on sufficient conditions for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems the specific notion under consideration is asymptotic stability independent of delay as an attempt to achieve a compromise between the complexity and tightness of various stability tests we present a number of sufficient stability conditions which improve several previously available sufficient conditions and which are also much easier to verify than the known necessary and sufficient conditions

optimal diagonal scaling for infinity norm optimization abstract a solution is presented for the previously unsolved diagonally scaled multivariable infinity norm optimization problem of minimizing d s a s s x s d 1 s over the set of stable minimum phase diagonal d s and stable x s this problem is of central importance in the synthesis of feedback control laws for robust stability and insensitivity in the presence of structured plant uncertainty the result facilitates the design of feedback controllers which optimize the excess stability margin 3 or equivalently the structured singular value 4 of diagonally perturbed feedback systems

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

generalized multiscale finite element method for a strain limiting nonlinear elasticity model abstract in this paper we consider multiscale methods for nonlinear elasticity in particular we investigate the generalized multiscale finite element method gmsfem for a strain limiting elasticity problem being a special case of the naturally implicit constitutive theory of nonlinear elasticity strain limiting relation has presented an interesting class of material bodies for which strains remain bounded even infinitesimal while stresses can become arbitrarily large the nonlinearity and material heterogeneities can create multiscale features in the solution and multiscale methods are therefore necessary to handle the resulting nonlinear monotone quasilinear elliptic equation we use linearization based on the picard iteration we consider two types of basis functions offline and online basis functions following the general framework of gmsfem the offline basis functions depend nonlinearly on the solution thus we design an indicator function and we will recompute the offline basis functions when the indicator function predicts that the material property has significant change during the iterations on the other hand we will use the residual based online basis functions to reduce the error substantially when updating basis functions is necessary our numerical results show that the above combination of offline and online basis functions is able to give accurate solutions with only a few basis functions per each coarse region and adaptive updating basis functions in selected iterations

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

an alternative solution to the h optimal control problems abstract in this paper we present an alternative solution to the problem min x h n n a bxc where a b rmand c are rational matrices in h n n the solution circumvents the need to extract the matrix inner factors of b and c providing a multivariable extension of sarason s h interpolation theory 1 to the case of matrix valued b s and c s the result has application to the diagonally scaled optimization problem int d a bxc d 1 where the infimum is over d x h n n d diagonal

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

closed finitely generated ideals in algebras of holomorphic functions and smooth to the boundary in strictly pseudoconvex domains define in a m a a natural estructure of banach resp fr6chet algebra in this paper we are interested in the closed finitely generated ideals of the algebras am as much as we know there are very few papers on the ideal structure of these algebras in dimension n 1 in 22 nagel proved that if d is piecewise real analytic and g ok are holomorphic in a neighbourhood o f the ideal in a generated by g gk is closed our first main result establishes a sort of reciprocal of nagel s theorem

technical communique output feedback stabilizing controller for time delay systems this paper considers the problem of output feedback stabilization of unstable linear time delay systems the major features of the approach are 1 the delay system is characterized by a fixed transfer function matrix that contains just the set of unstable or marginally unstable modes plus an h norm for the stable part 2 the controller design is accomplished by dynamic output feedback and 3 sufficient conditions in the form of two algebraic riccati equations and an upper bound explicitly characterize a stabilizing controller the method is restricted to delay systems that satisfy an upper bound on the stable part

flow through porous media due to high pressure gradients abstract while darcy s equations are adequate for studying a large class of flows through porous media there are several situations wherein it would be inappropriate to use darcy s equations one such example is a flow wherein the range of pressures involved is very large and high pressures and pressure gradients are at play here after developing an approximation for the flow through a porous solid that is a generalization of an equation developed by brinkman we study a simple boundary value problem that clearly delineates the difference between the solution to these equations and those due to the equations that are referred to as darcy law we find that the solutions for the equations under consideration exhibit markedly different characteristics from the counterpart for the brinkman equations or darcy s equations or the navier stokes equation if one neglects the porosity in that the solutions for the velocity as well as the vorticity lack symmetry and one finds the maximum value of the vorticity occurs at the boundary near which the fluid is less viscous in virtue of the pressure being lower we also find that for a certain range of values for the non dimensional parameters describing the flow boundary layers develop in that the vorticity is confined next to the boundary adjacent to which the viscosity is lower such boundary layers being absent in the other classical cases

