the largest singular value of e sup x a sub 0 e sup x is convex on convex sets of commuting matrices a short and direct proof of the convexity property is given it is shown that the theorem applies to any convex commuting set of matrices in r sup nxn where a sub 0 in r sup nxn is fixed it is also shown that the result does not hold if x is permitted to be a general square matrix a counterexample is supplied for noncommuting matrices

controller reduction in the two block h optimal design for distributed plants abstract in this paper we consider a two block mixed h sensitivity minimization problem for a class of siso possibly unstable infinite dimensional systems the main issue addressed here is the problem of reducing the order of h optimal controllers it is well known that the optimal controllers for distributed plants are infinite dimensional here we obtain a finite dimensional controller from approximations of the optimal controller in the gap metric topology we show that under certain mild conditions one can obtain a finite dimensional stabilizing controller achieving a performance arbitrarily close to the optimum we also provide an explicit bound for the performance deviation this bound depends on the approximations of the infinite dimensional parts of the optimum controller an example involving an unstable delay system is given to illustrate the computational aspects of this approach

on stabilization and the existence of coprime factorizations shows that any transfer function matrix whose elements belong to the quotient field of h sub infinity and which is stabilizable has a matrix fraction representation over h sub infinity which is coprime in the sense that a matrix bezout identity can be satisfied

on spl hscr sub spl infin control for dead time systems a mixed sensitivity spl hscr sub spl infin problem is solved for dead time systems it is shown that for a given bound on the spl hscr sub spl infin norm causal stabilizing controllers exist that achieve this bound if and only if a related finite dimensional riccati equation has a solution with a certain nonsingularity property in the case of zero time delay the riccati equation is a standard riccati equation and the nonsingularity condition is that the solution be nonnegative definite for nonzero time delay the nonsingularity condition is more involved but still allows us to obtain controllers all suboptimal controllers are parameterized and the central controller is shown to be a feedback interconnection of a finite dimensional system and a finite memory system both of which can be implemented some spl hscr sub spl infin problems are rewritten as pure rational spl hscr sub spl infin problems using a smith predictor parameterization of the controller

a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

optimal h robustness and the relationship to lqg design problems a solution to the hx optimal control problem is obtained by employing a standard lqg polynomial based solution procedure the derivation is straightforward and avoids many of the more abstract mathematical results usually employed the relationship between the lqg and hm design methods becomes transparent and the similarities and differences can be identified

comments on grimble s comments on stein s comments on rolloff of h sup infinity optimal controllers in m j grimble s comments see ibid vol 35 p 762 5 1990 the polynomial systems approach to h sup infinity is shown to have an advantage over the state space approach in that improper weighting functions can be used allowing one to obtain controllers that roll off at high frequencies it is shown that the same controller can be found with the state space approach using a simple problem reformulation

mixed sensitivity optimization for a class of unstable infinite dimensional systems abstract in this paper we solve the h mixed sensitivity minimization problem for a class of unstable distributed systems the solution is based on an extension of the skew toeplitz methodology the key mathematical fact used is that the skew toeplitz operators arising in the unstable case are finite rank perturbations of the classical skew toeplitz operators obtained from compressions of rational functions a system of linear equations the singular system is derived for this class of operators from which one can compute the associated singular values and vectors an example is included to illustrate the results

parameterization of suboptimal solutions of the nehari problem for infinite dimensional systems the nehari problem plays an important role in hinfin control theory it is well known that hinfin control problem can be reduced to solving this problem this note gives a parameterization of all suboptimal solutions of the nehari problem for a class of infinite dimensional systems many earlier solutions of this problem are seen to be special cases of this new parameterization it is also shown that for finite impulse response systems this parameterization takes a particularly simple form

well posedness of h optimal control problems this paper considers the effect of perturbations of a nominal single input single output linear plant or a band of uncertainty on the solution to certain frequency domain optimal control problems weighted h infty sensitivity minimization mixed and robust sensitivity minimization will be considered along with problems of more general type a brief discussion of h p optimal control problems will also be given typical examples will be presented where optimal sensitivity does not depend continuously on the plant ill posedness and conditions for well posedness will be given it is demonstrated that similar discontinuities can occur for more general problems also suggested are ways of defining an optimization problem so that continuous dependence of the infimum is ensured

