an h minimax approach to the design of robust control systems abstract a realistic feedback design problem is posed based on the minimization of a weighted combination of the sensitivity and complementary sensitivity matrices a solution is obtained which makes use of the recently proposed methods for minimizing the sensitivity function alone

on repeated games with complete information we consider n person repeated games with complete information and standard signalling we first prove several properties of the sets of feasible payoffs and nash equilibrium payoffs for the n stage game and for the discounted game in the second part we determine the set of equilibrium payoffs for the prisoner s dilemma corresponding to the critical value of the discount factor

impulsive delay differential inequality and stability of neural networks in this article a generalized model of neural networks involving time varying delays and impulses is considered by establishing the delay differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive delay model are obtained the results extend and improve the earlier publications an example is given to illustrate the theory

time varying versus time invariant compensation for rejection of persistent bounded disturbances and robust stabilization it is shown that time varying compensation does not improve the optimal rejection of persistent bounded disturbances this result is obtained by exploiting a key observation that any time varying compensator which yields a given degree of disturbance rejection must do so uniformly over time thereby removing any advantage of time variation this key observation is exploited to show that time varying compensation does not improve the optimal rejection of disturbances regardless of the norm used to measure the disturbances thus absolutely summable finite energy or persistent bounded disturbances may be treated in the same manner it is shown that time varying compensation does not help in the bounded input bounded output robust stabilization of time invariant plants with unstructured uncertainty in doing so it is also shown that the small gain theorem is both necessary and sufficient for the bounded input bounded output stability of certain linear time varying plants subject to unstructured linear time varying perturbations

a connection between normalized coprime factorizations and linear quadratic regulator theory given a transfer matrix described by a minimal state space triple a method is given for computing state space realizations for the numerator and denominator of a normalized stable right coprime factorization for the transfer matrix the method involves the solution of an algebraic riccati equation it allows the use of existing computational state space algorithms in finding normalized stable right coprime factorizations and avoids explicit calculations of spectral factors

technical communique upper bounds for the solution of the discrete algebraic lyapunov equation new upper bounds for the solution of the discrete algebraic lyapunov equation dale p apa t q are presented the only restriction on their applicability is that a be stable there are no restrictions on the singular values of a nor on the diagonalizability of a the new bounds relate the size of p to the radius of stability of a the upper bounds are computable when the large dimension of a make direct solution of the dale impossible the new bounds are shown to reflect the dependence of p on a better than previously known upper bounds

robust stabilization of linear multivariable systems relations to approximation the stabilization of a linear system modelled as g a where g is a known rational transfer function and a is a perturbation satisfying w a2 g1 or equivalently there does not exist g with fewer poles in c than g such that w1 g g w2 a simple characterization of all robustly stabilizing controllers is then derived and state space formulae for maximally robust controllers are given finally reduced order controllers are considered

on the robust stability of linear time invariant plants with unstructured uncertainty we consider general families of linear time invariant plants described by a nominal plant model with unstructured uncertainty we show under a rather weak assumption that when a family of systems is not robustly stabilizable by any linear time invariant feedback controller then no nonlinear time varying controller can robustly stabilize the given family

reduced order controller design using coprime factor model reduction two procedures for reduced order controller design that incorporate coprime factor model reduction techniques and a related robust stabilization problem are proposed it is shown that robust stability can be achieved with these controllers the results obtained show how to reduce the controller degree systematically they clearly indicate how the maximum stability margin influences allowable model reduction error

the robust regulation problem with robust stability a subspace valued function approach among the most common purposes are the tracking of reference signals and the rejection of disturbance signals in the face of uncertainties the related design problem is called the robust regulation problem here we investigate the tradeoff between the robust regulation constraint and the requirement of robust stability with respect to perturbations in the normalized coprime factors of the plant we use an approach in terms of subspace valued functions associated to plant and controller in this way necessary and sufficient conditions for robust regulation with robust stability can be related to a simple geometric property

