numerical analysis of a contact problem with wear abstract this paper represents a sequel to jureczka and ochal 2019 where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation the model takes into account wear of the contact surface of the body caused by the friction some preliminary error analysis for a fully discrete approximation of the contact problem was provided in jureczka and ochal 2019 in this paper we consider a more general fully discrete numerical scheme for the contact problem derive optimal order error bounds and present computer simulation results showing that the numerical convergence orders match the theoretical predictions

the projective method for solving linear matrix inequalities numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities lmi since solving an lmi amounts to a convex optimization problem such formulations are known to be numerically tractable however the interest in lmi based design techniques has really surged with the introduction of efficient interior point methods for solving lmis with a polynomial time complexity this paper describes one particular method called the projective method simple geometrical arguments are used to clarify the strategy and convergence mechanism of the projective algorithm a complexity analysis is provided and applications to two generic lmi problems feasibility and linear objective minimization are discussed

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

robust memoryless h controller design for linear time delay systems with norm bounded time varying uncertainty we consider the robust h control problem for linear time delay systems with norm bounded time varying uncertainty based on the riccati equation approach we present a method for designing a robust memoryless linear time invariant state feedback control law which stabilizes the system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties

constrained mpc algorithm for uncertain time varying systems with state delay in this note we present a model predictive control mpc algorithm for uncertain time varying systems with input constraints and state delay uncertainty is assumed to be polytopic and delay is assumed to be unknown but with a known upper bound for a memoryless state feedback mpc law we define an optimization problem that minimizes a cost function and relaxes it to two other optimization problems by finding an upper bound of the cost function one is solvable and the other is not we prove equivalence and feasibilities of the two optimization problems under a certain assumption on the weighting matrix based on these properties and optimality we show that feasible mpc from the optimization problems stabilizes the closed loop system then we present an improved mpc algorithm that includes relaxation procedures of the assumption on the weighting matrix and stabilizes the closed loop system finally a numerical example illustrates the performance of the proposed algorithm

robust guaranteed cost control for uncertain linear differential systems of neutral type in this paper the robust guaranteed cost control problem for a class of uncertain linear differential systems of neutral type with a given quadratic cost functions is investigated the uncertainty is assumed to be norm bounded and time varying nonlinear the problem is to design a state feedback control laws such that the closed loop system is robustly stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay a criterion for the existence of such controllers is derived based on the matrix inequality approach combined with the lyapunov method a parameterized characterization of the robust guaranteed cost controllers is given in terms of the feasible solutions to the certain matrix inequalities a numerical example is given to illustrate the proposed method

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

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

lagrange stability and performance analysis of discrete time piecewise affine systems with logic states in this paper we consider discrete time piecewise affine systems with boolean inputs outputs and states and show that they can be represented in a logic canonical form where the logic variables influence the switching between different submodels but not the continuous valued dynamics we exploit this representation for studying lagrange stability and developing performance analysis procedures based on linear matrix inequalities moreover by using arguments from dissipativity theory for non linear systems we generalize our approach to solve the h analysis problem

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

the generalized h 2 control problem abstract in this paper we consider the problem of finding an internally stabilizing controller such that the controlled or regulated signals have a guaranteed maximum peak value in response to arbitrary but bounded energy exogenous inputs more specifically we give a complete solution to the problem of finding a stabilizing controller such that the closed loop gain from l 2 0 to l 0 is below a specified level we consider both state feedback and output feedback problems in the state feedback case it is shown that if this synthesis problem is solvable then a solution can be chosen to be a constant state feedback gain necessary and sufficient conditions for the existence of solutions as well as a formula for a state feedback gain that solves this control problem are obtained in terms of a finite dimensional convex feasibility program after showing the separation properties of this synthesis problem the output feedback case is reduced to a state feedback problem it is shown that in the output feedback case generalized h 2 controllers can be chosen to be observer based controllers the theory is demonstrated with a numerical example