a note on essential spectra and norms of mixed hankel toeplitz operators in this brief hankel toeplitz operators which occur in feedback theory e g in the minimization of mixed h sensitivity and complementary sensitivity will be considered a method of computing their spectra eigenvectors and norms will be presented for infinite dimensional systems subject to continuous weightings

stable h controller design for systems with multiple input output time delays abstract the stable h controller design problem is considered for multi input multi output systems with multiple input output time delays an algorithm is presented to solve this problem the algorithm makes use of the small gain theorem and the structure of the h controller for the class of systems under consideration

robust stabilization of infinite dimensional systems by finite dimensional controllers abstract the problem of robustly stabilizing an infinite dimensional system with transfer function g subject to an additive perturbation is considered it is assumed that g b 0 of systems introduced by callier and desoer 3 the perturbation satisfies w1 w2 c now write w1gw2 g1 g1 where g1 is rational and totally unstable and g2 is stable generalizing the finite dimensional results of glover 12 this family of perturbed systems is shown to be stabilizable if and only if min g 1 the smallest hankel singular value of g 1 a finite dimensional stabilizing controller is then given by k w 2 k 1 i g 2 k 1 1 w 1 where 2 is a rational approximation of g2 such that g 2 g 2 min g 1 and k1 robustly stabilizes g1 to margin the feedback system g k will then be stable if w1 w2

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

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

weighted sensitivity minimization for delay systems in this note we discuss the h infty sensitivity minimization problem for linear time invariant delay systems while the unweighted case reduces to simple nevanlinna pick interpolation the weighted case turns out to be much more complicated and demands certain functional analytic techniques for its solution

optimal model matching control for time delay systems model matching control for time delay systems is formulated as an optimization problem in h2 norm space as well as h norm space wiener hopf techniques and the theory of optimal interpolation are successfully employed to treat this model matching problem including perfect and imperfect model matching cases prior to this work for time delay systems only the problem of perfect model matching control had been considered and no attempt had been made to examine that of imperfect model matching control with the optimization approach presented here an optimal model matching control scheme is constructed for the imperfect model matching case to produce perfect model matching results whenever possible

on standard h sub spl infin control of processes with a single delay this note presents a frequency domain method to solve the standard h sub spl infin control problem for processes with a single delay for a given bound on the closed loop h sub spl infin norm there exist proper stabilizing controllers that achieve this bound if and only if both the corresponding delay free h sub spl infin problem and an extended nehari problem with a delay or a one block problem are all solvable the solvability of the extended nehari problem or the one block problem is equivalent to the nonsingularity of a delay dependent matrix the solvability conditions of the standard h sub spl infin control problem with a delay are formulated in terms of the existence of solutions to two delay independent algebraic riccati equations and a delay dependent nonsingularity property all suboptimal controllers solving the three problems are respectively parameterized as a structure incorporating a modified smith predictor

tutorial review h optimal controller design for a class of distributed parameter systems this paper is a tutorial on a frequency domain design method for the two block h optimal control of a class of siso distributed parameter systems uncertainties in the system are assumed to be unmodelled dynamics represented in the form of either multiplicative or additive or coprime factor perturbations of a nominal infinite dimensional plant performance of the closed loop system is measured in terms of the energy amplification from external input signals to the outputs of interest in this paper transfer functions of the nominal plant and the weights are used in order to derive a solution to two block h control problems the solution presented here uses results from operator theory the h optimal performance and controller in this method are computed from a finite set of linear equations

