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

observer based h controller design for state delayed linear systems we present two alternative observer based h control design methods for linear dynamic systems with delay in the state based on the riccati equation approach we design observer based feedback control laws that guarantee the asymptotic stability if the closed loop control system and reduce the effect of the disturbance input on the controlled output to a prescribed level

h sub infinity optimal control with state feedback a h sub infinity optimal control problem in which the measured outputs are the states of the plant is considered the main result shows that the infimum of the norm of the closed loop transfer function using linear static state feedback equals the infimum of the norm of the closed loop transfer function over all stabilizing dynamic even nonlinear time varying state feedback controllers

linear quadratic differential games with cheap control abstract this paper considers a linear quadratic differential game in which the weighting on the minimizing control is allowed to approach zero it is shown that if a certain minimum phase condition is satisfied then the value of the game will approach zero as the weighting on the minimizing control approaches zero

h control for discrete time linear systems with frobenius norm bounded uncertainties in this paper we consider the problems of robust stability and control for the class of uncertain discrete time linear systems with frobenius norm bounded parameter uncertainties in all matrices of the system and output equations necessary and sufficient conditions for the above problems are proposed a linear static state feedback control law is designed which is in terms of a riccati inequality the results obtained here show that the robust control problem of the uncertain system is equivalent to the control problem for a corresponding uncertainty free system

complete results for a class of state feedback disturbance attenuation problems the author considers a problem of disturbance attenuation using full state feedback the particular class of linear systems under consideration is closely related to the one block problem in h sup infinity control the author gives a complete solution to this problem in terms of a certain algebraic riccati equation

rates of convergence to equilibrium in the prigogine misra courbage theory of irreversibility the rates of convergence to equilibrium in the prigogine misra courbage theory of irreversibility as developed by goldstein misra and courbage are examined it is found that arbitrarily slow convergence to equilibrium should be present in fact in a certain precise sense it should be the most abundant behavior this is compared with the common beliefs in kinetic theory

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

synthesis of dissipative systems using quadratic differential forms part ii the problem discussed is that of designing a controller for a linear system that renders a quadratic functional nonnegative our formulation and solution of this problem is completely representation free the system dynamics are specified by a differential behavior and the performance is specified through a quadratic differential form we view control as interconnection a controller constrains a distinguished set of system variables the control variables the resulting behavior of the to be controlled variables is called the controlled behavior the constraint that the controller acts through the control variables only can be succinctly expressed by requiring that the controlled behavior should be wedged in between the hidden behavior obtained by setting the control variables equal to zero and the plant behavior obtained by leaving the control variables unconstrained the main result is a set of necessary and sufficient conditions for the existence of a controlled behavior that meets the performance specifications the essential requirement is a coupling condition an inequality that combines the storage functions of the hidden behavior and the orthogonal complement of the plant behavior

adding one power integrator a tool for global stabilization of high order lower triangular systems a new feedback design tool called adding a power integrator is introduced and used to solve the problem of global robust stabilization for a significant class of uncertain nonlinear systems that are of a lower triangular form but neither necessarily feedback linearizable fully or partially nor affine in the control input and therefore cannot be dealt with via conventional approaches sufficient conditions are presented under which a globally stabilizing smooth state feedback control law can be explicitly constructed using repeatedly the adding one power integrator technique this novel design technique permits removal of the feedback linearizability and linearity of the control input which have been two common assumptions so far in the literature of nonlinear control

polynomial matrix solution of the h infinity filtering problem and the relationship to riccati equation state space results a solution to the standard suboptimal h filtering problem is presented using a new polynomial systems ap proach the polynomial matrix solution is closely related to the recent h state space based riccati equation results and the links between the polynomial and state equation methodologies are demonstrated the h filter is derived by solving a special type of minimum variance filtering problem using a technique based on game theory the solution of this game problem in a stochastic setting by polynomial methods is novel the cal culation of the h filter involves a j spectral factorization and the solution of two coupled diophantine equations there are several computational advantages over previous polynomial methods for calculating h filters

an lmi approach to h controller design for linear time delay systems we develop an output feedback h control design method for linear time delay systems based on the linear matrix inequality lmi approach a sufficient condition for the existence of h controllers of any order is given in terms of three lmis the condition is valid for both singular and regular problems we also give a characterization of h controllers in state space the lmi existence condition can be easily determined whether or not it is feasible and if it is then one can easily obtain h controller gain matrices via convex optimization