robust fuzzy control of nonlinear systems with parametric uncertainties addresses the robust fuzzy control problem for nonlinear systems in the presence of parametric uncertainties the takagi sugeno t s fuzzy model is adopted for fuzzy modeling of the nonlinear system two cases of the t s fuzzy system with parametric uncertainties both continuous time and discrete time cases are considered in both continuous time and discrete time cases sufficient conditions are derived for robust stabilization in the sense of lyapunov asymptotic stability for the t s fuzzy system with parametric uncertainties the sufficient conditions are formulated in the format of linear matrix inequalities the t s fuzzy model of the chaotic lorenz system which has complex nonlinearity is developed as a test bed the effectiveness of the proposed controller design methodology is finally demonstrated through numerical simulations on the chaotic lorenz system

decentralized dynamic output feedback controller design for guaranteed cost stabilization of large scale discrete delay systems in this paper we discuss how to solve dynamic output feedback controller design problem for decentralized guaranteed cost stabilization of large scale discrete delay system by convex optimization based on lyapunov second method an linear matrix inequality optimization problem is formulated to design the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function a numerical example is given to illustrate the proposed method

localising embeddings of comodule categories with applications to tame and euler coalgebras given a k coalgebra c and an injective left c comodule e we construct a coalgebra ce and fully faithful left exact embedding e ce comod c comod of comodule categories such that the image of e is the subcategory c comode consisting of the comodules m with an injective presentation 0 m e0 e1 where e0 and e1 are direct sums of direct summands of the comodule e the functor e preserves the indecomposability the injectivity and is right adjoint to the restriction functor rese c comod ce comod applications to the study of tame coalgebras betti numbers and cosyzygy comodules of simple comodules over a left euler coalgebra c are given a localising reduction to countably dimensional euler coalgebras is presented

dynamic output feedback guaranteed cost control for linear systems with interval time varying delays in states and outputs abstract this paper addresses the dynamic output feedback guaranteed cost control problem of a class of time delay systems where the state and output contain interval non differentiable time varying delays the proposed controller uses only the delayed output measurement to stabilize the closed loop system and guarantee an adequate level of system performance by constructing a set of multiple lyapunov krasovskii functionals which include triple integral terms a new criterion for the existence of dynamic output feedback guaranteed cost controllers is established and expressed in terms of linear matrix inequality lmi a numerical example is given to illustrate the obtained results

guaranteed cost control of affine nonlinear systems via partition of unity method we consider the problem of guaranteed cost control gcc of affine nonlinear systems in this paper firstly the general affine nonlinear system with the origin being its equilibrium point is represented as a linear like structure with state dependent coefficient matrices secondly partition of unity method is used to approximate the coefficient matrices as a result of which the original affine nonlinear system is equivalently converted into a linear like system with modeling error a gcc law is then synthesized based on the equivalent model in the presence of modeling error under certain error condition the control law ensures that the system under control is asymptotically stable as well as that a given cost function is upper bounded a suboptimal gcc law can be obtained via solving an optimization problem in terms of linear matrix inequality lmi in stead of state dependent riccati equation sdre or hamilton jacobi equations that are usually required in solving nonlinear optimal control problems finally a numerical example is provided to illustrate the validity of the proposed method

robust sliding mode control of nonlinear systems with delay a design via polytopic formulation this paper outlines the possibility to control nonlinear uncertain systems with single possibly time varying state delay these systems are submitted to additive perturbations possibly nonvanishing the control is of sliding mode type and the sliding surface is designed so to maximize the calculable set of delays which do not destabilize the system the way to deal with the nonlinear parts of the model relies on a polytopic formulation the conditions for the existence of the sliding regime are studied by using both a lyapunov krasovskii functionnal and a lyapunov razumikhin function the optmization precedure for the choice of the sliding surface is expressed in terms of lmis an example illustrates the proposed method

technical communique delay dependent output feedback guaranteed cost control for uncertain time delay systems this paper considers the problem of output feedback guaranteed cost controller design for uncertain time delay systems by representing the time delay system in the descriptor form and using a recent result on bounding of cross products of vectors we obtain new delay dependent sufficient conditions for the existence of the guaranteed cost output feedback controller in terms of matrix inequalities a numerical algorithm is proposed to construct a full order output feedback controller achieving a suboptimal guaranteed cost such that the system can be stabilized for all admissible uncertainties an example is presented which shows that the proposed method can produce a lower guaranteed cost than the delay independent method

