control lyapunov razumikhin functions and robust stabilization of time delay systems motivated by control lyapunov functions and razumikhin theorems on stability of time delay systems we introduce the concept of control lyapunov razumikhin functions clrf the main reason for considering clrfs is construction of robust stabilizing control laws for time delay systems most existing universal formulas that apply to clfs are not applicable to clrfs it turns out that the domination redesign control law applies achieving global practical stability and under an additional assumption global asymptotic stability this additional assumption is satisfied in the practically important case when the quadratic part of a clrf is itself a clrf for the jacobian linearization of the system the clrf based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin while in general construction of clrfs is an open problem we show that for several classes of time delay systems a clrf can be constructed in a systematic way

a procedure for simultaneously stabilizing a collection of single input linear systems using non linear state feedback control abstract this paper considers the problem of simultaneously stabilizing a finite collection of single input linear systems this stabilization is achieved using a single non linear state feedback controller the stability of the resulting closed loop system is established using a collection of quadratic lyapunov functions the main result of this paper is a sufficient condition for simultaneous stabilizability furthermore when this sufficient condition is satisfied the paper gives a formula for constructing the stabilizing feedback control law the paper includes an example in which the stabilization procedure is applied to the stabilization of an f4e fighter aircraft

on the synthesis of a stabilizing feedback control via lie algebraic methods let the n dimensional system of differential equations dx dt x x t have p in mathbb r n as a rest solution i e x p 0 even in cases when this rest solution is unstable one can often induce a strong stability asymptotic stability by the inclusion of one or more controls e g via a controlled system a dx dt x x uy x where say u leqq 1 lie theory gives a computable sufficient condition to determine when by use of the control u one can steer a full n dimensional neighborhood of p to p by solutions of a this condition is assumed to hold one prefers a feedback control i e that u u x the main result in this paper is an algorithm which determines a modified stabilizing feedback control specifically for given varepsilon 0 one measures the current state q and the algorithm determines u t q 0 leqq t leqq varepsilon such that the solution x cdot u of a initiating from q and corresponding to this control u satisfies distance x varepsilon u p q p in fact iterates are theoretically shown to converge to p numerical examples computed via a simple fortran program are included these substantiate the strong stability achieved via such a modified feedback control

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

optimal simultaneous stabilization of linear single input systems via linear state feedback control simultaneous stabilization of a collection of linear time invariant systems is considered the aim is to develop a practical method for the design of a single feedback controller such that all the systems involved are stabilized with good transient responses hurwitz s necessary and sufficient conditions are used as the required set of constraints for simultaneous stability for transient behaviour we introduce the usual quadratic objective function as performance index for each system their sum is the objective function for the collection of systems and the problem is to minimize it by choosing a feedback gain vector subject to boundedness and the hurwitz stability constraints a computational technique is proposed for solving this problem the results obtained give good transient behaviour for illustration two numerical examples are solved

asymptotic feedback stabilization a sufficient condition for the existence of control lyapunov functions abstract in this paper we study the feedback stabilization problem for a wide class of nonlinear systems that are affine in the control we offer sufficient conditions for the existence of control lyapunov functions that according to 3 23 and 28 30 guarantee stabilization at a specified equilibrium by means of a feedback law which is smooth except possibly at the equilibrium we note that the results of the paper present a local nature

a receding horizon generalization of pointwise min norm controllers control lyapunov functions clfs are used in conjunction with receding horizon control to develop a new class of receding horizon control schemes in the process strong connections between the seemingly disparate approaches are revealed leading to a unified picture that ties together the notions of pointwise min norm receding horizon and optimal control this framework is used to develop a clf based receding horizon scheme of which a special case provides an appropriate extension of sontag s formula the scheme is first presented as an idealized continuous time receding horizon control law the issue of implementation under discrete time sampling is then discussed as a modification these schemes are shown to possess a number of desirable theoretical and implementation properties an example is provided demonstrating their application to a nonlinear control problem finally stronger connections to both optimal and pointwise min norm control are proved