sampled data control of continuous time systems with an h optimality criterion abstract the synthesis of sampled data controllers for continuous time systems is studied in the context of h control theory the sampled data h optimal control problem consists of finding a sampled data controller which minimizes the l2 induced norm from the continuous time disturbance to the continuous time output the problem is here solved via a discrete system representation this is achieved by describing the closed loop system as a discrete system with finite state dimension and with a representation of the disturbance and the output signals of the discrete system as sequences of elements of certain infinite dimensional spaces via finite rank approximations of a compact integral operator associated with the system the sampled data h control problem can be solved to any degree of accuracy from the structure of the problem it follows that irrespective of the order of the approximation a feasible sampled data controller can be found which has the same order as the system

a skew toeplitz approach to the h optimal control of multivariable distributed systems in this paper the problem of the h infty optimization of multivariable distributed systems in the four block setting is studied this work is based on several previous papers and employs the skew toeplitz framework developed in operator theory adv appl 32 1988 pp 21 43 operator theory adv appl 32 1988 pp 93 112 operator theory and integral equations 11 1988 pp 726 767 j functional anal 74 1987 pp 146 159 siam j math anal 19 1988 pp 1081 1091

paper adaptive controllers for discrete time systems with arbitrary zeros an overview the paper presents a comprehensive review of the problem of designing discrete time adaptive controllers for systems with arbitrary zeros minimum or non minimum phase systems being particular cases the authors have attempted to give a unified presentation of the various existing schemes by stripping away the technical details and highlighting their close interrelation through the use of a common framework both algorithmic and theoretical aspects are discussed with particular emphasis on the stability of the schemes

a weighted mixed sensitivity h sub spl infin control design for irrational transfer matrices approximate solutions to a weighted mixed sensitivity h sub spl infin control problem for an irrational transfer matrix are obtained by solving the same problem for a reduced order rational transfer matrix upper and lower bounds for the sensitivity are obtained in terms of the sensitivity for the reduced order model and the approximation error moreover rational suboptimal controllers for the irrational transfer matrix are constructed which achieve a sensitivity close to the minimum

homogeneous lyapunov function for homogeneous continuous vector field the goal of this article is to provide a construction of a homogeneous lyapunov function p associated with a system of differential equations j f x x r n 1 under the hypotheses 1 f c r n vanishes at x 0 and is homogeneous 2 the zero solution of this system is locally asymptotically stable moreover the lyapunov function v x tends to infinity with 1 x i and belongs to c r 0 r n cp with p e as large as wanted as application to the theory of homogeneous systems we present two well known results of robustness in a slightly extended form and with simpler proofs

on decoupling the h optimal sensitivity problem for products of plants abstract in this note we show how to solve the h optimal sensitivity problem for a siso plant p s p 1 s p 2 s given the solutions for p 1 s p 2 s this allows us to solve the problem for systems of the form e hs p 0 s where p 0 s is the transfer function of a stable lti finite dimensional system

brief every stabilizing dead time controller has an observer predictor based structure this paper considers the stabilization problem for linear time invariant systems with a single delay h in the feedback loop two parametrizations of all stabilizing controllers are derived in terms of a state space realization of the rational part of the plant these parametrizations have simple structures and clear interpretations the first is in the form of a generalized dead time compensator smith predictor and the second is in the observer predictor form applications of the proposed parametrization to the h 2 optimization and the robust stabilization problems are discussed

global parametrization of feedback systems with nonlinear plants for unity feedback systems with a plant p and controller c we show that given a nonlinear stable p the class of all controller stabilizing the feedback system is globally parametrized by a stable map q we also show how q is useful in studying the effects of modeling errors on the stability

technical communique a small gain theorem for systems with non causal subsystems small gain theorems are used to verify the stability of a feedback interconnection of causal stable systems in this work we extend the small gain condition to test the stability of a feedback interconnection of two stable systems at least one of which is non causal this result may find application in the robust controller design for time delay systems

