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

a family of nonlinear h sup spl infin output feedback controllers state space formulas are derived for a family of controllers solving the nonlinear h sup spl infin output feedback control problem the formulas given are expressed in terms of the solutions to two hamilton jacobi inequalities in n independent variables these controllers are obtained by interconnecting the central controller with an asymptotically stable free system having l sup 2 gain spl les spl gamma all proofs given are simple and clear and provide deeper insight in the synthesis of the corresponding linear h sup spl infin controllers

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

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

control relevant model reduction problems for siso h2 h and μ controller synthesis abstract the problem of model reduction in the context of control system design is investigated starting from closed loop objectives h2 h and equivalent weighted open loop plant and controller reduction problems are developed the control relevant weight function incorporates explicitly all the important characteristics of the control problem such as the setpoint disturbance spectrum and the designer requirements for the sensitivity complementary sensitivity functions furthermore these control relevant reduction problems are complemented with validation procedures that indicate rigorously the effects of the reduction problem on the desired performance objectives a simple algorithm that uses standard regression routines is presented to solve these problems

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

asymptotically nonexpansive mappings in modular function spaces abstract in this paper we prove that if is a convex finite modular function satisfying a 2 type condition c a convex bounded a e compact subset of l and t c c a asymptotically nonexpansive mapping then t has a fixed point in particular any asymptotically nonexpansive self map defined on a convex subset of l 1 which is compact for the topology of local convergence in measure has a fixed point

efficient robust optimization for robust control with constraints this paper proposes an efficient computational technique for the optimal control of linear discrete time systems subject to bounded disturbances with mixed linear constraints on the states and inputs the problem of computing an optimal state feedback control policy given the current state is non convex a recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program while the reparameterized problem is theoretically tractable the number of variables is quadratic in the number of stages or horizon length n and has no apparent exploitable structure leading to computational time of mathcal o n 6 per iteration of an interior point method we focus on the case when the disturbance set is norm bounded or the linear map of a hypercube and the cost function involves the minimization of a quadratic cost here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem that is the policy optimization problem may be decomposed into a set of coupled finite horizon control problems this decomposition can then be formulated as a highly structured quadratic program solvable by primal dual interior point methods in which each iteration requires mathcal o n 3 time this cubic iteration time can be guaranteed using a riccati based block factorization technique which is standard in discrete time optimal control numerical results are presented using a standard sparse primal dual interior point solver that illustrate the efficiency of this approach

synchronization of chaotic trajectories using control we demonstrate that two identical chaotic systems can be made to synchronize by applying small judiciously chosen temporal parameter perturbations to one of them this idea is illustrated with a numerical example other issues related to synchronization are also discussed

a note on the admissibility of modular function spaces abstract in this paper we prove the admissibility of modular function spaces e considered and defined by kozlowski in 17 as an application we get that any compact and continuous mapping t e e has a fixed point moreover we prove that the same holds true for any retract of e

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

some geometric properties in modular spaces and application to fixed point theory abstract we prove that modular spaces l have the uniform kadec klee property w r t the convergence a e when they are endowed with the luxemburg norm we also prove that these spaces have the uniform opial condition w r t the convergence a e for both the luxemburg norm and the amemiya norm some assumptions over the modular need to be assumed the above geometric properties will enable us to obtain some fixed point results in modular spaces for different kind of mappings

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

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

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

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

h norm computation for ltv systems using nonlinear optimal control algorithms we discuss the computation for 2 induced norms of finite horizon linear time varying systems it is well known that 2 induced norm calculating problems can be converted into optimal control problems so with the help of optimal control algorithms we propose a numerical technique for 2 induced norm computation our approach is as follows first we present a new computational method for nonlinear optimal control problems that is numerically reliable stable and robust analysing the convergence property under some assumptions next by modifying the presented method we propose an algorithm for the 2 induced norm calculation of finite horizon linear time varying systems which is essentially different from all other existing methods finally the effectiveness of our algorithm is demonstrated by simulation

measurement of the lyapunov spectrum from a chaotic time series the exponential divergence or convergence of nearby trajectories lyapunov exponents is conceptually the most basic indicator of deterministic chaos we propose a new method to determine the spectrum of several lyapunov exponents including positive zero and even negative ones from the observed time series of a single variable we have applied the method to various known model systems and also to the rayleigh b enard experiment and have elucidated the dependence of the lyapunov exponents on the rayleigh number

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

relationship of calculating the jacobian matrices of nonlinear systems and population coding algorithms in neurobiology abstract in this paper we examine how the calculation of jacobian matrices in nonlinear systems is related to population coding algorithms in neurobiology population coding algorithms have been designed to retrodict sensory stimuli or predict motor behavior from neuronal responses we simulate the visuomotor hand movement task of reaching in a plane adaptive feedback control updating of joint angles of a three joint arm was used in the model the control signal is the dot product between the visual error signal and the jacobian matrix of the direct kinematic equation of hand movement the x and y hand trajectories can follow the x and y time series of lorenz and ro ssler systems of coupled nonlinear equations in this particular example the elements of the jacobian matrix can be estimated from observed changes in joint angles and cartesian coordinate values of the hand we also point out how the jacobian matrices in nonlinear biological systems can be estimated in general from observed time series e g joint angles cartesian coordinate values of hand movement neural or muscle activity estimating jacobian matrices of nonlinear functions from experimental observations can provide not only data analysis but also signal synthesis and can lead to a more realistic modeling of sensorimotor transformations

new approach to general nonlinear discrete time stochastic h_ infty control in this paper a new approach based on convex analysis is introduced to solve the h infty problem for discrete time nonlinear stochastic systems first by using the disintegration property of the conditional expectation sufficient necessary conditions are given for the internal stability of the concerned systems second in order to separate the unknown exogenous disturbance from the state variables the properties of convex functions are applied to prove the stochastic version of bounded real lemma brl third the state feedback h infty control problem is studied and an h infty control is designed based on the brl finally two numerical examples and one real world regulation control example of synthetic genetic circuit are presented to show the effectiveness of our developed theory

neural mechanisms underlying destabilization of cortex by sensory input abstract a mathematical model of the mechanism of olfaction has been developed in the form of coupled nonlinear integrodifferential equations the model was first constructed to simulate the performance of the separated bulb or cortex in response to electrical impulse stimulation of its input and output nerves with sufficiently high internal feedback gains the model entered a stable limit cycle state at frequencies characteristic of the eeg bursts the instability was diminished when the connection densities and input amplitude were spatially nonuniform though these factors could be compensated by increasing the internal gains connection strengths this model failed to simulate three important characteristics of olfactory activity 1 the dependence of spatial patterns of bulbar output on internal connectivity rather than on input patterns 2 the exquisite selective sensitivity of the bulb to learned inputs and 3 its broad spectrum and aperiodic wave forms the model was changed by including an asymmetric sigmoid nonlinearity and by introducing long feedback connections from the cortex to the bulb that had dispersive delays these changes sufficed to provide chaotic solutions of the equations and to selectively sensitize the system to destabilization by input thereby improving the simulations of the biological activity the conclusion is put forth that for pattern recognition to be done the chaotic activity of the sensory system must arise from a macroscopic attractor local fluctuations are everywhere damped by the distributions of return times and strengths owing to biological variability in neuron size and connection density thus high dimensional local stability is combined with low dimensional global instability so as to emphasize the relationships among local features in a holistic sensory input pattern

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

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

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

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

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

stabilization and sensitivity for eventually time invariant systems abstract this paper studies the stability and minimal sensitivity of a time varying system which as time passes becomes more and more time invariant