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

stabilizing controllers for bilinear systems the problem of finding stabilizing feedback controllers for continuous bilinear systems where the controls act additively and multiplicatively simultaneously is treated the applicability of the quadratic control law of jacobson 5 and others is extended to the case when the a matrix has arbitary eigenvalues under certain conditions a class of bilinear systems common among biochemical flow systems is defined the dyadic bilinear systems a control scheme the so called division controller for dyadic bilinear systems is suggested the practicality of the control schemes is demonstrated on the problem of controlling the neutron level in a fission reactor

a lyapunov like characterization of asymptotic controllability it is shown that a control system in bf r n is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can be made negative by appropriate choices of controls

local stabilization of minimum phase nonlinear systems abstract in this note we briefly review the notion of a nonlinear minimum phase system i e a system which when constrained in such a way as to produce zero output evolves with an asymptotically stable dynamics the main purpose of the paper is to show that any minimum phase nonlinear system can always be locally stabilized by smooth state feedback

feedback stabilization of single input nonlinear systems abstract nonlinear geometric techniques partial feedback linearization and center manifold theory allow to reduce the design of a feedback stabilizing control for single input nonlinear systems into a lower dimensional stabilization problem the reduced order control system is explicitly constructed

existence of control lyapunov functions and application to state feedback stabilizabilty of nonlinear systems the asymptotic and practical stabilization for the affine in the control nonlinear systems which extends the results of artstein sontag and tsinias is explored sufficient conditions for the existence of control lyapunov functions are presented guaranteeing stabilization the corresponding feedback laws are smooth except possibly at the equilibrium of the system

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

optimal realizations of floating point implemented digital controllers with finite word length considerations the closed loop stability issue of finite precision realizations is investigated for digital controllers implemented in floating point arithmetic unlike the existing methods which only address the effect of the mantissa bits in floating point implementation to the sensitivity of closed loop stability the sensitivity of closed loop stability is analyzed with respect to both the mantissa and exponent bits of floating point implementation a computationally tractable fwl closed loop stability measure is then defined and the method of computing the value of this measure is given the optimal controller realization problem is posed as searching for a floating point realization that maximizes the proposed fwl closed loop stability measure and a numerical optimization technique is adopted to solve for the resulting optimization problem simulation results show that the proposed design procedure yields computationally efficient controller realizations with enhanced fwl closed loop stability performance

two approaches based on pole sensitivity and stability radius measures for finite precision digital controller realizations this paper compares the two approaches based on pole sensitivity and the complex stability radius measures respectively for optimizing the closed loop stability robustness of digital controllers with respect to finite word length fwl errors in fixed point implementation design details and related optimization procedures are derived for the two methods the two measures although derived from different motivations can both be regarded as lower bound measures of a true but computationally intractable fwl stability measure in some senses an example is used to verify the theoretical analysis and to illustrate the two designs for determining optimal fwl controller realizations

event triggered non fragile control for linear systems with actuator saturation and disturbances abstract this paper investigates the problem of event triggered non fragile dynamic output feedback controller design for linear systems with actuator saturation and disturbances the controller to be designed is supposed to include additive gain variations by using lyapunov stability theory and adding slack matrix variables new sufficient conditions are derived to design the event triggered parameters and the controller gains compared with the existing non fragile dynamic output feedback controller design methods the structural restriction on the lyapunov matrix is relaxed the effectiveness of the proposed method is demonstrated by two examples

the abstract complex lorentz transformation group with real metric i special relativity formalism to deal with the holomorphic automorphism group of the unit ball in any complex hilbert space viewing the unit ball in a complex hilbert space as a set of relativistically admissible complex velocities the holomorphic automorphisms of the ball emerge as complex relativistic velocity additions and complex rotations that is unitary transformations hence newly discovered properties of the abstract real lorentz group a a ungar am j phys 59 824 1991 a a ungar am j phys 60 815 1992 which turn out to provide powerful tools for the study of the holomorphic automorphisms of the unit ball in any complex hilbert space are of interest in the literature w rudin function theory in the unit ball of cn springer verlag new york 1980 a particularly useful and important tool turns out to be provided by thomas gyration which is an abstraction of the well known thomas precession of special relativity theory and which gives rise to a gyrogroup structure underlying the ball results of this article set the stage for the study in a subsequent article of complex lorentz t