non fragile control for nonlinear networked control systems with long time delay this paper considers the non fragile control problem for uncertain nonlinear networked control systems ncss with long time delay and controller gain perturbations firstly the ncs model with random long time delay is transformed into a discrete time system model with uncertain parameters then the lyapunov stability theory and the linear matrix inequality lmi approach are applied to design a non fragile controller which results in the closed loop system being asymptotically stable and the system s cost function value being less than a determinate upper bound at the same time the existence condition and the design approach of a non fragile controller are presented finally simulation examples are employed to verify the validity of the proposed control algorithm

structure smith macmillan form and coprime mfds of a rational matrix inside a region p ω abstract the structure of the smith macmillan form of a rational matrix t s inside a region p where is asymmetric with respect to the real axis subset of the finite complex plane c is determined algorithmic procedures based on elementary row and column operations over the euclidean ring r p s consisting of all rational functions with no poles in p are given coprimeness in p of a pair of rational matrices is studied in detail these results lead to constructive procedures for determining the coprime in p matrix fraction descriptions of t a

robust regulation with h 2 performance abstract we consider the problem of minimizing the h 2 norm of a feedback system subject to the constraint that the controller robustly regulate against constants and sinusoids we show that for any 0 there exists a controller that both achieves robust regulation and renders the closed loop h 2 norm within of the optimal norm the norm achievable without the robust regulation constraint we also provide conditions that are both necessary and sufficient for there to exist a robustly regulating controller that achieves the optimal h 2 norm all proofs are constructive

feedback system design the tracking and disturbance rejection problems the problem of designing a compensator for a specified plant which simultaneously stabilizes the resultant feedback system and causes it to track a prescribed family of inputs and or reject prescribed disturbances is considered a set of linear design equations in the space of stable systems is formulated in a general linear systems setting and an explicit parameterization of the resultant solution space is obtained for a class of generalized multivariate systems the theory is illustrated with several single and multivariate examples

hemivariational inequality approach to the dynamic viscoelastic sliding contact problem with wear abstract the dynamic contact problem of sliding contact with wear between a viscoelastic body and a foundation is formulated as a hemivariational inequality the contact is modeled with a general normal damped response condition which is nonmonotone possibly multivalued and has the subdifferential form we establish the existence of weak solutions by using a surjectivity result for a class of pseudomonotone operators we also deliver conditions under which the solution of the evolution inclusion associated with the hemivariational inequality is unique

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

a duality based approach to the multiobjective h 2 h optimisation problem in this article a duality approach to multiobjective h 2 h problems is pursued in which real rational para hermitian multipliers and real valued ones are associated to h and as usual h 2 constraints respectively it is shown that the maximisation of a dual functional over all such multipliers yields the optimal value of the original multiobjective h 2 h problem to compute lower bounds on the latter and the corresponding approximate solutions to the original problem the maximisation of the dual functional over linearly parameterised finite dimensional classes of real rational multipliers is shown to be equivalent to semi definite linear programming problems once the optimal multipliers in such a class are obtained the corresponding approximate solutions can be computed from an unconstrained h 2 problem iterative modification of such classes is discussed to obtain increasing sequences of lower bounds on the optimal value of the original problem this is done on the basis of locally incr

proper and stable minimal macmillan degrees bases of rational vector spaces the structure of proper and stable bases of rational vector spaces is investigated we prove that if t s is a rational vector space then among the proper bases of 3 s there is a subfamily of proper bases which are 1 stable 2 have no zeros in c bigcup infty and therefore are column row reduced at infinity and 3 their macmillan degree is minimum among the macmillan degrees of all other proper bases of 3 s and it is given by the sum of the macmillan degrees of their columns taken separately it is shown that this notion is the counterpart of forney s concept of a minimal polynomial basis for the family of proper and stable bases of 3 s

memoryless stabilization of uncertain dynamic systems with time varying delayed states and controls we consider the feedback stabilization of uncertain dynamic systems with time varying delays in both states and controls we extend the so called riccati equation approach to include those systems and we give an example