exact computation of the infimum in h sub infinity optimization via output feedback the authors present a simple and noniterative procedure for the computation of the exact value of the infimum in the standard h sub infinity optimal control with output feedback the problem formulation is general and does not place any restrictions on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables the method is applicable to systems that satisfy the following conditions 1 the transfer function from the control input to the controlled output is right invertible and has no invariant zeros on the j omega axis and 2 the transfer function from the disturbance to the measurement output is left invertible and has no invariant zeros on the j omega axis

correction of the fi result in h sub infinity control and parameterization of h sub infinity state feedback controllers the authors correct the parameterization of the h sub infinity controller of the full information fi problem derived by j c doyle et al 1989 then they parameterize the h sub m0 state feedback controller and explain how dynamical free parameters implied in it are related to constant feedback gains different from the central solution f sub infinity

a non iterative method for computing the infimum in h optimization this paper presents a simple and non iterative procedure for the computation of the exact value of the infimum in the singular h optimization problem and is an extension of our earlier work the problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables our method is applicable to a class of singular h optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions the computation of the infimum in our method involves solving two well defined riccati and two lyapunov equations

the quadratic matrix inequality in singular h control with state feedback in this paper the standard h infty control problem using state feedback is considered given a linear time invariant finite dimensional system this problem consists of finding a static state feedback such that the resulting closed loop transfer matrix has h infty norm smaller than some a priori given upper bound in addition it is required that the closed loop system is internally stable conditions for the existence of a suitable state feedback are formulated in terms of a quadratic matrix inequality reminiscent of the dissipation inequality of singular linear quadratic optimal control where the direct feedthrough matrix of the control input is injective the results presented here specialize to known results in terms of solvability of a certain indefinite algebraic riccati equation

the singular h 2 control problem in this paper we discuss the standard h2 control problem for linear finite dimensional time invariant systems without any assumptions on the system parameters we give an explicit formula for the infimum over all internally stabilizing strictly proper compensators and give a characterization when the infimum is attained

linear control theory with an h 0e optimality criterion this expository paper sets out the principal results in bf h infty control theory in the context of continuous time linear systems the focus is on the mathematical theory rather than computational methods

the finite horizon singular h control problem with dynamic measurement feedback this paper is concerned with the finite horizon version of the h problem with measurement feedback given a finite dimensional linear time varying system together with a positive real number we obtain necessary and sufficient conditions for the existence of a possibly time varying dynamic compensator such that the l2 0 t1 induced norm of the closed loop operator is smaller than these conditions are expressed in terms of a pair of quadratic differential inequalities generalizing the well known riccati differential equations introduced recently in the context of finite horizon h control

brief paper singular h suboptimal control for a class of nonlinear cascade systems in the present paper singular state feedback h suboptimal control for a class of nonlinear cascade systems is addressed under the assumption that a regular state feedback h suboptimal control problem is solvable for a particular subsystem of the cascade system an auxiliary nonlinear system is defined it is shown that a state feedback solution to the singular h suboptimal control problem for the auxiliary system also applies to the original problem the advantage of the auxiliary problem to the original problem is that the auxiliary penalty variable has lower dimension than the original penalty variable it is shown how this fact can simplify the problem considerably for the case when the auxiliary system can be strongly input output decoupled the theory is applied to a problem of a rigid spacecraft with actuator dynamics application to the special case when a subsystem of the nonlinear cascade system is passive is also considered

a generalization of the hermitian and skew hermitian splitting iteration method for solving sylvester equations this paper is concerned with a generalization of the hermitian and skew hermitian splitting hss iteration method for solving large sparse continuous sylvester equations the analysis shows that the ghss iteration method will converge under certain assumptions numerical results show that this new method is more efficient and robust than the existing ones

high gain observer approach to disturbance attenuation using measurement feedback a procedure is developed for disturbance attenuation in a linear system via the use of measurement feedback a high gain observer is used to recover the disturbance attenuation properties asymptotically which can be achieved using full state feedback it is thus shown that the problem of disturbance attenuation via measurement feedback can be decomposed into two problems of disturbance attenuation via state feedback these problems of disturbance via state feedback can then be solved using existing methods based on the algebraic riccati equation