two classes of efficient digital controller structures with stability consideration in this note the efficient controller structure problem is investigated subject to minimizing finite word length fwl effects two classes of sparse controller structures characterized with a set of free parameters are derived the stability behavior of each class is analyzed with a newly defined stability related measure the optimal structure problems are studied in terms of maximizing the stability related measure for the two classes of sparse structures as well as the fully parametrized state space realizations a design example is given which shows that the optimized sparse structures can beat the fully parametrized optimal realizations in terms of both stability performance and computation efficiency

simultaneous stabilization via linear state feedback control the problem of simultaneously stabilizing a finite collection of plants via a single compensator utilizing full state information is considered the authors assume that the complete state can be measured and seek a static linear state feedback control law sufficient conditions for such full state gains to exist are given and they show via several examples how stabilizing compensators can be designed

clf based designs with robustness to dynamic input uncertainties abstract the problem of robust stabilization of nonlinear systems in the presence of input uncertainties is of great importance in practical implementation stabilizing control laws may not be robust to this type of uncertainty especially if cancellation of nonlinearities is used in the design by exploiting a connection between robustness and optimality domination redesign of the control lyapunov function clf based sontag s formula has been shown to possess robustness to static and dynamic input uncertainties in this paper we provide a sufficient condition for the domination redesign to apply this condition relies on properties of local homogeneous approximations of the system and of the clf we show that an inverse optimal control law may not exist when these conditions are violated and illustrate how these conditions may guide the choice of a clf which is suitable for domination redesign

brief paper non fragile h filter design for linear continuous time systems this paper studies the problem of non fragile h filter design for linear continuous time systems the filter to be designed is assumed to include additive gain variations which result from filter implementations a notion of structured vertex separator is proposed to approach the problem and exploited to develop sufficient conditions for the non fragile h filter design in terms of solutions to a set of linear matrix inequalities lmis the designs guarantee the asymptotic stability of the estimation errors and the h performance of the system from the exogenous signals to the estimation errors below a prescribed level a numerical example is given to illustrate the effect of the proposed method

finite wordlength controller realisations using the specialised implicit form a specialised implicit state space representation is introduced to deal with finite wordlength effects in controller implementations this specialised implicit form provides a macroscopic description of the algorithm to be implemented so it constitutes a unifying framework allowing to encompass various implementation forms such as the operator the direct form ii transposed observer based and many other realisations usually considered separately in the literature different measures quantifying the finite wordlength effects on the overall closed loop behaviour are defined in this new context they concern both stability and performance the gap with the infinite precision case is evaluated classically through the coefficient sensitivity and roundoff noise analysis the problem of determining a realisation with minimum finite wordlength effects can subsequently be solved using appropriate numerical methods the approach is illustrated with an example

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

simultaneous stabilization for a set of boolean control networks abstract this paper investigates simultaneous stabilization of a collection of boolean control networks bcns by using the semi tensor product method and presents a number of new results first an algebraic expression of the bcns is obtained by the semi tensor product based on which some necessary and sufficient conditions are presented to solve the simultaneous stabilization problem by a free control sequence a state feedback control and an output feedback control respectively second using the column stacking form of matrices a new procedure is established to design both state feedback and output feedback controllers for the simultaneous stabilization problem the study of two illustrative examples shows that the new results obtained in this paper are very effective in solving simultaneous stabilization of a collection of bcns

simultaneous stabilization of a set of nonlinear port controlled hamiltonian systems this paper investigates simultaneous stabilization of a set of nonlinear port controlled hamiltonian pch systems and proposes a number of results on the design of simultaneous stabilization controllers for the pch systems firstly the case of two pch systems is studied using the dissipative hamiltonian structural properties the two systems are combined to generate an augmented pch system with which some results on the control design are then obtained for the case that there exist parametric uncertainties in the two systems hamiltonian structures an adaptive simultaneous stabilization controller is proposed when there are external disturbances and parametric uncertainties in the two systems two simultaneous stabilization controllers are designed for the systems one is a robust controller and the other is a robust adaptive one secondly the case of more than two pch systems is investigated and a new result is proposed for the simultaneous stabilization of the systems finally two illustrative examples are studied by using the results proposed in this paper simulations show that the simultaneous stabilization controllers obtained in this paper work very well