robust anti windup controller design of time delay fuzzy systems with actuator saturations this study presents a robust anti windup fuzzy control approach for uncertain nonlinear time delay systems with actuator saturations the discussed system dynamics is presented by the takagi sugeno t s fuzzy model to facilitate the design process the nonlinearity of input saturation is characterized by a specific sector condition given a stabilizing dynamic output feedback fuzzy controller an anti windup control approach is then developed to maximize the size of estimate of the domain of attraction significantly the convergence of all admissible initial states within this region could be ensured based on the lyapunov krasovskii delay independent and delay dependent analyses sufficient conditions for the robust stabilization are derived these conditions are formulated as a convex optimization problem with constraints represented by a set of linear matrix inequalities allowing the fuzzy controller to be synthesized more efficiently finally numeric simulations are given to validate the proposed approach

robust reduced order nonstrictly proper state estimation via the optimal projection equations with guaranteed cost bounds a state estimation design problem involving parametric plant uncertainties is considered an estimation error bound suggested by multiplicative white noise modeling is utilized for guaranteeing robust estimation over a specified range of parameter uncertainties necessary conditions that generalize the optimal projection equations for reduced order state estimation are used to characterize the estimator that minimizes the error bound the design equations thus effectively serve as sufficient conditions for synthesizing robust estimators additional features include the presence of a static estimation gain in conjunction with the dynamic kalman estimator to obtain a nonstrictly proper estimator

on the effects of redundant control inputs this paper considers effects of redundant control inputs on system performance a necessary and sufficient condition for strict decrease of the quadratic performance index with input extension is introduced for the non strict decrease cases the initial state set is determined by using hamilton matrix eigenvectors and generalized eigenvectors the h 2 optimal control problem is similarly studied on the basis of state feedback and dynamic output feedback controllers both linear matrix inequality lmi and riccati equation based methods are established the guaranteed cost problem is also solved for uncertain systems with input extension an iterative optimization algorithm is presented for choosing the input matrix columns for a better performance index a satellite launch vehicle slv system is used to illustrate the results

diagonal stabilization of linear multivariable systems a new procedure is presented for the synthesis of diagonal compensators for n n linear multivariable systems that are free of fixed modes with respect to constant diagonal output feedbacks the synthesis procedure employs simple polynomial algebra and it is in the form of an n step algorithm the geometric configurations 2n and 2n cells in n space are shown to be especially suitable for visualizing diagonal feedback and aiding the application of the synthesis algorithm

delay dependent guaranteed cost stabilization criterion for neutral delay differential systems matrix inequality approach abstract in this paper we address the problem of the guaranteed cost stabilization for a class of neutral delay differential systems with a given quadratic cost function based on the lyapunov method delay dependent criteria which are expressed in terms of matrix inequalities are proposed to guarantee the asymptotic stability of the system the matrix inequalities can be easily solved by various efficient optimization algorithms

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

mixed spl hscr sub 2 and spl hscr sub spl infin performance objectives ii optimal control this paper considers the analysis and synthesis of control systems subject to two types of disturbance signals white signals and signals with bounded power the resulting control problem involves minimizing a mixed spl hscr sub 2 and spl hscr sub spl infin norm of the system it is shown that the controller shares a separation property similar to those of pure spl hscr sub 2 or spl hscr sub spl infin controllers necessary conditions and sufficient conditions are obtained for the existence of a solution to the mixed problem explicit state space formulas are also given for the optimal controller

a new approach to robust guaranteed cost control for uncertain multimodeling systems the guaranteed cost control problem for multimodeling systems with norm bounded uncertainty is investigated the main contribution in this paper is that a new independent controller is derived by solving the reduced order slow and fast algebraic riccati equations ares whose dimension is smaller than the dimension of full order multiparameter algebraic riccati equation mare it is shown that if these ares have a positive definite stabilizing solution then the closed loop system is quadratically stable and has the cost bound

a primal dual potential reduction method for problems involving matrix inequalities we describe a potential reduction method for convex optimization problems involving matrix inequalities the method is based on the theory developed by nesterov and nemirovsky and generalizes gonzaga and todd s method for linear programming a worst case analysis shows that the number of iterations grows as the square root of the problem size but in practice it appears to grow more slowly as in other interior point methods the overall computational effort is therefore dominated by the least squares system that taust be solved in each iteration a type of conjugate gradient algorithm can be used for this purpose which results in important savings for two reasons first it allows us to take advantage of the special structure the problems often have e g lyapunov or algebraic riccati inequalities second we show that the polynomial bound on the number ofiterations remains valid even if the conjugate gradient algorithm is not run until completion which in practice can greatly reduce the computational effort per iteration we describe in detail how the algorithm works for optimization problems with l lyapunov inequaliues each of size m we prove an overall worst case operation count of o mssll5 the average case complexity appears to be closer to o m4ll5 this estimate is justified by extensive numerical experimentation and is consistent with other researchers experience with the practical performance of interior point algorithms for linear programming this result means that the computational cost of extending current control theory based on the solution of lyapunov or riccati equations to a theory that is based on the solution of multiple coupled lyapunov or riccati inequalities is modest