a nonequilibrium entropy for dynamical systems it is proposed to define entropy for nonequilibrium ensembles using a method of coarse graining which partitions phase space into sets which typically have zero measure these are chosen by considering the totality of future possibilities for observation on the system it is shown that this entropy is necessarily a nondecreasing function of the timet there is no contradiction with the reversibility of the laws of motion because this method of coarse graining is asymmetric under time reversal under suitable conditions which are stated explicitly this entropy approaches the equilibrium entropy ast and the fine grained entropy ast in particular the conditions can always be satisfied if the system is ak system as in the sinai billiard models some theorems are given which give information about whether it is possible to generate the partition used here for coarse graining from time translates of a finite partition and at the same time elucidate the connection between our concept of entropy and the entropy invariant of kolmogorov and sinai

chapman kolmogorov equation for non markovian shift invariant measures we study the class c of probability measures invariant with respect to the shift transformation on k z where k is a finite set of integers which satisfies the chapman kolmogorov equation for a given stochastic matrix we construct a dense subset of measures in c distinct from the markov measure when is irreduable and aperiodic these measures are ergodic but not weary mixing we show that the set of measures with infinite memory is g dense in c and that the markov measure is the unique measure which maximizes the kolmogorov sinai k s entropy in c we give examples of ergodic measures in c with zero entropy

preconditioned hss iteration method and its non alternating variant for continuous sylvester equations abstract bai 2010 proposed an efficient hermitian and skew hermitian splitting hss iteration method for solving a broad class of large sparse continuous sylvester equations to further improve the efficiency of the hss method in this paper we present a preconditioned hss phss iteration method and its non alternating variant nphss for this matrix equation the convergence properties of the phss and nphss methods are studied in depth and the quasi optimal values of the iteration parameters for the two methods are also derived moreover to reduce the computational cost we establish the inexact variants of the two iteration methods numerical experiments illustrate the efficiency and robustness of the two iteration methods and their inexact variants

nonlinear h almost disturbance decoupling the l2 gain almost disturbance decoupling problem for siso nonlinear systems is formulated sufficient conditions are identified for the existence of a parametrized state feedback controller such that the l2 gain from disturbances to output can be made arbitrarily small by increasing its gain the controller is explicity constructed using a lyapunov based recursive scheme sufficient conditions for the solvability of the h almost disturbance decoupling problem and the explicit construction of teh controller are given for a more restrictive class of nonlinear systems

the role of the dissipation matrix in singular optimal control the optimal cost in the regular stationary linear quadratic optimal control problem is given by the maximal solution of an algebraic riccati equation this solution minimizes the rank of a certain matrix which we call the dissipation matrix the rank minimization problem is also meaningful in the singular case does it provide the optimal cost for the singular control problem this question was posed by j c willems in 1971 the answer is yes

state space formulae for all the stabilizing discrete controllers that satisfy an h norm bound part 1 main results and the full information problem given a linear discrete time system necessary and sufficient conditions for the existence of a linear or nonlinear controller which satisfies a specified closed loop h norm bound are stated in terms of the solutions to two uncoupled algebraic discrete riccati equations of the order of the system state space formulae for all the stabilizing controllers some of the order of the system which satisfy an achievable bound are also given in this first part of the paper new growth and convergence properties of the solution to a time varying discrete riccati equation are used to derive the necessary and sufficient conditions for the existence of a solution in the full information case these properties generalize those of the corresponding discrete riccati equation related to the lqr problem in the second part of the paper a non standard estimation problem is posed and solved this problem arises as a novel reinterpretation of the h norm objective its solution can be used to reduce a partial informa

brief paper explicit construction of h control law for a class of nonminimum phase nonlinear systems this paper addresses a nonlinear h control problem for a class of nonminimum phase nonlinear systems the given system is first transformed into a special coordinate basis in which the system zero dynamics is divided into a stable part and an unstable part a sufficient solvability condition is then established for solving the nonlinear h control problem moreover based on the sufficient solvability condition an upper bound of the best achievable l 2 gain from the system disturbance to the system controlled output is estimated for the nonlinear h control problem the proofs of our results yield explicit algorithms for constructing required control laws for solving the nonlinear h control problem in particular the solution to the nonlinear h control problem does not require solving any hamilton jacobi equations finally the obtained results are utilized to solve a benchmark problem on a rotational translational actuator rtac system