comparative study on optimizing closed loop stability bounds of finite precision controller structures with shift and delta operators the paper analyzes the sensitivity of closed loop stability with respect to w r t finite word length fwl effects in the implementation of the controller coefficients using both the shift and delta operator parameterizations a unified approach is established to optimize a closed loop stability lower bound for fwl controller structures this provides a general framework to compare the fwl closed loop stability characteristics of the controller structures based on the shift and delta operators respectively two numerical examples are given and the simulation results show that the optimal fwl controller realizations with the delta operator have better closed loop stability margins than those with the shift operator

simultaneous h infty control for nonlinear systems this note develops a novel method for designing simultaneous h infin state feedback controllers for a collection of single input nonlinear systems based on the kalman yakubovich popov lemma necessary and sufficient conditions for the existence of simultaneous h infin controllers are derived by the control storage function approach a universal formula for constructing continuous time invariant simultaneous h infin state feedback controllers is presented

reduction of controller fragility by pole sensitivity minimization presents a method for the reduction of controller fragility the method is based on the sensitivity of closed loop poles to perturbations in the controller parameters by means of a state space parameterization of the controller the closed loop pole sensitivity can be reduced a controller fragility measure based on the closed loop pole sensitivity is proposed conditions for the optimal state space realization of the controller are presented along with a numerical method for obtaining the solution

simultaneous stabilization of linear and nonlinear systems by means of nonlinear state feedback the simultaneous stabilization resp asymptotic stabilization of a countable family of control systems consists of finding a control which stabilizes resp asymptotically stabilizes all the systems in the family in this paper we introduce a new method which enables us to show that given any countable family of stabilizable nonlinear systems there exists a continuous state feedback law which simultaneously stabilizes not asymptotically the family then by enriching this method we prove that any finite family of stabilizable linear time invariant lti systems can be simultaneously exponentially stabilized by means of nonlinear time varying state feedback we also derive sufficient conditions for the simultaneous asymptotic stabilizability of countably infinite families of lti systems finally sufficient conditions for the simultaneous asymptotic stabilizability of finite families of nonlinear systems are provided and used for the simultaneous asymptotic stabilization of certain pairs of nonlinear homogeneous systems

small roundoff noise realization of fixed point digital filters and controllers a method for finding digital realizations of discrete time transfer functions by fixed point arithmetic is presented the obtained realizations attain very small roundoff noise intensity this intensity is significantly smaller than the intensities that have been achieved so far the method applies many 0 1 coefficients in the realization it therefore requires a small number of multiplications and additions and it is significantly faster than many other realization methods a detailed comparison is made between this method and other existing methods for digital realization two different cases are investigated a butterworth filtering realization and the realization of an lqg linear quadratic gaussian optimal controller

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

optimizing stability bounds of finite precision pid controller structures this paper investigates a recently derived lower bound stability measure for sampled data controller structures subject to finite wordlength fwl constraints the optimal realization of the digital pid controller with fwl considerations is formulated as a nonlinear optimization problem and an efficient strategy based on adaptive simulated annealing asa is adopted to solve this complex optimization problem a numerical example of optimizing the finite precision pid controller structure for a simulated steel rolling mill system is presented to illustrate the effectiveness of the proposed strategy

simultaneous stabilization with near optimal lqr performance we consider the use of linear time varying controllers for simultaneous stabilization and performance we prove that for every finite set of plants we can design a linear time varying controller which provides not only closed loop stability but also near optimal lqr type performance by adding a mild nonlinearity in the form of a nonlinear delay we end up with an improved controller which provides near optimal performance for each possible model as well as for the case when the plant changes occasionally

brief paper an efficient controller structure with minimum roundoff noise gain based on a polynomial operator approach a new sparse controller structure is derived which is actually an improved version of the recently proposed structure li g 2004 a polynomial operator based dfiit structure for iir filters ieee transactions on circuits and systems ii 51 147 151 the performance of the proposed structure is analyzed by deriving the corresponding expression of roundoff noise gain and the problem of finding optimized sparse structures is solved efficiently with a genetic algorithm ga a numerical example is given which shows that the newly developed structure can achieve much better performance than some well known structures and particularly outperforms the traditional optimal fully parametrized realization greatly in terms of reducing roundoff noise and implementation complexity