the value of markov chain games with lack of information on one side we consider a two player zero sum game given by a markov chain over a finite set of states and a family of matrix games indexed by states the sequence of states follows the markov chain at the beginning of each stage only player 1 is informed of the current state then the corresponding matrix game is played and the actions chosen are observed by both players before proceeding to the next stage we call such a game a markov chain game with lack of information on one side this model generalizes the model of aumann and maschler of zero sum repeated games with lack of information on one side which corresponds to the case where the transition matrix of the markov chain is the identity matrix we generalize the proof of aumann and maschler and from the definition and the study of appropriate nonrevealing auxiliary games with infinitely many stages show the existence of the uniform value an important difference with aumann and maschler s model is that here the notions for player 1 of using the information and revealing a relevant information are distinct

discrete halanay type inequalities and applications in this paper we derive new discrete halanay type inequalities and show some applications in the investigation of the asymptotic behavior of nonlinear di4erence equations in particular di4erence equations involving the maximum functional are considered 2003 elsevier ltd all rights reserved

reduced order compensators via balancing and central control design for a structural control problem real time control of a physical system necessitates controllers that are low order in this article we compare two balanced truncation methods as a means of designing low order controllers for a nonlinear cable mass system the first is the standard technique of balanced truncation the second linear quadratic gaussian lqg balanced truncation can be thought of as balancing based on the controller and states that are important from the perspective of control and filter design are retained the control design applied to each reduced order model is the central controller we provide an overview of the central controller and devote attention to the design of this controller in the presence of balancing also described in this article is a method for reducing computational time in solving algebraic riccati equations for the design of low order lqg balanced controllers

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

belief free communication equilibria in repeated games this paper considers a general model of repeated games with incomplete information and imperfect monitoring we study belief free communication equilibria bfce defined as follows players communicate with a mediator who receives types and signals and recommends actions a bfce is a communication device such that all players have an incentive to play faithfully irrespectively of their belief about the state we characterize bfce payoffs for any repeated game with incomplete information in terms of one shot payoff functions information and signaling structure

the value of markov chain games with incomplete information on both sides we consider zero sum repeated games with incomplete information on both sides where the states privately observed by each player follow independent markov chains it generalizes the model introduced by aumann and maschler in the sixties and solved by mertens and zamir in the seventies where the private states of the players were fixed it also includes the model introduced in renault 19 renault j 2006 the value of markov chain games with lack of information on one side math oper res 31 3 490 512 of markov chain repeated games with lack of information on one side where only one player privately observes the sequence of states we prove here that the limit value exists and we obtain a characterization via the mertens zamir system where the nonrevealing value function plugged in the system is now defined as the limit value of an auxiliary nonrevealing dynamic game this nonrevealing game is defined by restricting the players not to reveal any information on the limit behavior of their

stability conditions for linear retarded functional differential equations abstract the purpose of this note is to study the exponential stability for the linear retarded functional differential equation x t 1 0 d x t r where the delay function r 0 is continuous and is of bounded variation on the interval 1 0 it is shown that the spectral limit function for the equation above has a continuous dependence on the pair r the set of all functions of bounded variation for which the equation above is exponentially stable for every delay function r the so called region of stability globally in the delays is a cone therefore for a fixed r the set of all which make our equation exponentially stable that is the region of stability for the delay function r contains a cone a discussion of the characterization of these regions of stability as well as of the largest cone contained in each region of stability for a fixed delay function r is given some remarks are made with respect to a similar question for the equation x t ax t 1 0 d x t r where a is a real n by n matrix is bounded variation on 1 0 and r as before several examples illustrate the results obtained

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

controller reduction via stable factorization and balancing abstract a controller reduction procedure based on a representation of a controller as a matrix function defined using stable proper transfer functions and employing a balancing technique is studied in this paper for a certain right coprime factorization of an lqg designed controller k s n s d 1 s we approximate using a balancing technique the pair d s n s t by a low order pair d1 s n1 s t defining a factorization of the reduced order controller k 1 s n1 s d1 1 s we show that reducing the controller order in this way is motivated in a natural way which leads to the expectation of both good stability properties and good accuracy of approximation of closed loop behaviour this is also demonstrated in some examples