brief paper algebraic and topological aspects of the regulator problem for lumped linear systems the regulator problem with robustness is solved for systems modelled by rational transfer matrices a topology for possibly unstable plants is presented a necessary and sufficient condition is derived for the existence of a proper controller which provides internal stability and output regulation throughout an open neighbourhood of the plant a characterization of all such controllers is determined

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

lmi based reset mathcal h _ infty design for linear continuous time plants in this technical note an optimization based synthesis of a multi objective reset controller for linear plants is presented the result allows designing via convex tools with a line search a multi objective reset controller optimizing both the exponential converging rate and the mathcal l 2 gain a novel peculiarity of our scheme is that the underlying linear flow dynamics is not necessarily stabilizing this last property is the consequence of taking into account where the flowing trajectories lay and lead to improved performance especially in terms of decay rate some simulations illustrate the usefulness of our techniques

structure and smith macmillan form of a rational matrix at infinity the use of special row and column operations in the reduction of a rational matrix to its smith macmillan form at infinity is investigated the connections between this reduction procedure and the valuation approach are established a graphical method for finding the smith macmillan form of a rational matrix at infinity from its bode magnitude array and some new results on realization theory for polynomial matrices are presented

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

robust regulation in the presence of norm bounded uncertainty we consider robust regulation against steps and sinusoids in the presence of unstructured uncertainty the unstructured uncertainty is norm bounded by a constant that is given a priori this problem is equivalent to a certain multiobjective problem where one objective is robust regulation and the other is the standard objective of h sub spl infin suboptimal control it is shown that a solution to this problem exists if and only if the standard h sub spl infin problem admits a solution and certain matrix inequalities are satisfied these solvability conditions are readily computable controller synthesis is also addressed

localisation homotopique et tour de taylor pour une categorie abelienne on indique comment une sous categorie colocalisante d une categorie abelienne induit une localisation dans la categorie derive ceci permet une nouvelle construction de la tour de taylor d un foncteur a valeur dans une categorie de module

fuzzy guaranteed cost control for nonlinear systems with time varying delay this paper focuses on the problem of guaranteed cost control for takagi sugeno t s fuzzy systems with time varying delayed state a linear quadratic cost function is considered as a performance index of the closed loop fuzzy system then the guaranteed cost control of the closed loop fuzzy system is discussed and the sufficient conditions are provided for the construction of a guaranteed cost controller via state feedback and observer based output feedback when these conditions which are given in terms of the feasibility of linear matrix inequalities lmis are satisfied the designed state feedback controller and observer based controller gain matrices can be obtained via a convex optimization problem two illustrative examples are provided to demonstrate the effectiveness of the approaches proposed in this paper

explicit controller formulas for lmi based h synthesis the set of h controllers with closed loop performance c can be implicitly parametrized by the solutions r s of a system of linear matrix inequalities lmi the matrices r and s play a role analogous to that of the riccati solutions x and y in classical riccati based h control useful applications include lmi based h synthesis mixed h 2h design and h design with a pole placement constraint this paper is concerned with the reliable computation of h controllers given a solution r s of the characteristic system of lmis explicit formulas are derived for both the regular and singular cases remarkably these formulas are extensions of the usual central controller formulas where the lmi solutions r and s replace the riccati solutions x and y simple and numerically appealing new formulas for discrete time h controllers are also derived