chaotic dynamics markovian coarse graining and information abstract the conditions for mapping chaotic dynamics into a markov chain through finite coarse graining are derived a chapman kolmmogorov equation giving rise to an h theorem is deduced in which the transition probability matrix is expressed entirely in terms of the properties of the underlying deterministic dynamics and of the phase space partition the validity of the conditions ensuring the mapping is verified on simple models of dissipative as well as conservative dynamical systems the implications of the results in the problem of irreversibility and the relation between deterministic chaos information and complexity are discussed

intrinsic irreversibility of kolmogorov dynamical systems we give the mathematical details and various extensions of the results stated in previous work of courbage and prigogine intrinsic random systems are deterministic and conservative dynamical systems for which we can associate two dissipative markov processes through a one to one change of representation the first leading to equilibrium for t and the second for t the microscopic formulation of the second principle of thermodynamics permits to lift the degeneracy by the exclusion of all states that do not approach equilibrium for t the set of admitted initial conditions d is then characterized by a non equilibrium entropy functional which is infinite for rejected initial states and takes finite values for admitted initial conditions thus rejected initial states correspond to an infinite amount of information to realize this selection rule we consider general probability measures on phase space that are not necessarily absolutely continuous and we extend the theory of transition to markov processes to such measures owing to the non invariance of d under the time inversion the evolution of these states in the new representation can only be given by one of the two possible markov processes

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

the role of stable manifolds and information in the prigogine theory of irreversibility the image of dirac measures x by the operator of the construction of prigogine and collaborators is shown to be concentrated in the stable manifold xst x and its density function is studied for bernoulli shifts the valuev exp h t whereh t is the kolmogorov entropy appears as a critical point for the behavior of it is also proved that no loss of information is involved by passing from the dynamical system to the markov process when vx 1 2 the discussion is based on the introduction of an invariant for markov systems that generalizes the usual kolmogorov entropy for dynamical systems

strictly proper projective controllers for disturbance attenuation a design methodology is presented which applies projective controls to the disturbance attenuation problem for large flexible structures through this method low order strictly proper controllers are designed which improve the disturbance attenuation properties of the system a new parameterization of the closed loop system in terms of free parameters in the projective controller leads to an auxiliary minimization problem which determines the parameters of the controller a flexible structure example demonstrates the use of this methodology

a dynamic games approach to controller design disturbance rejection in discrete time it is shown that the discrete time disturbance rejection problem formulated in finite and infinite horizons and under perfect state measurements can be solved by making direct use of some results on linear quadratic zero sum dynamic games for the finite horizon problem an optimal minimax controller exists and can be expressed in terms of a generalized time varying discrete time riccati equation the existence of an optimum also holds in the infinite horizon case under an appropriate observability condition with the optimal control given in terms of a generalized algebraic riccati equation also being stabilizing in both cases the corresponding worst case disturbances turn out to be correlated random sequences with discrete distributions which means that the problem viewed as a dynamic game between the controller and the disturbance does not admit a pure strategy saddle point results for the delayed state measurement and the nonzero initial state cases are presented

quadratic controllability strong controllability and a related output feedback property quadratic controllability and strong controllability are the two system properties to be discussed for a special class of norm bounded uncertain linear systems the main contribution of this paper is twofold first we show that it is possible to reduce the problem of checking quadratic controllability or strong controllability of a given uncertain system to the same problem for a reduced order subsystem which we call the essential subsystem then we use this result to examine a related output feedback property specifically for a given uncertain system we will answer the following question what condition is necessary and sufficient for the existence of a dynamic output feedback controller such that the states of the closed loop system converge to the origin with an arbitrarily fast rate our aim is to provide an insight and better understanding of uncertain systems through these results

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

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

solution of the state feedback singular h control problem for linear time varying systems a procedure for the solution of the h control problem when the system is time varying and the feedthrough matrix between the control input and the controlled output is not full column rank is proposed

some open problems in matrix theory arising in linear systems and control control theory has long provided a rich source of motivation for developments in matrix theory accordingly we discuss some open problems in matrix theory arising from theoretical and practical issues in linear systems theory and feedback control the problems discussed include robust stability matrix exponent induced norms stabilizability and pole assignability and nonstandard matrix equations a substantial number of references are included to acquaint matrix theorists with problems and trends in this application area feedback control theory has long provided a rich source of motivation for developments in matrix theory the purpose of this paper is to discuss several open problems in matrix theory that arise from theoretical and practical issues in feedback control theory and the associated area of linear systems theory many of these problems are remarkably simple to state are of intense interest in control theory and applications and yet remain unsolved besides leading to the resolution of these problems it is hoped that this paper will help to stimulate increased interaction between matrix and control theorists accord