complex manifolds in q convex boundaries we consider a c infty boundary b omega subset mathbb c n which is q convex in the sense that its levi form has positive trace on every complex q plane we prove that b omega is tangent of infinite order to the complexification of each of its submanifolds which is complex tangential and of finite bracket type this generalizes diederich and fornaess ann math 107 371 384 1978 from pseudoconvex to q convex domains we also readily prove that the rows of the levi form are frac 1 2 subelliptic multipliers for the bar partial neumann problem on q forms cf ho in math ann 290 3 18 1991 this allows to run the kohn algorithm of acta math 142 79 122 1979 in the chain of ideals of subelliptic multipliers for q forms if b omega is real analytic and the algorithm gets stuck on q forms then it produces a variety of holomorphic dimension q and in fact by our result above a complex q manifold which is not only tangent but indeed contained in b omega altogether the absence of complex q manifolds in b omega produces a subelliptic estimate on q forms

quadratic stability with real and complex perturbations it is shown that the equivalence between real and complex perturbations in the context of quadratic stability to linear fractional unstructured perturbations does not hold when the perturbations are block structured for a limited class of problems quadratic stability in the face of structured complex perturbations is equivalent to a particular class of scaled norms and hence appropriate synthesis techniques coupled with diagonal constant scalings can be used to design quadratically stable systems

robustness margin calculation with dynamic and real parametric uncertainty the problem of robust stability in feedback control systems with real uncertain parameters and unmodeled dynamics is considered a robust margin r sub m is defined and an algorithm to calculate r sub m and the closely related multivariable stability margin k sub m is developed how robust performance for real parametric uncertainty can be handled in this framework is also shown the result essentially provides a method to check whether or not the infinity norm of a closed loop transfer matrix is less than a specified level over a bounded set of real parametric variations

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

frequency sweeping tests for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems given in a state space form we consider specifically the notion of asymptotic stability independent of delay systems with both commensurate and noncommensurate delays are investigated we present for each class of systems a necessary and sufficient condition in terms of structured singular values and further we demonstrate how these conditions may be extended to study stability independent of delay for uncertain systems our results consist of several frequency sweeping tests that can be systematically implemented and that should complement the previous work

computation of delay intervals for stability of time delay systems abstract this paper addresses the problem of computing the delay intervals for stability of time delay systems time delays are frequently a source of instability and quite often difficult to estimate the major features of the method are 1 the delay uncertainty is represented by a relative error i e h h 0 1 2 the time delay system is recast by a representation that is compatible with robust control analysis which requires a norm bounded modeling uncertainty and stable transfer function and 3 a new tool i e singular phase value is proposed to find the exact bounds on the delay that sufficiently stabilize the time delay system the method can be used to find the first delay interval for stability but it can also be extended to find other delay intervals using standard robust control tools therefore the proposed method is suitable for computer implementation with a simple modification the proposed method can also be used to test the robust stability of various controller schemes under closed loop conditions

generalized multiscale finite element methods gmsfem in this paper we propose a general approach called generalized multiscale finite element method gmsfem for performing multiscale simulations for problems without scale separation over a complex input space as in multiscale finite element methods msfems the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space in the proposed approach we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage the enrichment in the online stage is performed based on a spectral decomposition of the offline space in the online stage for any input parameter a multiscale space is constructed to solve the global problem on a coarse grid the online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues the computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re used for solving the forward problem with any forcing and boundary condition compared with the other approaches where global snapshots are used the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse grid level we present various examples in the paper and some numerical results to demonstrate the effectiveness of our method