global exponential stability of impulsive integro differential equation abstract in this paper an impulsive integro differential equation is considered by establishing an integro differential inequality with impulsive initial conditions and using the properties of m cone and eigenspace of the spectral radius of nonnegative matrices some new sufficient conditions for global exponential stability of impulsive integro differential equation are obtained the results extend and improve the earlier publications an example is given to demonstrate the effectiveness of the theory

two player repeated games with nonobservable actions and observable payoffs this paper studies two person repeated games in which after each stage a player is informed about the payoff he received at the previous stage the information can in some cases include more than that four kinds of nash equilibrium concepts are defined by the limit of the means a characterization of the equilibrium payoffs sets and several properties of these sets are given as a specific example the standard information case that of the folk theorem is provided

a partial folk theorem for games with unknown payoff distributions repeated games with unknown payoff distributions are analogous to a single decision maker s multi armed bandit problem each state of the world corresponds to a different payoff matrix of a stage game when monitoring is perfect information about the state is public and players are sufficiently patient the following result holds for any function that maps each state to a payoff vector that is feasible and individually rational in that state there is a sequential equilibrium in which players experiment to learn the realized state and achieve a payoff close to the one specified for that state

optimal robustness in the gap metric the application of the gap metric to robust stabilization of feedback systems is considered in particular a solution to the problem of robustness optimization in the gap metric is presented the problem of robust stabilization under simultaneous plant controller perturbations is addressed and the least amount of combined plant controller uncertainty measured by the gap metric that can cause instability of a nominally stable feedback system is determined included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the t gap metric a key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations this settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well defined metric

the existence of almost periodic solutions of some delay differential equations abstract a set of sufficient conditions is derived for the existence of almost periodic solutions of some delay differential equations by using exponential dichotomy and fixed point theorem this criterion provides a method for the existence analysis of almost periodic solution of time delay systems

robust game theory we present a distribution free model of incomplete information games both with and without private information in which the players use a robust optimization approach to contend with payoff uncertainty our robust game model relaxes the assumptions of harsanyi s bayesian game model and provides an alternative distribution free equilibrium concept which we call robust optimization equilibrium to that of the ex post equilibrium we prove that the robust optimization equilibria of an incomplete information game subsume the ex post equilibria of the game and are unlike the latter guaranteed to exist when the game is finite and has bounded payoff uncertainty set for arbitrary robust finite games with bounded polyhedral payoff uncertainty sets we show that we can compute a robust optimization equilibrium by methods analogous to those for identifying a nash equilibrium of a finite game with complete information in addition we present computational results

robust controllers for uncertain linear multivariable systems abstract this paper is addressed to three distinct yet related topics in the design of controllers for imprecisely known linear multivariable systems in the first part it is supposed that the plant to be stabilized is subject to additive or multiplicative uncertainties and necessary and sufficient conditions are derived for the existence of a controller that stabilizes all plants within this band of uncertainty in the second part in contrast with the first part it is supposed that the number of unstable poles of the plant to be stabilized is not precisely known the type of plant uncertainty is the so called stable factor uncertainty and necessary and sufficient conditions are given for robust stabilization in the third part the model of uncertainty is a ball in the space of rational matrices metrized by the so called graph metric and sufficient conditions for robust stabilization are derived

stability and existence of multiple periodic solutions for a quasilinear differential equation with maxima we study the stability of periodic solutions of the scalar delay differential equation where f t is a periodic forcing term and p r we study stability in the first approximation showing that the non smooth equation can be linearized along some non singular periodic solutions then the corresponding variational equation together with the krasnosel skij index are used to prove the existence of multiple periodic solutions to finally we apply a generalization of halanay s inequality to establish conditions for global attractivity in equations with maxima

robust performance assessment of feedback control systems the proper measure of closed loop performance variation in the presence of model plant mismatch is discussed in this paper a generalized closed loop error transfer function which is a special representation of the dual youla parameter and has a close relationship with the pointwise n gap metric is proposed as the suitable means of representing closed loop performance variation in case of plant perturbation and the closed loop performance variation measure is accordingly defined as its maximum singular value frequency by frequency it is shown that this measure is essential and informative in characterizing closed loop performance variation this measure is also shown to be readily applicable to on line closed loop performance assessment or monitoring even without the explicit model of the plant its variant defined as the h function which features the relative performance variation as well as generalized stability margin variation with respect to the nominal plant is also discussed