memoryless stabilization of uncertain linear systems including time varying state delays the problem of stabilizing a class of uncertain time delay systems via memoryless linear feedback is examined the systems under consideration are linear systems with time varying state delays they also contain uncertain parameters possibly time varying whose values are known only to within a prescribed compact bounding set the main contribution given is to enlarge the class of time delay systems for which one can construct a stabilizing memoryless linear feedback controller within this framework a novel notion of robust memoryless stabilizability is first introduced via the method of lyapunov functionals then a sufficient condition for the stabilizability is proposed it is shown that solvability of a parameterized riccati equation can be used to determine whether the time delay system satisfies the sufficient condition if there exists a positive definite symmetric solution satisfying the riccati equation a suitable memoryless linear feedback law can be derived

decentralized diagonal dynamic stabilization of linear multivariable systems abstract the diagonal stabilization problem dsp is defined over the ring of proper rational functions which have no poles inside a prescribed region of the finite complex plane solvability is intimately related to systems which exhibit the property of cyclicity necessary and sufficient conditions are established for the existence of solutions to the dsp a complete parametrization of stabilizing controllers for the 2 2 case is given conditions of nonsolvability and hence nonstabilizability yield an explicit expression for the fixed modes of the system

robust overlapping guaranteed cost control of uncertain state delay discrete time systems this note presents a new extension of the inclusion principle to cope with the problem of designing robust overlapping controllers for state delayed discrete time systems with norm bounded uncertainties using the concept of guaranteed cost control expansion contraction relations for systems and contractibility conditions for output guaranteed cost memoryless controllers are proved including conditions on the equality of guaranteed performance bounds the controllers are designed in the expanded space using a linear matrix inequality lmi delay independent procedure specifically adapted to this class of problems the designed controllers are then contracted and implemented into the original system the results are specialized for the overlapping decentralized control design the method enables an effective construction of block tridiagonal controllers a numerical illustrative example is supplied

technical communique an lmi approach to guaranteed cost control of linear uncertain time delay systems the guaranteed cost control problem via memoryless state feedback controllers is studied in this paper for a class of linear time delay systems with norm bounded time varying parametric uncertainty and a given quadratic cost function sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequalities lmis furthermore a convex optimization problem with lmi constraints is formulated to design the optimal guaranteed cost controller which minimizes the guaranteed cost of the closed loop uncertain system

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

existence results for evolution hemivariational inequalities of second order abstract in this paper we consider evolution hemivariational inequalities of second order with a time dependent pseudomonotone operator and nonmonotone multivalued perturbations we present the existence of solutions for such inequality the proof profits from a result on the surjectivity of operators of pseudomonotone type we discuss some examples which indicate the practical importance of our theoretical findings

delay dependent nonfragile guaranteed cost control for nonlinear time delay systems abstract this paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear dynamic systems with multiple time delays and controller gain perturbations guaranteed cost control law is designed under two classes of perturbations namely additive form and multiplicative form the problem is to design a memoryless state feedback control law such that the closed loop system is asymptotically stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainties based on the linear matrix inequality lmi approach some delay dependent conditions for the existence of such controller are derived a numerical example is given to illustrate the proposed method

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

robust stabilization of a class of nonlinear time delay systems the problem of robust stabilization for a class of uncertain dynamic systems with multiple delayed state perturbations is considered it is assumed that perturbations of the time delayed sections are not bounded by first order linear functions but bounded by high order functions with unknown gains and the time delay considered is time varying two classes of controllers are proposed when the time derivative of each time varying time delay is less than 1 a class of adaptive state feedback controllers are proposed based on lyapunov krasovskii method which can render the closed loop systems uniformly ultimately bounded stable novel nonlinear feedback controllers are developed by employing razumikhin lemma and the controller also can render the closed loop systems stable in the sense of uniform ultimate boundedness finally several examples are given to show the potential of the proposed techniques

on design of dynamic output feedback controller for gcs of large scale systems with delays in interconnections lmi optimization approach this paper considers the dynamic output feedback controller design problem for decentralized guaranteed cost stabilization gcs of large scale systems with time delays in subsystem interconnections based on the lyapunov method a linear matrix inequality lmi convex optimization problem is formulated to find the controller which guarantees the asymptotic stability and minimizes the upper bound of a given quadratic cost function

