveness of the algorithm and validate the new method

the optimal projection equations for static and dynamic output feedback the singular case oblique projections have been shown to arise naturally in both static and dynamic optimal design problems for static controllers an oblique projection was inherent in the early work of levine and athans while for dynamic controllers an oblique projection was developed by hyland and bernstein this note is motivated by the following natural question what is the relationship between the oblique projection arising in optimal static output feedback and the oblique projection arising in optimal fixed order dynamic compensation we show that in nonstrictly proper optimal output feedback there are indeed three distinct oblique projections corresponding to singular measurement noise singular control weighting and reduced compensator order moreover we unify the levine athans and hyland bernstein approaches by rederiving the optimal projection equations for combined static dynamic nonstrictly proper output feedback in a form which clearly illustrates the role of the three projections in characterizing the optimal feedback gains even when the dynamic component of the nonstrictly proper controller is of full order the controller is characterized by four matrix equations which generalize the standard lqg result

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

laplace approximation of high dimensional integrals summary it is shown that the usual laplace approximation is not a valid asymptotic approximation when the dimension of the integral is comparable with the limiting parameter n the formal laplace expansion for multidimensional integrals is given and used to construct asymptotic approximations for high dimensional integrals one example is considered in which the dimension of the integral is o n 1 2 and the relative error of the unmodified laplace approximation is 0 1 nevertheless it is possible to construct a valid asymptotic expansion by regrouping terms in the formal expansion according to asymptotic order in n

static output feedback stabilization with h sub spl infin performance for linear discrete time systems this note presents a new sufficient condition for the static output feedback stabilization of linear discrete time systems this new condition is expressed as a linear matrix inequality feasibility problem and hence easily tractable numerically an extension of this condition is given in order to incorporate h sub spl infin performance objectives the applicability of the proposed approach is shown through numerical examples and compared to some recent methods

comments on consistency of quadratic forms a remark related to earlier papers cheng and martin 1995 geromel et al 1988 trofino neto and kucera 1993 is made with an extension

impact of generalized benefit functions on the evolution of cooperation in spatial public goods games with continuous strategies cooperation and defection may be considered to be two extreme responses to a social dilemma yet the reality is much less clear cut between the two extremes lies an interval of ambivalent choices which may be captured theoretically by means of continuous strategies defining the extent of the contributions of each individual player to the common pool if strategies are chosen from the unit interval where 0 corresponds to pure defection and 1 corresponds to the maximal contribution the question is what is the characteristic level of individual investments to the common pool that emerges if the evolution is guided by different benefit functions here we consider the steepness and the threshold as two parameters defining an array of generalized benefit functions and we show that in a structured population there exist intermediate values of both at which the collective contributions are maximal however as the cost to benefit ratio of cooperation increases the characteristic threshold decreases while the corresponding steepness increases our observations remain valid if more complex sigmoid functions are used thus reenforcing the importance of carefully adjusted benefits for high levels of public cooperation

technical communique stabilization of discrete time singular systems a matrix inequalities approach this paper is concerned with the state feedback stabilization problem of discrete time singular systems the singular system under consideration is not assumed to be regular the problem we address is to design state feedback controllers such that the resulting closed loop system is regular causal and stable conditions for the existence of solutions to this problem are obtained expressed in terms of certain matrix inequalities when these conditions are satisfied the explicit formula of desired state feedback controllers is also given without resorting to decomposing the system matrices

second order asymptotics for score tests in generalised linear models summary this paper develops finite sample corrections for score tests in generalised linear models when the dispersion parameter is unknown thus generalising the results of cordeiro ferrari paula 1993 we show that the coefficients which define the edgeworth expansion for the null distribution of the score statistic when the dispersion parameter is unknown are the coefficients obtained by these authors plus some extra terms we also give closed form expressions for such coefficients an important special case of our results is the normal linear regression model simulation results for this model show that the corrections can be very effective reducing the probability of conflict with other asymptotically equivalent testing criteria