belief free equilibria in games with incomplete information we define belief free equilibria in two player games with incomplete information as sequential equilibria for which players continuation strategies are best replies after every history independently of their beliefs about the state of nature we characterize a set of payoffs that includes all belief free equilibrium payoffs conversely any payoff in the interior of this set is a belief free equilibrium payoff the characterization is applied to the analysis of reputations

controller reduction concepts and approaches the problem of passing from a linear time invariant high order controller designed for a linear time invariant plant of presumably high order to a low order approximation of the controller is discussed the approximation problem is often best posed as a frequency weighted l sub infinity approximation problem many different controller representations are possible giving different performances of the various reduction algorithms

optimal h multivariable robust controllers and the relationship to lqg design problems a new solution for the multivariable minimax optimal robust design problem is presented the relationship between lqg and h design methods is considered and the h solution is obtained from the solution of a related lqg problem the approach provides insights into the relationship between the h and lqg design philosophies the h solution involves the same type of steps which are involved in the polynomial based solutions of the lqg problem namely spectral factorization and the solution of linear diophantine equations a simplified design procedure is described which requires only the solution of a standard eigenvalue eigenvector problem

the graph metric for unstable plants and robustness estimates for feedback stability in this paper a graph metric is defined that provides a measure of the distance between unstable multivariable plants the graph metric induces a graph topology on unstable plants which is the weakest possible topology in which feedback stability is robust using the graph metric it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of rhp poles if the perturbed and unperturbed systems have the same rhp poles then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations as an application of these results the design of stabilizing controllers for unstable singularly perturbed systems is studied finally the relationship of the graph metric to the gap metric introduced by zames and el sakkary is studied in detail in particular it is shown that the robustness results of zames and el sakkary do not enable one to conclude the causality of the perturbed system whereas the present results do

existence and stability of almost periodic solutions for quasilinear delay systems and the halanay inequality abstract we present some easily verifiable conditions for the existence and global asymptotical stability of almost periodic solutions to systems of delay differential equations in the form u t au t wg t ut f t where a w l r n and f t g t are almost periodic in t uniformly on from bounded subsets of c h 0 r n with this purpose we use the exponential dichotomy theory together with usual positivity arguments in particular the semigroup version of the so called perron frobenius theorem is applied to study the generalized halanay inequality finally systems with maxima are studied in detail

frequency domain uncertainty and the graph topology a new metric on linear time invariant systems is defined this metric is no greater than the gap metric and is in fact the smallest metric for which a certain robust stabilization result holds unlike other known metrics which induce the graph topology it has a clear frequency response interpretation this allows questions regarding robustness in the face of parametric uncertainty to be considered in terms of this metric

player type distributions as state variables and information revelation in zero sum repeated games with discounting this paper examines the role of the player type distributions in repeated zero sum games of incomplete information with discounting of payoffs in particular the strategic sufficiency of the posterior distributions for histories and the limiting properties of the posterior sequence are discussed it is shown that differentiability of the value function is sufficient to allow the posteriors to serve as state variables for histories the limiting properties of the posterior distributions are considered and a characterization given of the set of possible limit points of the posterior distribution this characterization is given in terms of the value of information in the one stage game

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

bibo stability robustness in the presence of coprime factor perturbations a necessary and sufficient condition for robustly stabilizing a family of plants described by perturbations of fixed coprime factors of a plant is given the computation of the largest stability margin is discussed via solving a nonsquare l sup 1 optimal control problem an algorithm for obtaining lower approximations of the minimum value of the optimization problem mu sub 0 is proposed this together with the standard algorithm which provides upper approximations allows mu sub 0 to be computed within any degree of accuracy