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

the linear quadratic control problem for infinite dimensional systems with unbounded input and output operators this paper establishes a general semigroup framework for solving quadratic control problems with infinite dimensional state space and unbounded input and output operators

local stabilization and controllability of a class of non triangular nonlinear systems this paper considers the problems of local asymptotic stabilization using continuous static state feedback lcfs and small time local controllability stlc of single input nonlinear systems a specific class of nontriangular systems called the essentially triangular form is introduced for this class of systems sufficient conditions for lcfs and necessary and sufficient conditions for stlc are obtained in particular it is shown that stlc implies lcfs a motivating physical example of the etf system is presented

on h sub 2 control of systems with multiple i o delays the h2 optimal control problem of systems with multiple i o delays is solved the problem is tackled by first transforming it to what is called the two sided regulator problem the latter is solved using orthogonal projection arguments and spectral factorization the resulting controller is an interconnection of rational blocks nonrational blocks having finite impulse response and delay operators all of which are implementable

on the h optimal sensitivity problem for systems with delays in this paper we extend some of the results of ieee trans automat control ac 31 1986 pp 763 766 to more general delay systems in particular we analyze the effect of the interaction of delays and nonminimum phase zeros on the h infty optimal weighted sensitivity

on the mixed sensitivity minimization for systems with infinitely many unstable modes in this note we consider a class of linear time invariant systems with infinitely many unstable modes by using the parameterization of all stabilizing controllers and a data transformation we show that h controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes

a hamiltonian based solution to the mixed sensitivity optimization problem for stable pseudorational plants this paper considers the mixed sensitivity optimization problem for a class of infinite dimensional stable plants this problem is reducible to a two or one block h control problem with structured weighting functions we first show that these weighting functions violate the genericity assumptions of existing hamiltonian based solutions such as the well known zhou khargonekar formula then we derive a new closed form formula for the computation of the optimal performance level when the underlying plant structure is specified by a pseudorational transfer function 2005 elsevier b v all rights reserved

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

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

intermittent redesign of analog controllers via the youla parameter the paper studies digital redesign of linear time invariant analog controllers under intermittent sampling the sampling pattern is only assumed to be uniformly bounded but otherwise irregular and unknown a priori the contribution of the paper is twofold first it proposes a constructive algorithm to redesign any analog stabilizing controller so that the closed loop stability is preserved second it is shown that when applied to sub optimal boldsymbol h 2 and boldsymbol h infty controllers the algorithm produces sub optimal sampled data solutions under any a priori unknown sampling pattern the proposed solutions are analytic computationally simple implementable and transparent transparency pays off in showing the optimality under a fixed sampling density of uniform sampling for both performance measures studied

unstable and nonproper weights in h control an h control problem is examined in which the controller can and need only stabilize a part of the generalized closed loop due to unstable weights the procedure is a simple extension of known results and is computationally the easiest method available

weight selection in feedback design with degree constraints we present an approach for feedback design which is based on recent developments in analytic interpolation with a degree constraint performance is cast as an interpolation problem with bounded analytic functions minimizers of a certain weighted entropy functional provide interpolants having degree less than the number of constraints the choice of weight parameterizes all such bounded degree solutions however the relationship between the weights and the shape of corresponding transfer functions is not direct thus in this paper we develop a formalism that guides weight selection

output feedback decentralized control of large scale systems using weighted sensitivity functions minimization this paper considers the problem of achieving stability and desired dynamical transient behavior for linear large scale systems by decentralized control it can be done by making the effects of the interconnections between the subsystems arbitrarily small sufficient conditions for stability and diagonal dominance of the closed loop system are introduced these conditions are in terms of decentralized subsystems and directly make a constructive h control design possible a mixed h pole region placement is suggested such that by assigning the closed loop eigenvalues of the isolated subsystems appropriately the eigenvalues of the overall closed loop system are assigned in desirable range the designs are illustrated by an example

h control with transients in h infty or uniformly optimal control problems it is usually assumed that the system initial conditions are zero in this paper an h infty like control problem that incorporates uncertainty in initial conditions is formulated this is done by defining a worst case performance measure both finite and infinite horizon problems are considered necessary and sufficient conditions are derived for the existence of controllers that yield a closed loop system for which the above mentioned performance measure is less than a prespecified value state space formulae for the controllers are also presented