brief paper robust finite word length controller design a novel finite word length fwl controller design is proposed in the framework of a mixed m theory a robust fwl controller performance measure is first developed which takes into account the standard robust control requirements as well as the fwl implementation considerations and the corresponding controller design problem is naturally reformulated as a mixed m problem which can be treated effectively with the results of the mixed m theory

stabilization of uncertain systems with norm bounded uncertainty a control a robust stabilization problem in a state space setting is treated it is assumed that the states are available for feedback using a fixed lyapunov function approach quadratic stability it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state feedback controller as a consequence it is shown that the existence of a quadratically stabilizing nonlinear time varying dynamic state feedback controller implies the existence of a quadratically stabilizing memoryless linear time invariant state feedback compensator

simultaneous quadratic stabilization for discrete time nonlinear systems a constructive method is developed for designing simultaneously quadratically stabilizing state feedback controllers for a collection of single input discrete time nonlinear systems in the context of quadratic control lyapunov functions a necessary and sufficient condition for the existence of simultaneously quadratically stabilizing state feedback laws is derived an explicit formula for constructing continuous simultaneously stabilizing controllers is presented the obtained results are verified by a numerical example

optimal realisations of fixed point implemented digital controller with the smallest dynamic range a novel approach is proposed to design optimal finite word length fwl realizations of digital controllers implemented in fixed point arithmetic a minimax based search procedure is first formulated to obtain an optimal controller realization that optimizes an fwl closed loop stability measure since this fwl closed loop stability measure is solely linked to the fractional part or precision of fixed point format the resulting realization may not have the smallest dynamic range a measure is then derived to indicate the dynamic range of fixed point implemented realization by choosing an appropriate orthogonal transformation of this dynamic range measure of the optimal precision controller realization a numerical optimization method is developed to make the controller realization having the smallest dynamic range without sacrificing fwl closed loop stability robustness the proposed approach is more efficient than a direct optimization of some combined fwl closed loop stability and dynamic range measure

j lossless and extended j lossless factorizations approach for domain h control the paper addresses problems of numerical conditioning of the discrete time h x control design based on j lossless factorizations of the chain scattering representation of a plant it is demonstrated that for a sufficiently small sampling period forward shift operator techniques may become ill conditioned and numerical robustness and reliability of design procedures can be significantly improved by utilizing a so called i operator form of the source problem state space models of all i domain controllers are given the solutions are obtained by considering two coupled i domain algebraic riccati equations that can be solved by applying a generalized eigenproblem formulation numerical conditioning of these solutions can effectively be evaluated by using a suitable relative condition number an extended j lossless factorization for generalized plants with zeros on the stability boundary circle is also given a so called zero compensator technique adapted to the i domain models is utilized to cancel suc

further comments on the stabilizability of the angular velocity a rigid body abstract we prove that the angular velocity equations can be smoothly stabilized with a single torque controller for bodies having an axis of symmetry this complements a recent result of aeyels and szafranski

optimal finite precision state estimate feedback controller realizations of discrete time systems investigates the stability issue of a discrete time control system where a state estimate feedback controller sefc digitally implemented with a fixed point format is used a tractable closed loop stability related measure is derived with finite word length implementation consideration of the controller the optimal realizations of the sefc are defined as those that maximize this measure and can be shown as the solutions of a nonlinear programming problem a sophisticated optimization strategy is presented to provide an efficient method for solving this problem and a numerical example is given to illustrate the design procedure

feedback stabilization for multiinput switched nonlinear systems two subsystems case in this note based on the control lyapunov function approach a new method for solving the feedback stabilization problem of switched systems that are switching arbitrarily between two multiinput nonlinear subsystems is introduced necessary and sufficient conditions for the existence of globally uniformly asymptotically stabilizing state feedback controllers are derived additionally a universal formula for constructing implementable stabilizing controllers is given when the presented conditions hold one numerical example is given to illustrate the results