disturbance observer for estimating higher order disturbances in time series expansion in the note a generalized disturbance observer capable of estimating higher order disturbances in the time series expansion is newly proposed initiated from a constant disturbance observer we extend it systematically to cope with ramp disturbance and general order disturbances the generalized form for disturbance observer exhibits the novel structure incorporating the system model and integrals to be practical the noisy measurement and the performance in the frequency domain are addressed in addition for a class of linear systems an output based disturbance observer of reduce order is newly derived from the proposed full state disturbance observer and its potential applicability will be demonstrated by an example

almost disturbance decoupling for a class of high order nonlinear systems the problem of almost disturbance decoupling with internal stability add is formulated in terms of an l sub 2 l sub 2p instead of an l sub 2 gain for a class of high order nonlinear systems which consist of a chain of power integrators perturbed by a lower triangular vector field a significant feature of the systems considered in the paper is that they are neither feedback linearizable nor affine in the control input which have been two basic assumptions made in all the existing add nonlinear control schemes using the technique of adding a power integrator we solve the add problem via static smooth state feedback under a set of growth conditions that can be viewed as a high order version of the feedback linearization conditions we also show how to explicitly construct a smooth state feedback controller that attenuates the disturbance s effect on the output to an arbitrary degree of accuracy with internal stability

global output regulation for a class of lower triangular nonlinear systems a feedback domination approach abstract an alternative but new nonlinear output regulation approach is proposed for a class of lower triangular nonlinear systems by using the tool of adding a power integrator the invariant manifold is solved and represented in terms of various derivatives of disturbances and references as such it is unnecessary to suppose that the external disturbances being governed by certain exosystems anymore the nonlinearities are not restricted to be sufficiently smooth due the utilization of feedback domination approach it is shown that the time taken to reach the desired invariant manifold from any initial states under external disturbances is guaranteed to be finite time the control law is concise in structure for implementation since the feedback domination is implemented in each of the recursive design step

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

entropy functionals associated to shifts dynamical systems abstract we construct entropy functionals which discriminate the measures which converge to equilibrium in the case of shifts dynamical systems in particular for k shifts it is proved that some functionals associated to them decrease monotonically to zero

cooperative output regulation of heterogeneous multi agent systems an h_ infty criterion in this note the cooperative output regulation problem of heterogeneous linear multi agent systems is investigated our approach is based on internal model and dynamic error feedback among the agents under some standard assumptions the problem is solved by an internal model and a stabilizing h controller we showed that the exo signal free system is stabilized if each controlled agent is robust in the sense of h norm to resist the disturbance measured by the second largest eigenvalue of the graph adjacency matrix then the synthesis problem is solved using algebraic riccati equation furthermore we showed that this condition is a generalization of existing results

monotonicity of maximal solutions of algebraic riccati equations abstract a monotonicity result for the maximal solution of the equation xbb x a x xa q 0 q q a b stabilizable is proved

robust h control for uncertain discrete singular systems with pole placement in a disk abstract this paper addresses the design of robust h controllers for uncertain discrete singular systems with time invariant uncertainty in both the state and measurement matrices the singular system to be controlled is not assumed to be regular a regular dynamic output feedback controller is designed such that a prescribed h performance condition is satisfied and the closed loop poles are placed in a specified disk while the regularity causality and stability of the closed loop system can be guaranteed for all admissible uncertainties the desired controller can be obtained by solving a set of matrix inequalities a numerical example is given to demonstrate the application of the proposed method

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

riccati equation approach to maximizing the complex stability radius by state feedback in this paper we study the problem of maximizing the complex stability radius of a linear time invariant state space system by linear state feedback we show that the supreme achievable stability radius can be characterized via parametrized riccati equations the dependency on the parameters is examined and the limiting behaviour described finally the relationship between the supremum of the achievable stability radii and the distance of a system from non stabilizabilky is investigated

effects of using observers on stabilization of uncertain linear systems the effects of observers on robust linear feedback controllers are studied sufficient conditions are obtained that guarantee full recovery of the allowable uncertainty bounds attainable by full state feedback the effects of the resulting high gain observers on the disturbance rejection bounds are also studied it is shown that full recovery of the uncertainty bound leads to possible large degradation in disturbance rejection however if there is only additive plant disturbance and no measurement disturbance this degradation can be prevented