approximation of delay systems a case study abstract the approximation of delay systems is studied a numerically well behaved method for computing hankel optima rational approximations for delay systems is presented based on certain properties of hankel matrices and the theory of laguerre polynomials the cf method of trefethen and certain pade approximations of delay systems are also considered the importance of a certain wiener algebra property in the analysis of the rational approximation of an important class of delay systems in the l norm and the hankel norm is shown completing certain results presented in the literature for systems satisfying certain nuclearity or absolute continuity conditions a case study and numerical comparison is presented for the approximation of the parametric family of first order stable delay systems g s exp s ts 1 numerical experience indicates that l optimized cf approximations based on short truncated maclaurin series give in general somewhat smaller l approximation errors than hankel optim

brief paper reliable stabilization using a multi controller configuration given a plant p we consider the problem of designing a pair of controllers c 1 and c 2 such that their sum stabilizes p and in addition each of them also stabilizes p should the other one fail this is referred to as the reliable stabilization problem it is shown that every strongly stabilizable plant can be reliably stabilized moreover one of the two controllers can be specified arbitrarily subject only to the constraint that it should be stable the stabilization technique is extended to reliable regulation

on the relation between local controllability and stabilizability for a class of nonlinear systems the problem of local stabilizability of locally controllable nonlinear systems is considered it is well known that contrary to the linear case local controllability does not necessarily imply stabilizability a class of nonlinear systems for which local controllability implies local asymptotic stabilizability using continuous static state feedback is described as for this class of systems the well known hermes controllability condition is necessary and sufficient for local controllability

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

approximation of unstable infinite dimensional systems using coprime factors abstract the effectiveness of comprime factor techniques in l 2 and l model reduction of unstable linear systems is analysed asymptotic estimates are given of the achievable error in the stable and unstable parts of the approximate system measured in a number of different norms some involving the associated hankel operators the chordal metric is introduced as a measure of approximation and is shown to yield the graph topology finally it is deduced that asymptotically optimal l 2 and l convergence rates can be obtained for a large class of unstable systems

h output feedback of infinite dimensional systems via approximation abstract as in the finite dimensional case a state space based controller for the infinite dimensional h disturbance attenuation problem may be calculated by solving two riccati equations these operator riccati equations can rarely be solved exactly we approximate the original infinite dimensional system by a sequence of finite dimensional systems the solutions to the corresponding finite dimensional riccati equations are shown to converge to the solution of the infinite dimensional riccati equations furthermore the corresponding finite dimensional controllers yield performance arbitrarily close to that obtained with the infinite dimensional controller

h sup spl infin optimal and suboptimal controllers for infinite dimensional siso plants this paper presents a simple formula for h sup spl infin optimal and suboptimal controllers for unstable siso distributed plants with rational weighting functions the controller is expressed in terms of i inner and outer parts of the plant ii a finite dimensional spectral factor obtained from the weighting functions and iii a rational function satisfying certain interpolation conditions under certain genericity assumptions this rational function is of dimension less than or equal to n sub 1 l 1 n sub 1 l in the suboptimal case where l is the number of unstable poles of the plant and n sub 1 is the order of the sensitivity weighting function there are 2 n sub 1 l 2 n sub 1 l 1 in the suboptimal case linear equations which determine this rational function these linear equations can be written directly from the structure of the controller

a self stabilizing 23 approximation algorithm for the maximum matching problem the matching problem asks for a large set of disjoint edges in a graph it is a problem that has received considerable attention in both the sequential and the self stabilizing literature previous work has resulted in self stabilizing algorithms for computing a maximal 12 approximation matching in a general graph as well as computing a 23 approximation on more specific graph types in this paper we present the first self stabilizing algorithm for finding a 23 approximation to the maximum matching problem in a general graph we show that our new algorithm when run under a distributed adversarial daemon stabilizes after at most o n2 rounds however it might still use an exponential number of time steps