on the linear static output feedback problem the annihilating polynomial approach abstract one of the fundamental open problems in control theory is that of the stabilization of a linear time invariant dynamical system through static output feedback we are given a linear dynamical system defined through w a w b u y c w the problem is to find if it exists a feedback u k y such that the matrix a b k c has all its eigenvalues in the complex left half plane and if such a feedback does not exist to prove that it does not substantial progress has not been made on the computational aspect of the solution to this problem in this paper we consider instead which annihilating polynomials can a matrix of the form a b k c possess we give a simple solution to this problem when the system has either a single input or a single output for the multi input multi output case we use these ideas to characterize the annihilating polynomials when k has rank one and suggest possible computational solutions for general k we also present some numerical evidence for the plausibility of this approach for the general case as well as for the problem of shifting the eigenvalues of the system

classification of proper bases of rational vector spaces minimal macmillian degree bases abstract the algebraic structure of the get of all proper rational vectors contained in a given rational vector space x1d4af s is shown to be that of a noothorian pr s motiulo m ropf pr a is the ring of proper rational functions the proper submodules mt of m form an ascending chain of submodules partially ordered by an invariant of mt defined as the valuation at s ofmt tho various bases of mt are examined and classified according to their property of column reduceness at s the concept of a prime column reduced at basis of mt is introduced it is shown that tho prime bases of mt can be further classified by their macmillan degrees and the existence of minimal macmillan degree bases for mt is established a prime and minimal macmillan degree basis ofmt extends forney s concept of a minimal polynomial basis of s for the rpr mt module the macmillan degrees of the columns of such bases form a set of invariants mt for which are defined as the x1d4af s generalized invariant dynamicol indices o

guaranteed cost control for bilinear systems by static output feedback this paper proposes a static output feedback controller design technique for bilinear systems based on lyapunov s direct method a nonlinear control law is derived to stabilize the system in the presence of external disturbances sufficient condition is derived in terms of a state dependent nonlinear matrix inequality and then it is converted into a sum of squares sos optimization problem semidefinite programming and sos decomposition techniques are employed to solve the optimization problem the obtained output feedback controller guarantees an upper bound of the performance index the effectiveness of the proposed method is demonstrated through simulation results

guaranteed cost stabilization of neutral differential systems with parametric uncertainty in this paper we address the problem of the guaranteed cost stabilization for a class of neutral systems with parametric uncertainties and a given quadratic cost function the parametric uncertainties are real time varying norm bounded and state delay is a constant the problem is to design the state feedback control laws such that the closed loop system is asymptotically stable and the closed loop cost function value is not more than a specified upper bound for all admissible uncertainty and delay two criteria for the existence of such controllers are derived based on the matrix inequality approach combined with the lyapunov method the developed guaranteed cost controllers can be synthesized in terms of the feasible solutions to the certain matrix inequalities

fuzzy robust dynamic output feedback control of nonlinear systems with linear fractional parametric uncertainties in this paper the problem of robust dynamic output feedback control for a class of discrete time nonlinear systems with parametric uncertainties is studied the parametric uncertainties are assumed to be of a linear fractional form first the takagi sugeno t s fuzzy model is employed to represent the nonlinear system then novel approaches are developed to design the dynamic output feedback controller and sufficient conditions for robust stabilization are obtained in the form of linear matrix inequalities lmis the proposed approaches not only have abilities to effectively handle the parametric uncertainties but also are suitable for the fuzzy system with immeasurable premise variables simulation examples are presented to illustrate the design procedures and the effectiveness of the proposed methods

robust delay dependent guaranteed cost controller design for uncertain neutral systems in this paper a novel robust delay dependent guaranteed cost controller is introduced for a class of uncertain nonlinear neutral systems with both norm bounded uncertainties and nonlinear parameter perturbations a neutral memory state feedback control law is chosen such that a quadratic cost function is minimized on the basis of a descriptor type model transformation an augmented descriptor form lyapunov krasovskii functional is proposed in order to derive a linear matrix inequality lmi condition of the synthesis of a robust stabilizing guaranteed cost controller for uncertain nonlinear neutral systems the descriptor approach is applied for both the delay differential equation and the neutral difference operator allowing to introduce several additional free weighting matrices in order to obtain further relaxation in the synthesis process the proposed method of introducing some relaxation into design problem also leads to develop lmi conditions which can be easily solved using interior point algorithms two numerical examples have been introduced to show the application of the theoretical results which indicate that the proposed approach improves the guaranteed cost performance