output feedback stabilization the stabilization of control systems using output feedback is addressed necessary and sufficient lyapunov conditions are established generalizing the artstein s stabilization theorem for linear control systems a necessary and sufficient lyapunov condition is provided for stabilization by means of a linear output feedback law

global stabilizability of homogeneous vector fields of odd degree abstract in this paper we deal with global stabilizability at the origin of a homogeneous vector field by means of homogeneous feedbacks of the same degree we give a sufficient condition which turns out to be also necessary in the linear case for a particular class of systems this condition is implied by a local controllability assumption

an improved closed loop stability related measure for finite precision digital controller realizations the pole sensitivity approach is employed to investigate the stability issue of the discrete time control system where a digital controller implemented with finite word length fwl is used a stability related measure is derived which is more accurate in estimating the closed loop stability robustness of an fwl implemented controller than some existing measures for the pole sensitivity analysis this improved stability measure thus provides a better criterion to find the optimal realizations for a generic controller structure that includes output feedback and observer based controllers a numerical example is used to verify the theoretical analysis and to illustrate the design procedure

hyperbolic trigonometry in the einstein relativistic velocity model of hyperbolic geometry abstract hyperbolic geometry is a fundamental aspect of modern physics we explore in this paper the use of einstein s velocity addition as a model of vector addition in hyperbolic geometry guided by analogies with ordinary vector addition we develop hyperbolic vector spaces called gyrovector spaces which provide the setting for hyperbolic geometry in the same way that vector spaces provide the setting for euclidean geometry the resulting gyrovector spaces enable euclidean trigonometry to be extended to hyperbolic trigonometry in particular we present the hyperbolic law of cosines and sines and the hyperbolic pythagorean theorem emerges when the common vector addition is replaced by the einstein velocity addition

brief paper insensitive h filter design for continuous time systems with respect to filter coefficient variations this paper is concerned with the problem of designing insensitive h filters for linear continuous time systems coefficient sensitivity functions of transfer functions with respect to filter additive multiplicative coefficient variations are defined and the h norms of the sensitivity functions are used to measure the sensitivity of the transfer functions with respect to additive filter coefficient variations in addition in order to deal with the filter design problem for the multiplicative filter coefficient variation case new measures based on the average of the sensitivity functions are also defined consequently the insensitive h filter design problem is reduced to a multi objective filter design problem which minimizes the coefficient s sensitivity and meets the prescribed h norm constraint simultaneously first a novel method for designing insensitive h filters subjected to additive filter coefficient variations is given in terms of the linear matrix inequality lmi optimization techniques furthermore based on the new sensitivity measures the obtained results are extended to the multiplicative coefficient variation case in addition an indirect method for solving the multiplicative variations is also proposed finally two numerical examples are provided to demonstrate the effectiveness of the proposed method

robust h control for polytopic nonlinear control systems this technical note develops a robust control storage function method for solving the h control problem of single input polytopic nonlinear control systems necessary and sufficient conditions for verifying robust control storage functions are provided moreover conditions for the existence of continuous robust h state feedback controllers are derived an explicit formula for constructing continuous robust h controllers is presented finally a numerical example is given for illustration

asymptotic stabilization of two dimensional real analytic systems abstract we investigate the local asymptotic stabilizability of a real analytic control system around an equilibrium point and give necessary and sufficient conditions for local asymptotic stabilization using continuous feedback

simultaneous stabilization of linear single input systems by linear state feedback control a necessary and sufficient condition for the existence of a linear state feedback controller which will simultaneously stabilize a finite collection of single input linear systems is presented this condition can be checked numerically through the solution of a non linear programming problem presented here and can be used to determine whether or not a particular simultaneous stabilization problem has a solution if the stabilization problem has a solution the method provides a means of constructing a suitable controller the proposed method is very versatile it is a simple matter to limit the size of elements of the feedback gain vector and thus ensure that the control action is not excessive in addition for simultaneous stabilization problems which have a range of possible solutions the proposed method makes it possible to select one which yields good performance