on computing the spectral radius of the hankel plus toeplitz operator the square root of the spectral radius of the hankel plus toeplitz operator has been shown to be the achievable performance of the mixed sensitivity h sup infinity design the computation of the spectral radius is the bottleneck in the synthesis of the h sup infinity controller in this paper the spectral properties of the hankel plus toeplitz operator are investigated a finite procedure for computing the spectral radius of the hankel plus toeplitz operator is proposed

on the synthesis of stable spl hscr sup spl infin controllers a sufficient condition is derived for the existence of a stable suboptimal spl hscr sup spl infin controller it is shown that if a certain algebraic riccati equation determined from a parameterization of all suboptimal spl hscr sup spl infin controllers has a positive definite stabilizing solution then a stable spl hscr sup spl infin controller of order 2n can be constructed where n is the order of the generalized plant

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

adding an integrator for the stabilization problem abstract we study the relationship between the following two properties p1 the system x f x y y v is locally asymptotically stabilizable and p2 the system x f x u is locally asymptotically stabilizable where x r n y r dayawansa martin and knowles have proved that these properties are equivalent if the dimension n 1 here using the so called control lyapunov function approach a we propose another more constructive and somewhat simpler proof of dayawansa martin and knowles s result b we show that in general p1 does not imply p2 for dimensions n larger than 1 c we prove that p2 implies p1 if some extra assumptions are added like homogeneity of the system by using the latter result recursively we obtain a sufficient condition for the local asymptotic stabilizability of systems in a triangular form

h2 optimal control of linear systems with tracking disturbance rejection constraints this paper considers the design of two degree of freedom linear multivariable controllers for four block matrix transfer functions with objectives pertaining to both random and deterministic signals the former are taken into account in the cost functional whereas the latter entail that the controller is constrained to solve a servomechanism problem involving a class of reference signals and two classes of disturbances the cost functional is set up by adding quadratic terms to the usual lqg wiener hopf cost in such a way as to ensure the existence of unique solutions even when the signals to be tracked rejected as well as models have poles on the imaginary axis the solutions of the servomechanism problem are explicitly parametrized by free stable rational and proper parameters under two sets of assumptions one which is necessary and sufficient for the existence of solutions and another stronger set which avoids kronecker products and the associated higher dimensional factorizations involved in

two properties of l sub 1 optimal controllers the solution of the l sub 1 sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better known h infinity sensitivity minimization problem or the lqg linear quadratic gaussian problem is given of a one parameter family of first order plants where the order of the l sub 1 optimal compensator can be arbitrarily large and thus it is impossible to bound the order of an l sub 1 optimal compensator in terms of the order of the plant a plant is considered which has a continuous one parameter family of l sub 1 optimal compensators and thus l sub 1 optimal compensators need not be unique the author s two examples are considered to answer two questions left open by m a daleh and j b pearson ibid vol 32 p 314 23 1987

nonsmooth stabilization of a class of nonlinear cascaded systems a global nonsmooth stabilization scheme is presented for a class of nonlinear cascaded systems with uncontrollable linearization a stepwise constructive control methodology is proposed for the driving subsystem by using the adding a power integrator technique under suitable conditions and based on homogeneous properties it is proved that the stabilization of the driving subsystem implies the stabilization of the overall cascaded system due to the versatility of the adding a power integrator technique and homogeneous properties the proposed controller not only can be used to stabilize the cascaded system asymptotically but also is able to lead to an interesting result of finite time stabilization under appropriate conditions

on the minimization of sensitivity to additive disturbances for linear distributed parameter mimo feedback systems the problem of minimizing the sensitivity of the output or input of a plant under a feedback control with respect to external additive disturbances is considered the mathematical model assumed for the plant is a rectangular matrix of transfer functions which can arise from both lumped parameter and distributed parameter systems including time delays the feedback controller is assumed to guarantee the closed loop stability it is shown that an arbitrarily small sensitivity function on a compact set of complex frequencies can be obtained by a suitable choice of feedback transfer function provided no zero of the plant transfer function is in this set additionally the sensitivity function can be designed to be bounded on an unbounded region containing the imaginary axis if there are no zeros of the plant in the right half plane and a certain hypothesis holds multiplicative delays are not excluded if there are zeros in the right half plane the latter design is not realizable since minimizing the sen