variational multiscale analysis the fine scale green s function projection optimization localization and stabilized methods we derive an explicit formula for the fine scale green s function arising in variational multiscale analysis the formula is expressed in terms of the classical green s function and a projector which defines the decomposition of the solution into coarse and fine scales the theory is presented in an abstract operator format and subsequently specialized for the advection diffusion equation it is shown that different projectors lead to fine scale green s functions with very different properties for example in the advection dominated case the projector induced by the h 1 0 seminorm produces a fine scale green s function which is highly attenuated and localized these are very desirable properties in a multiscale method and ones that are not shared by the l 2 projector by design the coarse scale solution attains optimality in the norm associated with the projector this property combined with a localized fine scale green s function indicates the possibility of effective methods with local character for dominantly hyperbolic problems the constructs lead to a new class of stabilized methods and the relationship between h 1 0 optimality and the streamline upwind petrov galerkin supg method is described

a numerical method for computing the structured singular value abstract this article suggests a new approach to computing doyle s structured singular value ssv of a matrix the ssv is a notion important in robust control and several iteration schemes exist for approximation a solution 1 2 4 8 10 11 our idea is to pick a special case of the general problem which we believe to be natural and give an algorithm for studying it based on off the shelf packages once we are committed to this special case we discuss a very general plant uncertainty problem it embraces real as well as complex plant perturbations of many kinds the idea is simple and we believe very natural to the problem

an asymptotic modal observer for linear autonomous time lag systems a full state vector observer is derived for a class of linear autonomous time lag systems represented by differential equations the major features of the approach are 1 an observer is constructed just for the set of unstable or poorly damped modes of the delayed system once they have been determined and 2 the design is accomplished by using a partial fraction expansion separating the unstable part from the system and then applying well known finite dimensional state vector techniques a procedure for the construction is given along with some numerical results to illustrate the simplicity of the observer

compactness of the neumann problem on convex domains the neumann operator on 0 q forms 1 q n on a bounded convex domain in cnis compact if and only if the boundary of contains no complex analytic equivalently affine variety of dimension greater than or equal toq

a generalized multiscale finite element method for poroelasticity problems i in this paper we consider the numerical solution of poroelasticity problems that are of biot type and develop a general algorithm for solving coupled systems we discuss the challenges associated with mechanics and flow problems in heterogeneous media the two primary issues being the multiscale nature of the media and the solutions of the fluid and mechanics variables traditionally developed with separate grids and methods for the numerical solution we develop and implement a generalized multiscale finite element method gmsfem that solves problem on a coarse grid by constructing local multiscale basis functions the procedure begins with construction of multiscale bases for both displacement and pressure in each coarse block using a snapshot space and local spectral problems we construct a basis of reduced dimension finally after multiplying by a multiscale partitions of unity the multiscale basis is constructed in the offline phase and the coarse grid problem then can be solved for arbitrary forcing and boundary conditions we implement this algorithm on two heterogeneous media and compute error between the multiscale solution with the fine scale solutions randomized oversampling and forcing strategies are also tested

on noncompactness of the neumann problem on pseudoconvex domains in c3 abstract we prove that a smooth bounded pseudoconvex domain c 3 with a one dimensional complex manifold m in its boundary has a noncompact neumann operator on 0 1 forms under the additional assumption that b has finite regular d angelo 2 type at a point of m

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

characterization and efficient computation of the structured singular value the concept of structured singular value was recently introduced by doyle 1 as a tool for the analysis and synthesis of feedback systems with structured uncertainties it is a key to the design of control systems under joint robustness and performance specifications and it very nicely complements the h infty approach to control system design in this paper it is shown that the structured singular value can be obtained as the solution of several smooth optimization problems properties of these optimization problems are exhibited leading to a fast algorithm that always yields the structured singular value for block structures of size no larger than 3 and often does for block structures of larger size

a maximum modulus theorem for linear fractional transformations abstract a main result in the structured singular value theory is a maximum modulus like theorem for a special case of linear fractional transformations we extend that result to general linear fractional transformations

splitting schemes for poroelasticity and thermoelasticity problems abstract in this work we consider the coupled systems of linear unsteady partial differential equations which arise in the modelling of poroelasticity processes stability estimates of weighted difference schemes for the coupled system of equations are presented approximation in space is based on the finite element method we construct splitting schemes and give some numerical comparisons for typical poroelasticity problems the results of numerical simulation of a 3d problem are presented special attention is given to using high performance computing systems

feedback stabilization of linear autonomous time lag systems a stabilization theory which employs well established finite dimensional control system tools is developed for the stabilization of linear autonomous time lag systems the main ideas include 1 a set whose elements are matrices each of which is a left zero of the system characteristic quasi polynomial matrix and 2 a linear transformation which reduces the delay system to a delay free system whose state matrix is a direct sum of n elements of the matrix set where n is some positive integer from the definition of this matrix set it is shown that each of its elements inherits its spectrum from that of the delay system so that by design the system unstable poles may be embedded in the spectrum of the delay free system under the assumption of spectral stabilizability it is then shown how to obtain a stabilizing feedback control law on the basis of the delay free system numerical examples are presented to confirm the theory

controller design for plants with structured uncertainty this paper addresses the problem of designing feedback controllers to achieve good performance in the presence of structured plant uncertainty and bounded but unknown disturbances a general formulation for the performance robustness problem is presented and exact computable conditions are furnished these conditions are then utilized for synthesizing robust controllers which involves solving l1 optimization problems these solutions are computed using the duality theory of lagrange multipliers approximations and computational issues are discussed

synthesis of non rational controllers for linear delay systems this paper addresses the control of linear delay systems using non rational controllers the structure of the controller is chosen so as to copy the structure of the plant reproducing the delays in the state and in the output the resulting stabilization and performance design problems are entirely expressed as linear matrix inequalities although the design inequalities are based on delay independent stability conditions the overall design is delay dependent in the sense that the controller makes use of the delay parameter of the plant this parameter is assumed to be constant yet arbitrary using non rational controllers we overcome the main difficulty faced when designing rational controllers for linear delay systems which is to incorporate in the design problem the matrix multiplier used to prove stability with respect to the delayed part of the system we illustrate the paper with several examples and provide extensive comparisons with existent results

analytic discs attached to conormal bundles of cr manifolds abstract letmbe a cr submanifold ofx c n t m xthe conormal bundle tominx zo resp po a point ofm resp t m x def t m x 0 with po zo aa small analytic disc c1up to the boundary attached tomthroughzo a aliftofatot xthroughpoattachedt m x if the levi form ofmhas a constant number of negative eigenvalues in a neighborhood ofp0then we show that in factais contained inmanda int m x whenmis a hypersurface and it is pseudoconvex i e the number of its negative levi eigenvalues is identically 0 then the inclusiona mis classical and follows from the hopf lemma applied to a plurisubharmonic exhaustion function as in d f note that in this case the existence of a lifta t m xis automatic according to b f 1980 math subject classification 1985 revision 32 f

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

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

large scale optimization of eigenvalues optimization problems involving eigenvalues arise in many applications let x be a vector of real parameters and let a x be a continuously differentiable symmetric matrix function of x we consi

robustness under bounded uncertainty with phase information the authors consider uncertain linear systems where the uncertainties in addition to being bounded also satisfy constraints on their phase in this context the authors define the phase sensitive structured singular value ps ssv of a matrix and show that sufficient and sometimes necessary conditions for stability of such uncertain linear systems can be rewritten as conditions involving ps ssv they then derive upper bounds for ps ssv computable via convex optimization they extend these results to the case where the uncertainties are structured diagonal or block diagonal for instance

a generalized multiscale finite element method for poroelasticity problems ii nonlinear coupling in this paper we consider the numerical solution of some nonlinear poroelasticity problems that are of biot type and develop a general algorithm for solving nonlinear coupled systems we discuss the difficulties associated with flow and mechanics in heterogenous media with nonlinear coupling the central issue being how to handle the nonlinearities and the multiscale scale nature of the media to compute an efficient numerical solution we develop and implement a generalized multiscale finite element method gmsfem that solves nonlinear problems on a coarse grid by constructing local multiscale basis functions and treating part of the nonlinearity locally as a parametric value after linearization with a picard iteration the procedure begins with construction of multiscale bases for both displacement and pressure in each coarse block by treating the staggered nonlinearity as a parametric value using a snapshot space and local spectral problems we construct an offline basis of reduced dimension from here an online parametric dependent space is constructed finally after multiplying by a multiscale partitions of unity the multiscale basis is constructed and the coarse grid problem then can be solved for arbitrary forcing and boundary conditions we implement this algorithm on a geometry with a linear and nonlinear pressure dependent permeability field and compute error between the multiscale solution with the fine scale solutions

systems with structured uncertainty relations between quadratic and robust stability the relation between the notions of robust stability and quadratic stability for uncertain systems with structured uncertainty due to both real and complex parameter variations is discussed examples are presented to demonstrate that for systems containing at least two uncertain blocks the notions of robust stability for complex parameter variations and quadratic stability for real parameter variations are not equivalent a byproduct of these examples is that for this class of systems quadratic stability for real perturbations need not imply quadratic stability for complex perturbations this is in stark contrast with the situation in the case of unstructured uncertainty for which it is known that quadratic stability for either real or complex perturbations is equivalent to robust stability for complex perturbations and thus equivalent to a small gain condition on the transfer matrix that the perturbation experiences

boundary invariants of pseudoconvex domains the purpose of this paper is to describe an invariant ax z which is associated with each point z in the boundary of a smoothly bounded pseudoconvex domain in cn the motivation for defining the invariant ax z referred to as the multitype of z comes from the study of the boundary regularity properties of solutions of the d neumann problem on domains of finite type by a domain of finite type we mean one that satisfies the definition given by d angelo 5 namely a domain such that at any boundary point the maximum order of contact of one dimensional complex analytic varieties with the boundary is bounded in 4 the author showed how one can give a proof of global regularity of the a neumann problem for pseudoconvex domains of finite type if there is an invariant such as the one described in this paper in a forthcoming article this invariant will be used to obtain a proof of subelliptic estimates for the same class of domains before giving the definition of the multitype ax z we must introduce some

an interior point method for minimizing the maximum eigenvalue of a linear combination of matrices we consider the problem of finding lambda opt mathop inf limits x in r m lambda max a 0 sum limits i 1 m x i a i 1 and an optimal solution xopt if it exists here the a i are given symmetric matrices in ir n n for 0 i m and max a is the largest eigenvalue of a matrix a problem 1 can be rewritten as a convex differentiable problem with a positive definite constraint positive definiteness can easily be verified numerically via cholesky decomposition moreover the cone of positive definite matrices a is characterized by the domain of the smooth convex barrier function log det a

predictor based control of linear systems with large and variable measurement delays this paper concerns the problem of the control of linear systems by means of feedback from delayed output where the delay is known and time varying the main advantage of the approach is that it can be applied to systems with any delay bound i e not only small delays the predictor is based on a combination of finite dimensional elementary predictors whose number can be suitably chosen to compensate any delay the single predictor element is an original proposal and the class of delays to which the schema can be applied includes but it is not limited to continuous delay functions

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

localization of elliptic multiscale problems this paper constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients the basis functions are solutions of local problems on vertex patches the error of the corresponding generalized finite element method decays exponentially with respect to the number of layers of elements in the patches hence on a uniform mesh of size h patches of diameter h log 1 h are sufficient to preserve a linear rate of convergence in h without pre asymptotic or resonance effects the analysis does not rely on regularity of the solution or scale separation in the coefficient this result motivates new and justifies old classes of variational multiscale methods see more at http www ams org journals mcom 2014 83 290 s0025 5718 2014 02868 8 sthash z2ccfxig dpuf

a property of the functions and distributions annihilated by a locally integrable system of complex vector fields page introduction 387 1 basic notation and ingredients 389 2 approximation and constancy on the fibers of the classical solutions of the homogeneous equations 393 3 first consequences and interpretation of the fundamental theorem 398 4 distribution solutions of the homogeneous equations 402 5 regularity of the solutions of the homogeneous equations 409 6 example of a system that is analytic hypo elliptic but not co hypo elliptic 413 references 420

a chain scattering matrix approach to the h output feedback control for state delayed systems a state space coprime factorization approach to the h controllers design for state delayed systems is developed the coprime factors that are generated by the present factorization possess the same delayed state as that of the original system this property together with the well known youla parameterization and the chain scattering matrix description provides a relatively simple method to obtain a family of the internally stabilizing h output feedback controllers a numerical example is given to demonstrate the validity and the applicability of the proposed approach

analytic discs plurisubharmonic hulls and non compactness of the neumann operator we show that a complex manifold m in the boundary of a smooth bounded pseudoconvex domain in open image in new window is an obstruction to compactness of the open image in new window neumann operator on provided that at some point of m the levi form of b has the maximal possible rank n 1 dim m i e the boundary is strictly pseudoconvex in the directions transverse to m in particular an analytic disc is an obstruction provided that at some point of the disc the levi form has only one zero eigenvalue i e the eigenvalue zero has multiplicity one we also show that a boundary point where the levi form has only one zero eigenvalue can be picked up by the plurisubharmonic hull of a set only via an analytic disc in the boundary

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 uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

robust h sub infinity control for linear systems with norm bounded time varying uncertainty robust h sub infinity control design for linear systems with uncertainty in both the state and input matrices is treated a state feedback control design which stabilizes the plant and guarantees an h sub infinity norm bound constraint on disturbance attenuation for all admissible uncertainties is presented the robust h sub infinity control problem is solved via the notion of quadratic stabilization with an h sub infinity norm bound necessary and sufficient conditions for quadratic stabilization with an h sub infinity norm bound are derived the results can be regarded as extensions of existing results on h sub infinity control and robust stabilization of uncertain linear systems

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

observer based output feedback control of linear systems with input and output delays abstract this paper is concerned with observer based output feedback control of linear systems with both multiple input and output delays our recently developed truncated predictor feedback tpf approach for state feedback stabilization of time delay systems is generalized to the design of observers by imposing some restrictions on the open loop system two classes of observer based output feedback controllers one being finite dimensional and the other infinite dimensional are constructed it is further shown that the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time varying input and output delays it is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers but does not hold for the finite dimensional ones numerical examples are worked out to illustrate the effectiveness of the proposed approaches

a method for computing the interval of delay values for which a differential delay system is stable a test for determining the interval of delay values for which delay differential system is asymptotically stable is presented i e an explicit method is given for calculating h such that for 0

generalized multiscale finite element method for the poroelasticity problem in multicontinuum media abstract in this paper we consider a poroelasticity problem in heterogeneous multicontinuum media that is widely used in simulations of the unconventional hydrocarbon reservoirs and geothermal fields mathematical model contains a coupled system of equations for pressures in each continuum and effective equation for displacement with volume force sources that are proportional to the sum of the pressure gradients for each continuum to illustrate the idea of our approach we consider a dual continuum background model with discrete fracture networks that can be generalized to a multicontinuum model for poroelasticity problem in complex heterogeneous media we present a fine grid approximation based on the finite element method and discrete fracture model dfm approach for two and three dimensional formulations the coarse grid approximation is constructed using the generalized multiscale finite element method gmsfem where we solve local spectral problems for construction of the multiscale basis functions for displacement and pressures in multicontinuum media we present numerical results for the two and three dimensional model problems in heterogeneous fractured porous media we investigate relative errors between reference fine grid solution and presented coarse grid approximation using gmsfem with different numbers of multiscale basis functions our results indicate that the proposed method is able to give accurate solutions with few degrees of freedoms

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

norm preserving dilations and their applications to optimal error bounds the problem is given a b c to find d such that left begin array 20 c a c b d end array right leqq mu here we deal with hilbert space operators a b and c ar

partial fraction expansions for delay systems abstract partial fraction decompositions for single input single output delay systems are studied the results have application in rational l approximations which play an important role in robust compensator design for delay systems