the general distance problem in h optimal control theory abstract the general distance problem that arises in h optimal control theory is considered transformations that reduce the general h problem to the general distance problem are reviewed and an iterative scheme called iteration is considered in which the general distance problem is reduced to a standard best approximation problem the iteration is viewed as a problem of finding the zero crossing of a function this function is shown to be continuous monotonically decreasing convex and bounded by some very simple functions these properties make it possible to obtain very rapid convergence of the iterative process the issues of model reduction and approximation in h synthesis will also be addressed

robust stabilization of delay systems by approximation of coprime factors given a delay system with transfer function g s h2 s h1 s where h1 s 01npi s e is and h2 s 02nqi s e is with 0 0 1 n1 0 0 n2 the pi being polynomials of degree i and i 0for i 0 and the qi polynomials of degree di 0 for each i the robust stabilization of a class of perturbed coprime factors of this system is considered asymptotic estimates are obtained based on recent results on the approximation and stabilization of normalized coprime factors an explicit formula is given for the normalized coprime factor stability margin for the case of a multivariable transfer function of the form g s e str s with r rational

smooth weight optimization in ℋ loop shaping design abstract smooth variation in the magnitude response of weights facilitates loop shaping design as it prevents the cancellation of important modes of the system for example lightly damped poles zeros of flexible structures when the shaped plant is formed based on closed loop design specifications for accurate fitting of transfer functions to magnitude data smooth weights also allow low order transfer functions to be used when such smooth variations in their magnitude responses are computed point wise in frequency in this paper smoothness constraints for weights expressed as gradient constraints on a log scale in db decade which is intuitive from a design perspective are imposed in a weight optimization framework for loop shaping control this work builds on a lanzon weight optimization in loop shaping automatica 41 1 2005 1201 1208 where additional constraints are formulated in linear matrix inequality lmi form to cast a complete weight optimization framework the resulting algorithm thus maximizes the robust stability margin and simultaneously synthesizes smooth weights along with a stabilizing controller a numerical example is given to elucidate the efficacy of the smoothness constraints in loop shaping control

some asymptotic results in discounted repeated games of one sided incomplete information the paper analyzes the nash equilibria of two person discounted repeated games with one sided incomplete information and known own payoffs if the informed player is arbitrarily patient relative to the uninformed player then the characterization for the informed player s payoffs is essentially the same as that in the undiscounted case this implies that even small amounts of incomplete information can lead to a discontinuous change in the equilibrium payoff set for the case of equal discount factors however and under an assumption that strictly individually rational payoffs exist a result akin to the folk theorem holds when a complete information game is perturbed by a small amount of incomplete information

learning sets in state dependent signalling game forms a characterization we consider repeated game forms with incomplete information and state dependent signalling structure we study the information a player can learn about the state of nature through a communication procedure in a way robust to unilateral deviations more precisely we say that playeri can distinguish state from state if there exists a strategy profile such that if is the true state and at most one player deviates from the profile then playeri will know after a finite number of stages that is not the true state the learning set of playeri at is the set of states that playeri cannot distinguish from it corresponds to the information playeri can learn in a way immune against unilateral deviations if the state is and players communicate through the game form for a finite number of stages this notion was introduced in a joint paper with t tomala renault and tomala 2000 we provide here a general characterization of the learning sets

exact computation of infimum for a class of continuous time h optimal control problem with a nonzero direct feedthrough term from the disturbance input to the controlled output a noniterative method for the computation of infimum for a class of continuous time h optimal control problem is considered in this paper the problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems the method is applicable to systems where i the transfer function from the disturbance input to the measurement output is free of imaginary axis invariant zeros and left invertible and ii the transfer function from the control input to the controlled output of the given system is free of imaginary axis invariant zeros and right invertible the result presented in this paper is a continuation of the previous work of the author and his co workers chen et al 1992 in which the direct feedthrough term from the disturbance input to the measurement output of the given system are required to be zero

games with incomplete information played by bayesian players i iii this article originally appeared in management science november 1967 volume 14 number 3 pp 159 182 published by the institute of management sciences the paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation such as the payoff functions the strategies available to various players the information other players have about the game etc however each player has a subjective probability distribution over the alternative possibilities in most of the paper it is assumed that these probability distributions entertained by the different players are mutually consistent in the sense that they can be regarded as conditional probability distributions derived from a certain basic probability distribution over the parameters unknown to the various players but later the theory is extended also to cases where the different players subjective probability distributions fail to satisfy this consistency assumption in cases where the consistency assumption holds the original game can be replaced by a game where nature first conducts a lottery in accordance with the basic probability distribution and the outcome of this lottery will decide which particular subgame will be played i e what the actual values of the relevant parameters will be in the game yet each player will receive only partial information about the outcome of the lottery and about the values of these parameters however every player will know the basic probability distribution governing the lottery thus technically the resulting game will be a game with complete information it is called the bayes equivalent of the original game part i of the paper describes the basic model and discusses various intuitive interpretations for the latter part ii shows that the nash equilibrium points of the bayes equivalent game yield bayesian equilibrium points for the original game finally part iii considers the main properties of the basic probability distribution

normalised coprime factorizations for nonstrictly proper systems some earlier results of d g meyer and g f franklin see ibid vol ac 32 pp 227 8 march 1987 are extended and a procedure is derived for obtaining directly a normalized right coprime factorization of a system that may not be strictly proper

communication equilibria in repeated games with incomplete information correlated equilibria in the sense of aumann i e normal form correlated equilibria are studied in two person infinitely repeated games with lack of information on one side extensions of the solution concept are introduced several of which are shown to be payoff equivalent in the model under consideration a normal form correlated equilibrium is a nash equilibrium of the game where each player gets a private output from a correlation device before the beginning of the original game an r device r 0 1 is a communication device receiving an input from each player before every stage t 1 r and selecting a pair of outputs one for each player at every stage t 1 2 according to a memory dependent transition probability an r communication equilibrium is a nash equilibrium of the game extended by means of an r device let c resp dr r 0 1 be the set of normal form correlated resp r communication equilibrium payoffs d0 is the set of extensive form correlated equilibrium payoffs achieved by means of an autonomous device acting only by sending a stream of outputs to each player and d is the set of all communication equilibrium payoffs corresponding to communication devices which can receive inputs at every stage even arbitrarily large the paper characterizes the different sets and investigate whether they coincide

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

gap metric problem for mimo delay systems parametrization of all suboptimal controllers we consider the problem of robustness optimization in the gap metric for mimo systems with a scalar time delay we present an algorithm for the parametrization of all suboptimal controllers in our algorithm the aak theory plays the central role using this approach suboptimal controllers can be found by computing solutions to certain infinite rank operator equations we show that these equations can be solved numerically by modifying the two point boundary value problem approach reported earlier for the computation of optimal robustness radius we present a numerical example to illustrate the procedure

guaranteed performance regions in markovian systems with competing decision makers a decision maker is facing a dynamic system which is being controlled by himself herself as well as by other decision makers he she considers a vector of performance measures acceptable performance is defined through a set in the space of performance vectors whether this decision maker can guarantee a time averaged performance vector which approaches this desired set is considered for the worst case scenario in which other decision makers may for selfish reasons try to exclude his her vector from the desired set for a controlled markov model of the system a sufficient condition for approachability is given and appropriate control strategies are constructed under certain recurrence conditions a complete characterization of approachability is then provided for convex sets the mathematical formulation leads to a theory of approachability for stochastic games with vector payoffs a simple queuing example illustrates this approach

dissipativity and asymptotic stability of nonlinear neutral delay integro differential equations this paper is concerned with the dissipativity and asymptotic stability of the theoretical solutions of a class of nonlinear neutral delay integro differential equations ndides we first give a generalization of the halanay inequality which plays an important role in the study of dissipativity and stability of differential equations then we apply the generalization of the halanay inequality to ndides and the dissipativity and the asymptotic stability results of the theoretical solution of ndides are obtained from a numerical point of view it is important to study the potential of numerical methods in preserving the qualitative behavior of the analytical solutions therefore the results presented in this paper provide the theoretical foundation for analyzing the dissipativity and the asymptotic stability of the numerical methods when they are applied to these systems

feedback stability under simultaneous gap metric uncertainties in plant and controller abstract the stability robustness of a feedback system is studied in this paper by assuming that the plant and the controller are subject to independent uncertainties and that the uncertainties are measured by the gap metric a fairly complete solution is obtained by exploring the trigonometric structure of the graphs of the plant and the controller

distance measures for uncertain linear systems a general theory in this paper we propose a generic notion of distance between systems that can be used to measure discrepancy between open loop systems in a feedback sense under several uncertainty structures when the uncertainty structure is chosen to be four block or equivalently normalized coprime factor uncertainty then this generic distance measure reduces to the well known nu gap metric associated with this generic distance notion we also define a generic stability margin notion that allows us to give the distance measure a feedback interpretation by deriving generic robust stability and robust performance results the proposed distance notion and the corresponding results exploit a powerful generalization of the small gain theorem which handles perturbations in rfrl infin rather than only in rfrh infin when the uncertainty structure is fixed to one of the standard structures e g additive multiplicative inverse multiplicative coprime factor four block or any mixtures of the above we give a step by step procedure based on model validation ideas that shows how the generic notion of distance and the correspondingly generic winding number conditions can be reduced to simple formulae this work provides a unified framework that captures and embeds previous results in this area and also completes the picture by showing how other results of a similar nature can be obtained from the same framework the techniques used involve only basic linear algebra so they also provide a simplification of previous advanced proofs furthermore the various distance measures so created can be used for non conservative model embedding into the smallest uncertain family an illustrative example is also given that demonstrates the superior qualities above the nu gap metric of a particular distance measure obtained from this work in situations where the plant is lightly damped all systems considered in this paper are linear time invariant

non zero sum two person repeated games with incomplete information characterization of all equilibria of nonzero sum two person repeated games with incomplete information in the standard one sided information case informally each such equilibrium is described by a sequence of communications between the players consisting of information transmission and coordination leading to some individually rational agreement formally the concept of a bi martingale is introduced

a new set of invariants for linear systems application to reduced order compensator design a new set of invariants for linear systems weighting the contribution of each state component to the inherent closed loop lqg behavior of the system is presented together with applications to model order reduction and reduced order compensator design

survey paper from youla kucera to identification adaptive and nonlinear control some 20 years ago formulae were presented for the set of all linear time invariant controllers stabilizing a linear time invariant plant this paper traces the development of many ideas from these formulae covering linear h 2 and h control identification adaptive control and nonlinear systems

a controller degree bound for h 0e control problems of the second kind this paper is a continuation of our work on mathcal h infty optimal control problems which may be embedded in the linear fractional configuration of fig 1 in two previous articles 19 20 a controller degree bound was established for problems in which both p 12 s and p 21 s are square problems of the first kind if the mcmillan degree of p s is n it was shown that there exist mathcal h infty optimal controllers with mcmillan degree no greater than n 1 here we switch our attention to problems of the second kind that is we allow p 12 s to have more rows than columns with p 21 s square or alternatively we allow p 21 s to have more columns than rows with p 12 s square our main result shows that the degree bound derived previously for problems of the first kind carries over to problems of the second kind without change in addition to the controller degree bound our analysis suggests a number of modifications which are easily made to cur

on two player repeated games with lack of information on one side and state independent signalling we consider two person undiscounted repeated games with lack of information on one side and state independent signalling and prove the existence of a joint plan uniform equilibrium

robust stabilization of normalized coprime factor plant descriptions with h sub infinity bounded uncertainty the problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by h sub infinity bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system this problem can be reduced to a nehari extension problem directly and gives an optimal stability margin all controllers satisfying a suboptimal stability margin are characterized and explicit state space formulas are given

reputation and commitment in two person repeated games without discounting two person repeated games with no discounting are considered where there is uncertainty about the type of the players if there is a possibility that a player is an automaton committed to a particular pure or mixed stage game action then this provides a lower bound on the nash equilibrium payoffs to a normal type of this player the lower bound is the best available and is robust to the existence of other types the results are extended to the case of two sided uncertainty this work extends schmidt 1993 who analysed the restricted class of conflicting interest games