distance k knowledge in self stabilizing algorithms many graph problems seem to require knowledge that extends beyond the immediate neighbors of a node the usual self stabilizing model only allows for nodes to make decisions based on the states of their immediate neighbors we provide a general transformation for constructing self stabilizing algorithms which utilize distance k knowledge our transformation has both a slowdown and space overhead in n o l o g k and might be thought of as a distance k resource allocation algorithm our main application is a polynomial time self stabilizing algorithm for finding maximal irredundant sets a problem which seems to require distance 4 information these results can be generalized to efficiently find maximal p sets for properties p which we call local monotonic our techniques extend results in a recent paper by gairing et al for achieving distance two information

linear feedback systems and the graph topology it is established for general linear systems that the gap metric induces the coarsest topology with respect to which both closed loop stability and closed loop performance are robust properties in earlier works similar topological results were obtained by exploiting the existence of particular coprime factor system representations not known to exist in general by contrast the development here does not rely on any specific system representations systems are simply characterized as subspaces of norm bounded input output pairs and the analysis hinges on the underlying geometric structure of the feedback stabilization problem unlike other work developed within such a framework fundamental issues concerning the causality of feedback interconnections are discussed explicitly the key result of this paper concerns the difference between linear feedback interconnections with identical controllers in terms of a performance robustness related closed loop mapping upper and lower bounds on the induced norm of this difference are derived allowing for possibly infinite dimensional input output spaces and time varying behavior the bounds are both proportional to the gap metric distance between the plants which clearly demonstrates the gap to be an appropriate measure of the difference between open loop systems from the perspective of closed loop behavior to conclude an example is presented to show that bounds of the form derived here for linear systems do not hold in a general nonlinear setting

delay dependent stability and h control for a class of fuzzy descriptor systems with time delay this paper addresses issues of stability analysis and h control for a class of fuzzy time delay descriptor systems described by an extended takagi sugeno t s fuzzy model a delay dependent stability criterion is first presented and a h control synthesis approach is then developed both the stability criterion and the h controller synthesis are based on the solutions of linear matrix inequalities lmis finally two examples are given to illustrate the effectiveness of the approaches proposed in this paper

infinite horizon h control for nonlinear stochastic markov jump systems with x u v dependent noise via fuzzy approach in this paper the h control problem is studied for nonlinear stochastic markov jump systems with state control and external disturbance dependent noise x u v dependent noise for short a sufficient condition is derived for the infinite horizon h control of such systems in terms of a set of coupled second order hamilton jacobi inequalities hjis in general it is difficult to solve these coupled hjis by using fuzzy approach the infinite horizon h control design for nonlinear stochastic markov jump systems is developed via solving a set of linear matrix inequalities lmis instead of hjis two numerical examples are presented to illustrate the effectiveness of the proposed design methods

further results on limitations to the capability of feedback in this paper we study the limitations of the capability of the feedback mechanism in dealing with structural uncertainty for a class of pth order non linear autoregressive control systems the size of the structural uncertainty is characterized by multiple lipschitz constants say l 1 l 2 lp of the uncertain non linear function it is shown that if l 1 l 2 lp satisfy certain algebraic conditions then there exists no globally stabilizing feedback control law for the corresponding uncertain systems the result here is an extension of the previous result obtained by zhang and guo 2002

optimal sensitivity theory for multivariate distributed plants in this note we generalized the results of foias and tannenbaum 1986 a and foias et al 1987 on optimal sensitivity minimization to a much broader class of distributed plants we relate our results to certain kinds of hankel norm approximation problems that frequently appear in control engineering applications