h sub spl infin memoryless control with an spl alpha stability constraint for time delay systems an lmi approach focuses on the design of h sub spl infin memoryless state feedback controllers satisfying some spl alpha stability constraints on the closed loop poles for a class of linear systems with delayed state subject to disturbance inputs a sufficient condition for feasibility is derived in terms of linear matrix inequalities furthermore we also consider a particular optimization problem the maximal bound allowed on time delay such that the prescribed level on disturbance attenuation and the spl alpha stability constraints are still preserved this problem is converted into a linear matrix inequality lmi optimization problem and we give a suboptimal bound on the delay

robust h sub spl infin control for linear discrete time systems with norm bounded nonlinear uncertainties this paper studies the problem of robust control of a class of uncertain discrete time systems the class of uncertain systems is described by a state space model with linear nominal parts and norm bounded nonlinear uncertainties in the state and output equations the authors address the problem of robust h sub spl infin control in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties it has been shown that instead of the nonlinear uncertain system one may only consider a related linear uncertain system and thus a linear static state feedback control law is designed which is in terms of a riccati inequality

a structure preserving doubling algorithm for nonsymmetric algebraic riccati equation in this paper we propose a structure preserving doubling algorithm sda for the computation of the minimal nonnegative solution to the nonsymmetric algebraic riccati equation nare based on the techniques developed for the symmetric cases this method allows the simultaneous approximation to the minimal nonnegative solutions of the nare and its dual equation requiring only the solutions to two linear systems and several matrix multiplications per iteration similar to newton s method and the fixed point iteration methods for solving nares we also establish global convergence for sda under suitable conditions using only elementary matrix theory we show that sequences of matrices generated by sda are monotonically increasing and quadratically convergent to the minimal nonnegative solutions of the nare and its dual equation numerical experiments show that the sda algorithm is feasible and effective and outperforms newton s iteration and the fixed point iteration methods

memoryless h sup spl infin controllers for state delayed systems in this note a memoryless h sup spl infin controller for the state delayed system is presented the controller is a delay independent stabilizer for the state delayed system which also reduces the h sup spl infin norm of the closed loop transfer function from the disturbance to the controlled output to a prescribed level the controller can be obtained by solving a modified riccati equation

the singular minimum entropy h control problem abstract in this paper we search for controllers which minimize an entropy function of the closed loop transfer matrix under the constraint of internal stability and under the constraint that the closed loop transfer matrix has h norm less than some a priori given bound we find an explicit expression for the infimum moreover we give a characterization when the infimum is attained contrary to the regular case for the singular minimum entropy h control problem the infimum is not always attained

memoryless h controller design for linear systems with delayed state and control we present a memoryless h control design method for linear time invariant systems that have no parametric uncertainty but delay in the state and control based on the riccati equation approach we design a memoryless linear time invariant state feedback control law which guarantees the asymptotic stability of the closed loop control system and reduces the effect of the disturbance input on the controlled output to a prescribed level

closed form h infinity optimal control for a class of infinite dimensional systems h infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators diffusion equations are an important example in this class explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given unlike traditional methods for h infinity synthesis no iteration is needed to obtain the optimal solution moreover the optimal performance for both the state feedback and state estimation problems are explicitly calculated this is shown to be useful for problems of h infinity optimal actuator and sensor location furthermore the results can be used in testing and bench marking of general purpose algorithms for h infinity synthesis the results also apply to finite dimensional systems

symbolic dynamics of noisy chaos abstract one model of randomness observed in physical systems is that low dimensional deterministic chaotic attractors underly the observations a phenomenological theory of chaotic dynamics requires an accounting of the information flow from the observed system to the observer the amount of information available in observations and just how this information affects predictions of the system s future behavior in an effort to develop such a description we discuss the information theory of highly discretized observations of random behavior metric entropy and topological entropy are well defined invariant measures of such an attractor s level of chaos and are computable using symbolic dynamics real physical systems that display low dimensional dynamics are however inevitably coupled to high dimensional randomless e g thermal noise we investigate the effects of such fluctuations coupled to deterministic chaotic systems in particular the metric entropy s response to the fluctuations we find that the entropy increases with a power law in the noise level and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory we also argue that in addition to the metric entropy there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations i0 the maximum average information obtainable about the initial condition that produces a particular sequence of measurements or symbols

robust h sub spl infin output feedback control for nonlinear systems in this paper we present a new approach to the solution of the output feedback robust h sub spl infin control problem we employ the recently developed concept of information state for output feedback dynamic games and obtain necessary and sufficient conditions for the solution to the robust control problem expressed in terms of the information state the resulting controller is an information state feedback controller and is intrinsically infinite dimensional stability results are obtained using the theory of dissipative systems and our results are expressed in terms of dissipation inequalities

all optimal controls for the singular linear quadratic problem without stability a new interpretation of the optimal cost abstract the singular linear quadratic control problem without stability is solved by means of a generalized dual structure algorithm in order to generate all optimal inputs furthermore it is shown that the optimal cost can be interpreted as the smallest nonnegative rank minimizing solution of a certain matrix inequality the so called dissipation inequality

the state feedback h problem at optimality abstract we discuss the infinite horizon h control problem by state feedback for a linear time invariant plant which is not restricted with respect to its finite or infinite zero structure we provide an algebraic characterization for the optimal value to be attained in terms of the solvability of a nonstrict riccati inequality and propose possibilities for verifying these criteria if the optimum is not achieved we give a complete test for the need of high gain feedback in order to approach the optimal value

the robust optimal control of uncertain systems state space method the robust optimal control of linear uncertain systems with l sub 2 bounded uncertainties is addressed the optimal state feedback control law in the so called worst disturbance case is derived the lql method minimax state estimation maximin state feedback closed loop control scheme lql means linear quadratic l sub 2 bounded uncertainties is proposed in a sense the lql method uses the idea of the linear quadratic gaussian lqg method to treat h sub infinity optimizing design problems

robust h control for linear time invariant systems with norm bounded uncertainty in the input matrix abstract this paper focuses on the problem of robust h control design for a class of linear time invariant systems with uncertainty in the state space model we consider uncertain systems with norm bounded parameter uncertainty in the input matrix the paper presents a state feedback control design which stabilizes the plant for all admissible uncertainties and also guarantees an h norm bound constraint on disturbance attenuation paralleling to the theory of robust control the robust h control problem is solved via the notion of quadratic stabilization with an h norm bound constraint necessary and sufficient conditions for quadratic stabilization with an h norm bound are derived it is shown that the solution to this problem involves solving a parameter dependent algebraic riccati equation the results can be regarded as extensions of existing results on robust stabilization of linear uncertain systems and h optimal control

an algebraic approach to robust h control via state feedback abstract this paper considers the problem of robust h control design for linear uncertain systems we show that for a certain type of time varying norm bounded parameter uncertainty the problem is equivalent to an h control problem therefore a complete solution is achieved by using the existing results of h control theory the paper presents a state feedback design which stabilizes the plant for all admissible uncertainties and also guarantees a prescribed level of disturbance attenuation in a certain sense

system order reduction in robust stabilization problems robust stabilization via state feedback is considered using a fixed quadratic lyapunov function approach quadratic stabilization we investigate the possibility of reducing the quadratic stabilization problem of a given uncertain system to a similar problem for an uncertain subsystem with a fewer number of states this subsystem is the so called regular subsystem associated with the original system it is shown that when some of the control input channels of the given uncertain system are free of uncertainty this reduction is possible we show that a given uncertain system is quadratically stabilizable via linear state feedback if and only if the same holds for its regular subsystem when the regular subsystem is quadratically stabilizable via linear state feedback a simple formula for a controller that quadratically stabilizes the original system is given we also present an example of an uncertain system that is not quadratically stabilizable even though its regular subsystem can be quadratically

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

approach to equilibrium for locally expanding maps in ℝ k by using a well known technique from classical statistical mechanics of one dimensional lattice spin systems we prove existence of an absolutely continuous invariant asymptotic measure for certain locally expanding mapst of the unit cube in k we generalize herewith in a certain sense the results of lasota and yorke on piecewise expanding maps of the unit interval to higher dimensions we show a kuzmin type theorem for these systems from which exponential approach to equilibrium and strong mixing properties follow

h disturbance attenuation for state delayed systems in this note the differential game and dissipation inequality are applied to the disturbance attenuation or h control for linear systems with delayed state firstly a simple sufficient condition on the existence of a suboptimal h state feedback controller is given which is independent of delay and an observer based dynamic output feedback solution is presented in terms of riccati inequalities or riccati equations secondly a sufficient condition on the existence of a delay dependent state feedback is presented and the criterion is presented by a matrix inequality which can be solved by numerical methods