on a conservative concept for output static stabilizability analysis consequences and related problems this communication is concerned with the problem of stabilization via output static feedback of linear time invariant finite dimensional systems a new output static stabilization concept is introduced output static stabilization in the relaxed sense this conservative stabilization concept is the result of imposing an additional condition to a set of necessary and sufficient conditions for output static stabilization this paper is devoted to exhaustively study the introduced new stabilization concept i it is shown that for a particular class of plants the stabilization problem in the above sense can be cast as a convex programming problem ii a full characterization of the class of plants that are stabilizable in the above new sense is presented some of the important consequences of that study are as follows 1 the identification of a class of plants stabilizable via output static feedback for which stabilizing feedback matrices can be almost expressed in analytic closed form 2 it is

on the existence of linear optimal control with output feedback a necessary and sufficient condition is established for the existence of an output feedback u ky that is lq optimal with respect to some nonsingular quadratic cost a fact that entails robustness in the closed loop systems it is shown that if the system with equal number of inputs and outputs is strict minimum phase and has nonsingular high frequency gain then there exists a linear static output feedback that minimizes a certain quadratic cost functional the minimization of h infty norm of the closed loop system with output feedback is also discussed

a modified score test statistic having chi squared distribution to order n 1 summary we give a general modified score test statistic whose nuil distribution is chi squared to order n 1 where n is the sample size the modified statistic depends on the joint cumulants of log likelihood derivatives for the full data some applications are discussed following cox reid 1987a we also derive a general formula for bartlett type corrections to improve test statistics whose null asymptotic distributions are chi squared

phase diagrams for three strategy evolutionary prisoner s dilemma games on regular graphs evolutionary prisoner s dilemma games are studied with players located on square lattice and random regular graph defining four neighbors for each one the players follow one of the three strategies tit for tat unconditional cooperation and defection the simplified payoff matrix is characterized by two parameters the temptation b to choose defection and the cost c of inspection reducing the income of tit for tat the strategy imitation from one of the neighbors is controlled by pairwise comparison at a fixed level of noise using monte carlo simulations and the extended versions of pair approximation we have evaluated the b c phase diagrams indicating a rich plethora of phase transitions between stationary coexistence absorbing and oscillatory states including continuous and discontinuous phase transitions by reasonable costs the tit for tat strategy prevents extinction of cooperators across the whole span of b determining the prisoner s dilemma game irrespective of the connectivity structure we also demonstrate that the system can exhibit a repetitive succession of oscillatory and stationary states upon changing a single payoff value which highlights the remarkable sensitivity of cyclical interactions on the parameters that define the strength of dominance

confidence intervals for a random effects meta analysis based on bartlett type corrections in medical meta analysis the dersimonian laird confidence interval for the average treatment effect has been widely adopted in practice however it is well known that its coverage probability the probability that the interval actually includes the true value can be substantially below the target level one particular reason is that the validity of the confidence interval depends on the assumption that the number of synthesized studies is sufficiently large in typical medical meta analyses the number of studies is fewer than 20 in this article we developed three confidence intervals for improving coverage properties based on i the bartlett corrected likelihood ratio statistic ii the efficient score statistic and iii the bartlett type adjusted efficient score statistic the bartlett and bartlett type corrections improve the large sample approximations for the likelihood ratio and efficient score statistics through numerical evaluations by simulations these confidence intervals demonstrated better coverage properties than the existing methods in particular with a moderate number of synthesized studies the bartlett and bartlett type corrected confidence intervals performed well an application to a meta analysis of the treatment for myocardial infarction with intravenous magnesium is presented

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

bias correction in generalized linear models summary in this paper we derive general formulae for first order biases of maximum likelihood estimates of the linear parameters linear predictors the dispersion parameter and fitted values in generalized linear models these formulae may be implemented in the glim program to compute bias corrected maximum likelihood estimates to order n 1 where n is the sample size with minimal effort by means of a supplementary weighted regression for linear logistic models it is shown that the asymptotic bias vector of j8 is almost collinear with f3 the approximate formula flp m for the bias of s in logistic models where p dim and m e mi is the sum of the binomial indices is derived and checked numerically

improved score tests for generalized linear models summary we present in matrix notation an asymptotic expansion for the null distribution of the score statistic in generalized linear models corrected up to order n 1 where n is the sample size the expansion has advantages for numerical purposes because it requires only simple operations on matrices it is also sufficiently simple to be used analytically to obtain several closed form expressions analogous to bartlett corrections in a variety of important score tests improved score tests for these models are discussed and various applications to some special tests are given we show by simulation that two asymptotically equivalent adjusted score tests seem to improve at least for continuous data on the usual score test