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

on standard h control problems for systems with infinitely many unstable poles abstract in this paper h control for a class of linear time invariant systems with infinitely many unstable poles is studied an example of such a plant is a high gain system with delayed feedback we formulate the problem via a generalized plant which consists of a rational transfer matrix and the inverse of a scalar possibly irrational inner function it is shown that the problem can be decomposed into a finite dimensional h control problem and an additional rank condition

algorithm to find a maximum 2 packing set in a cactus abstract in this paper we address the problem of finding a maximum 2 packing set in a cactus let g v g e g be an undirected connected graph then a subset s v g is a 2 packing set if for every pair of vertices u v s the shortest path between them is at least three edges long this type of sets results in a wide range of applications such as the study of molecules network modeling allocation of facilities and frequency assignment the cactus is a planar graph such that any edge belongs to at most one cycle hitherto to the best of the authors knowledge no algorithm finds a maximum 2 packing set in a cactus this problem is np hard in arbitrary graphs our approach to solving this problem was first finding a maximum 2 packing set in a unicyclic graph then we adapted this algorithm to run in a cactus the time complexity of the resulting algorithm is o n 2 where n v g

an approach to h control of a class of nonlinear systems this paper considers robust h control of a class of nonlinear systems that can be represented by a heterogeneous model a new controller design method using both state feedback is proposed based on quadratic stability theory a number of necessary and sufficient conditions are derived for quadratic stabilizability with disturbance attenuation of the control system concerned an example is also given to demonstrate the performance of the proposed controller design methods

brief the weighted incremental norm approach from linear to nonlinear h control weighted induced norms can be used to handle robustness and sensitivity requirements in the linear context as shown by zames in its seminal work this paper deals with an attempt to extend linear h control concepts to the nonlinear context making use of a weighted incremental norm it is shown how these concepts make it possible to handle basic requirements such as robust stability disturbance attenuation and steady state behaviors

some applications of small gain theorem to interconnected systems based on small gain theorem decentralized control of interconnected systems is studied linear matrix inequality conditions are given for stabilizability of interconnected systems interconnections can be used to improve system robustness in the sense of small gain theorem an example is given to illustrate the results finally interconnected systems composed of symmetric subsystems are studied

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

finite rank criteria for h infty control of infinite dimensional systems this paper studies the hinfin control of infinite dimensional systems whose transfer matrices are expressible as a series connection of a rational transfer matrix and a scalar possibly irrational inner function this class of systems is adequate for describing many control problems in practice when weighting functions are rational and plants have at most finitely many unstable modes we show that this problem can be reduced to solving two matrix valued riccati equations and an additional rank condition furthermore the obtained controller structure is characterized by the inner function and controllers for the finite dimensional part this result provides us with a solution that is easily implementable without much prior knowledge on infinite dimensional control theory a numerical example is given to illustrate the result

rate based flow controllers for communication networks in the presence of uncertain time varying multiple time delays an h based robust controller is designed for a rate feedback flow control problem in single bottleneck communication networks the controller guarantees stability robustness to uncertain time varying multiple time delays in different channels it also brings the queue length at the bottleneck node to the desired steady state value asymptotically and satisfies a weighted fairness condition lower bounds for stability margins for uncertainty in the time delays and for the rate of change of the time delays are derived a number of simulations are included to demonstrate the time domain performance of the controller trade offs between robustness and time domain performance are also discussed

entropy minimizing and risk sensitive control rules abstract glover and doyle 4 have shown that the entropy minimising criterion is identical with the infinite horizon form of the leqg optimality criterion leqg linear exponential of quadratic gaussian whittle and kuhn 11 have given a hamiltonian formulation which provides a natural treatment of leqg optimisation this paper contains a direct proof that the control yielded by these hamiltonian methods is entropy minimising the conclusion would follow from the two assertions above but a simple adjoining of the proofs of these two assertions yields an argument so circuitous that a direct proof is of interest

optimal mixed sensitivity for siso distributed plants the authors extend previous results for the single input single output siso mixed sensitivity problem for distributed parameter systems to a more general setting in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts these developments were originally motivated by the computation of the infimal h sup spl infin norm of the weighted mixed sensitivity for the irrational transfer function model of a damped flexible beam