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

filtered noise can mimic low dimensional chaotic attractors this contribution presents four results first calculations indicate that when examined by the grassberger procaccia algorithm alone filtered noise can mimic low dimensional chaotic attractors given the ubiquity of signal filtering in experimental investigations this is potentially important second a criterion is derived which provides an estimate of the minimum data accuracy needed to resolve the dimension of an attractor third it is shown that a criterion derived by eckmann and ruelle physica d 56 185 1992 to estimate the minimum number of data points required in a grassberger procaccia calculation can be used to provide a further check on these dimension estimates fourth it is shown that surrogate data techniques recently published by theiler and his colleagues in nonlinear modeling and forecasting edited by m casdagli and s eubanks addison wesley reading ma 1992 can successfully distinguish between linearly correlated noise and nonlinear structure these results and most particularly the first indicate that grassberger procaccia results must be interpreted with far greater circumspection than has previously been the case and that the algorithm should be used in combination with additional procedures such as calculations with surrogate data when filtered signals are examined by this algorithm alone a finite noninteger value of mathit d 2 is consistent with low dimensional chaotic behavior but it is certainly not a definitive diagnostic of chaos

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

transfer function synthesis using frequency response data an improved method for transfer function synthesis from measured frequency response data is presented the improvement is due to a new scheme of matrix adaptation that eliminates measurement dependent inaccuracies step by step arbitrary coefficients can be set to any preassigned values so that account can be taken of previous knowledge of the investigated system an extension to integrating systems is developed the efficiency of the proposed method is demonstrated for an example taken from the literature

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

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

computation of lyapunov spectra effect of interactive noise and application to a chemical oscillator abstract a refined version of the sano sawada algorithm to compute lyapunov spectra has been implemented and tested with several models which include periodic chaotic and hyperchaotic attractors under conditions designed to mimic experimental situations it was found that reliable lyapunov exponents can be obtained for time series of moderate length and point density also in the presence of interactive noise as long as its amplitude does not exceed 1 of the oscillation amplitude the algorithm was then applied to experimental data from the co oxidation on pt 110 clearly showing the occurrence of chaos as well as hyperchaos

robustness with simultaneous pole and zero movement across the jω axis in this paper we present some new tests for assessing the robustness of the stability property of a feedback design the tests offer a wider scope of application than those previously described in the literature the main result is a robustness test which can be used to assess closed loop stability when the nominal plant model and perturbed plant model representing uncertainty have different numbers of poles and zeros in the right half plane this test also indicates over which frequencies good sensitivity and robust stability are compatible objectives and over which frequencies a compromise has to be made contrary to popular belief if there are no uncertain zeros which can move across the imaginary axis then good sensitivity and robust stability are compatible objectives over the same frequencies

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

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

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

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

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

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

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

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

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

brief analytical pid parameter expressions for higher order systems most approaches to feedback synthesis are numerical design techniques that produce their results in form of numerical values for the controller parameters in contrast analytical design techniques produce the controller parameters as explicit expressions that are a function of open loop system parameters and the desired closed loop advantages include fast commissioning in terms of physical system parameters gain scheduling without extra design effort and analytical sensitivity insights so far it has not been known how to derive analytical pid expressions for higher than second order systems the paper proposes a technique to address this problem analyses its properties demonstrates computational simplicity and shows that its performance is comparable to known numerical techniques

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

frequency response algorithms for h sub infinity optimization with time domain constraints a very broad framework for control system design is considered that encompasses frequency response methodologies for h sub infinity optimization that solve various aspects of the control design problem and that are less well known that state space methods the focus is on linear programming lawson s algorithm and trefethen s algorithm a modified lawson s algorithm is proposed and related to trefethan s method the modified algorithm is shown to be significantly faster than linear programming and lawson s algorithm it is also shown how to extend the modified lawson s algorithm so as to handle time domain constraints in addition to frequency domain specifications which distinguishes it from other h sub infinity optimization methods some steps are taken toward dealing with time domain constraints within an h sub infinity optimization framework