on the structure of digital controllers with finite word length consideration it is well known that a stable discrete time control system may become unstable when the digital controller is actually implemented with a digital control processor due to the finite word length effects and that the stability behavior of the system depends on the structure of the digital controller due to the difficulties in adopting the existing stability robustness measures a new measure is derived which is tractable and hence enables us to handle the digital controller structure problem easily the optimal controller structure problem is formulated by maximizing this measure an analytical solution is presented an algorithm is developed for finding sparser structures

a search algorithm for a class of optimal finite precision controller realization problems with saddle points with game theory we review the optimal digital controller realization problems that maximize a finite word length fwl closed loop stability measure for a large class of these optimal fwl controller realization problems which have saddle points a minimax based search algorithm is derived for finding a global optimal solution the algorithm consists of two stages in the first stage the closed form of a transformation set is constructed which contains global optimal solutions in the second stage a subgradient approach searches this transformation set to obtain a global optimal solution this algorithm does not suffer from the usual drawbacks associated with using direct numerical optimization methods to tackle these fwl realization problems furthermore for a small class of optimal fwl controller realization problems which have no saddle point the proposed algorithm also provides useful information to help solve them

universal construction of feedback laws achieving iss and integral iss disturbance attenuation we study nonlinear systems with both control and disturbance inputs the main problem addressed in the paper is design of state feedback control laws that render the closed loop system integral input to state stable iiss with respect to the disturbances we introduce an appropriate concept of control lyapunov function iiss clf whose existence leads to an explicit construction of such a control law the same method applies to the problem of input to state stabilization converse results and techniques for generating iiss clfs are also discussed

simultaneous stabilization for a collection of single input nonlinear systems this paper presents a novel method for designing a controller that simultaneously stabilizes a collection of single input nonlinear systems the control lyapunov function approach is used to derive necessary and sufficient conditions for the existence of time invariant simultaneously stabilizing state feedback controllers additionally a universal formula for constructing a continuous simultaneously stabilizing controller when the provided sufficient condition is satisfied is presented for any collection of second order and third order feedback linearizable systems in canonical form global simultaneous stabilization via a single state feedback controller is shown to be always possible two examples are included for illustration

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

robust stabilization of nonlinear systems with pointwise norm bounded uncertainties a control lyapunov function approach the authors give a necessary and sufficient condition for globally stabilizing a nonlinear system robustly with respect to unstructured uncertainties spl phi spl tilde u x t norm bounded for each fixed x and u this condition requires one to find a smooth proper and positive definite solution v x of a suitable partial differential inequality depending only on the system data a procedure based on the knowledge of v x is outlined for constructing almost smooth robustly stabilizing controllers our approach based on lyapunov functions generalizes previous results for linear uncertain systems and establishes a precise connection between robust stabilization on one hand and h sub spl infin control sector conditions and input to state stabilization on the other

semiconcave control lyapunov functions and stabilizing feedbacks we study the general problem of stabilization of globally asymptotically controllable systems we construct discontinuous feedback laws and particularly we make it possible to choose these continuous outside a small set closed with measure zero of discontinuity in the case of control systems which are affine in the control moreover this set of singularities is shown to be repulsive for the caratheodory solutions of the closed loop system under an additional assumption

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

erratum the abstract complex lorentz transformation group with real metric i special relativity formalism to deal with the holomorphic automorphism group of the unit ball in any complex hilbert space j math phys 35 1408 1426 1994

input output stability of sampled data systems the authors study the l sub p input output stability of a continuous time controller using the usual arrangement of periodic sampling and zero order hold it is noted that even if the hybrid system is exponentially stable this arrangement does not yield l sub p 1

a µ based optimal finite word length controller design a novel optimal finite word length fwl controller design is proposed in the framework of m theory a computationally tractable close loop stability measure with fwl implementation considerations of the controller is derived based on the m theory and the optimal fwl controller realizations are obtained by solving the resulting optimal fwl realization problem using linear matrix inequality techniques

a unified closed loop stability measure for finite precision digital controller realizations implemented in different representation schemes a computationally tractable unified finite word length closed loop stability measure is derived which is applicable to fixed point floating point and block floating point representation schemes both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure for each arithmetic scheme the optimal controller realization problem is defined and a numerical optimization approach is adopted to solve it numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes