delay dependent h filtering for singular markovian jump systems with general uncomplete transition probabilities this paper is devoted to the investigation of the delay dependent h filtering problem for a kind of singular markovian jump time delay systems with general unknown transition probabilities in this model the transition rates of the jumping process are assumed to be partly available that is some elements have been exactly known some ones have been merely known with lower and upper bounds others may have no information to use using the lyapunov functional theory a stochastically stable filter is designed to guarantee both the mean square exponential admissibility and a prescribed level of h performance for the singular markovian jump time delay systems with general unknown transition probabilities a sufficient condition is derived for the existence of such a desired filter in terms of linear matrix inequalities lmis a numerical example is provided to demonstrate the effectiveness of the proposed theory

complex earthquakes and teichmuller theory it is known that any two points in teichmuller space are joined by an earthquake path in this paper we show any earthquake path r t s extends to a proper holomorphic mapping of a simplyconnected domain d into teichmuller space where r d c these complex earthquakes relate weil petersson geometry projective structures pleated surfaces and quasifuchsian groups using complex earthquakes we prove grafting is a homeomorphism for all 1 dimensional teichmuller spaces and we construct bending coordinates on bers slices and their generalizations in the appendix we use projective surfaces to show the closure of quasifuchsian space is not a topological manifold

on reliable stabilization via rectangular dilated lmis and dissipativity based certifications in this short note we consider the problem of reliable stabilization for multi channel systems where our main objective is to maintain the robust stability of the perturbed closed loop system when there is a single controller failure in any of the control channels specifically we present a less conservative result than results in the literature in terms of a set of dilated lmis for the reliable state feedback stabilization of the nominal system while a dissipativity based certification is used to extend the stability condition when there is an additive model perturbation in the system finally a numerical example is presented to illustrate the applicability of the proposed technique

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

on monodromy of complex projective structures we prove that for any nonelementary representation 1 s sl 2 of the fundamental group of a closed orientable hyperbolic surfaces there exists a complex projective structure ons with the monodromy

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

model reduction of nonstationary lpv systems this paper focuses on the model reduction of nonstationary linear parameter varying nslpv systems we provide a generalization of the balanced truncation procedure for the model reduction of stable nslpv systems along with a priori error bounds then for illustration purposes this method is applied to reduce the model of a two mass translational system furthermore we give an approach for the model reduction of stabilizable and detectable systems which requires the development and use of coprime factorizations for nslpv models for the general class of eventually periodic lpv systems which includes periodic and finite horizon systems as special cases our results can be explicitly computed using semidefinite programming

statistical learning methods in linear algebra and control problems the example of finite time control of uncertain linear systems abstract in this paper we show how some difficult linear algebra problems can be approximately solved using statistical learning methods we illustrate our results by considering the state and output feedback finite time robust stabilization problems for linear systems subject to time varying norm bounded uncertainties and to unknown disturbances in the state feedback case the paper provides a sufficient condition for finite time stabilization in the presence of time varying disturbances such condition requires the solution of a linear matrix inequality lmi feasibility problem which is by now a standard application of linear algebraic methods in the output feedback case however we end up with a bilinear matrix inequality bmi problem which we tackle by resorting to a statistical approach

randomized algorithms for robust controller synthesis using statistical learning theory by now it is known that several problems in the robustness analysis and synthesis of control systems are np complete or np hard these negative results force us to modify our notion of solving a given problem an approach that is recently gaining popularity is that of using randomized algorithms which can be used to solve a problem approximately most of the time we begin with the premise that many problems in robustness analysis and synthesis can be formulated as the minimization of an objective function with respect to the controller parameters it is argued that in order to assess the performance of a controller as the plant varies over a prespecified family it is better to use the average performance of the controller as the objective function to be minimized rather than its worst case performance as the worst case objective function usually leads to rather conservative designs then it is shown that a property from statistical learning theory known as uniform convergence of empirical means ucem plays an important role in allowing us to construct efficient randomized algorithms for a wide variety of controller synthesis problems in particular whenever the ucem property holds there exists an efficient i e polynomial time randomized algorithm using very recent results in statistical learning theory it is shown that the ucem property holds in any problem in which the satisfaction of a performance constraint can be expressed in terms of a finite number of polynomial inequalities in particular several problems such as robust stabilization and weighted h 2 h norm minimization are amenable to the randomized approach

minimal norm static feedbacks using dissipative hamiltonian matrices abstract in this paper we characterize the set of static state feedbacks that stabilize a given continuous linear time invariant system pair using dissipative hamiltonian matrices this characterization results in a parametrization of feedbacks in terms of skew symmetric and symmetric positive semidefinite matrices and leads to a semidefinite program that computes a static state stabilizing feedback this characterization also allows us to propose an algorithm that computes minimal norm static feedbacks the theoretical results extend to the static output feedback sof problem and we also propose an algorithm to compute the minimal norm sof we illustrate the effectiveness of our algorithm compared to state of the art methods for the sof problem on numerous numerical examples from the compleib library

projective structures with discrete holonomy representations let zg be a compact oriented differentiable surface of genus g 2 a projective structure or cp1 structure on z9 is a maximal system of charts with transition maps in the projective automorphism group of cp1 namely psl2 c let p9 denote the space of all projective structures on eg with markings since elements of psl2 c are holomorphic a projective structure determines its underlying complex structure hence there is a natural map r pg tg where 7 denotes the teichmiiller space for each projective structure we can take its developing map on the universal cover and have a holomorphic quadratic differential or a projective connection on the riemann surface the underlying complex structure under the projective structure by taking the schwarzian derivative it is well known cf section 2 for detail that this procedure gives a natural identification between r pg tg and the bundle of holomorphic quadratic differentials over the teichmiiller space r q tg in this paper we will investigate the set of projective structures on yz9 with discrete holonomy representations with respect to the parametrizationby q let k c q be the set of all projective structures with discrete holonomy representations it is well known that there is an open set qf of q which is a neighborhood of the 0 section 0 x tg of q tg consisting of all projective structures with univalent developing maps and quasifuchsian holonomy representations for any riemann surface x c tg the fiber of wr qf qf tg over x which wre denote by qf x is a domain which is holomorphically equivalent to the teichrniller space and is called a bers slice one of our main results shows that a similar phenomenon occurs for each component of the interior point set int k let q x denote the fiber over x of q t namely q x is the space of projective structures on the complex structure x let k x denote the fiber of

lower order h_ infty filter design for bilinear systems with bounded inputs we propose an optimization based method for designing a lower order luenberger type state estimator while providing l 2 gain guarantees on the error dynamics when the estimator is used with the higher order system suitable filter parameters can be computed by modelling the bilinear system as a linear differential inclusion and solving a set of bilinear matrix inequality constraints since these constraints are nonconvex in general we also show that one can solve a suitably defined semi definite program to compute a bound on the level of suboptimality the design method also allows one to explicitly take account of linear parameter uncertainties in order to provide a priori robustness guarantees the h infinity estimator not only has lower real time computational requirements compared with a kalman filter but also does not require knowledge of the noise spectrum for a numerical example we consider the estimation of the radiation force for a wave energy converter where a low order model is used to approximate the radiation dynamics

robust stabilization of linear systems with norm bounded time varying uncertainty abstract in this paper robust stabilization of a class of linear systems with norm bounded time varying uncertainties is considered it is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a parameter dependent riccati equation also a construction for the stabilizing feedback law is given in terms of the solution to the riccati equation

design of hermite subdivision schemes aided by spectral radius optimization we present a method for constructing multivariate refinable hermite interpolants and their associated subdivision algorithms based on a combination of analytical and numerical approaches as the limit of a linear iterative procedure the critical l2 sobolev smoothness of a refinable hermite interpolant is given by the spectral radius of a matrix dependent upon the refinement mask the design question is given certain constraints support size symmetry type refinement pattern etc how can one choose the refinement mask so that the resulting refinable function has optimal smoothness this question naturally gives rise to a spectral radius optimization problem in general the objective function is not convex and may not be differentiable or even lipschitz at a local minimizer nonetheless a recently developed robust solver for nonsmooth optimization problems may be applied to find local minimizers of the spectral radius objective function in fact we find that in specific cases that are of particular interest in the present context the objective function is smooth at local minimizers and may be accurately minimized by standard techniques we present two necessary mathematical tricks that make the method practical i compression of matrix size based on symmetry and ii efficient computation of gradients of the objective function we conclude by reporting some computational results

dynamic output feedback h control of continuous time switched affine systems this paper deals with output feedback switching function control design for continuous time switched affine systems assuring global asymptotic stability of a desired equilibrium point the set of all attainable equilibrium points is provided more specifically the main purpose is to design a full order switched affine filter together with a switching rule assuring not only global asymptotic stability but also a guaranteed h performance level the design conditions do not require that the open loop subsystems be stable and outperform other techniques available in the literature to date the results are compared with recent ones based on a quadratic lyapunov function and on a max type lyapunov function numerical examples illustrate the theoretical results and are used for comparisons

h control of parameter dependent state delayed systems using polynomial parameter dependent quadratic functions this paper presents the issue of robust disturbance attenuation and robust asymptotic stability problem for finite dimensional linear parameter dependent state delayed systems the use of polynomial parameter dependent quadratic lyapunov functions and linear matrix inequalities lmis formulations for robust h control are considered it is shown that the state feedback control can be determined to guarantee the stability of the closed loop system independently of the time delay we present an illustrative example to demonstrate the applicability of the proposed design approach

polynomial root radius optimization with affine constraints the root radius of a polynomial is the maximum of the moduli of its roots zeros we consider the following optimization problem minimize the root radius over monic polynomials of degree n with either real or complex coefficients subject to k linearly independent affine constraints on the coefficients we show that there always exists an optimal polynomial with at most k 1 inactive roots that is roots whose moduli are strictly less than the optimal root radius we illustrate our results using some examples arising in feedback control

brief probabilistic solutions to some np hard matrix problems during recent years it has been shown that a number of problems in matrix theory are np hard including robust nonsingularity robust stability robust positive semidefiniteness robust bounded norm state feedback stabilization with structural and norm constraints etc in this paper we use standard bounds on empirical probabilities as well as recent results from statistical learning theory on the vc dimension of families of sets defined by a finite number of polynomial inequalities to show that for each of the above problems as well as for still more general and more difficult problems there exists a polynomial time randomized algorithm that can provide a yes or no answer to arbitrarily small levels of accuracy and confidence

two numerical methods for optimizing matrix stability consider the affine matrix family a x a0 m 1 xkak mapping a design vector x r m into the space of n n real matrices we are interested in the question of how to choose x to optimize the stability of the matrix a x a typical motivation is that one wishes to control the stability of the dynamical system a x z a classic example is stabilization by output feedback we take two approaches let x denote the spectral abscissa the largest real part of the eigenvalues of a matrix x as is well known this quantity bounds the asymptotic decay rate of the trajectories of the associated dynamical system z xz our first approach to optimizing stability is to directly minimize the function a x the spectral abscissa x is a continuous but non smooth in fact non lipschitz function of the matrix argument x and finding a global minimizer of a x is hard we introduce a novel random gradient bundle method for approximating local minimizers motivated by recent work on nonsmooth analysis of the function x our second approach is to minimize a related function a x where is a robustness parameter in 0 1 one motivation for the definition of the robust spectral abscissa x is that it bounds transient peaks as well as asymptotic decay of trajectories of xz the function x is lipschitz but non convex for 0 1

solvability of static output feedback stabilization for lti positive systems abstract this paper addresses the stabilization problem of positive linear systems which have nonnegative states whenever the initial conditions are nonnegative the synthesis of static output feedback controllers that ensure the positivity and asymptotic stability of the closed loop system is investigated it is shown that this important problem is completely solved for single input and single output positive systems the proposed approach can be applied to multi input positive systems with controllers having one rank gains all the provided conditions are necessary and sufficient and can be solved in terms of linear programming

stability optimization of hybrid periodic systems via a smooth criterion we consider periodic orbits of controlled hybrid dynamic systems and want to find open loop controls that yield maximally stable limit cycles instead of optimizing the spectral or pseudo spectral radius of the monodromy matrix a which are non smooth criteria we propose a new approach based on the smoothed spectral radius rhoalpha a a differentiable criterion favorable for numerical optimization like the pseudo spectral radius the smoothed spectral radius rhoalpha a converges from above to the exact spectral radius rho a for alphararr 0 its derivatives can be computed efficiently via relaxed lyapunov equations we show that our new smooth stability optimization program based on rhoalpha a has a favorable structure it leads to a differentiable nonlinear optimal control problem with periodicity and matrix constraints for which tailored boundary value problem methods are available we demonstrate the numerical viability of our method using the example of a walking robot model with nonlinear dynamics and ground impacts as a complex open loop stability optimization example

pole placement via static output feedback is np hard this note proves that the problem of pole placement via static output feedback for linear time invariant systems is np hard

grafting pruning and the antipodal map on measured laminations grafting a measured lamination on a hyperbolic surface de nes a self map of teichmuller space which is a homeomorphism by a result of scannell and wolf in this paper we study the large scale behavior of pruning which is the inverse of grafting speci cally for each conformal structure x t s pruning x gives a map ml s t s we show that this map extends to the thurston compacti cation of t s and that its boundary values are the natural antipodal involution relative to x on the space of projective measured laminations we use this result to study thurston s grafting coordinates on the space of cp structures on s for each x t s we show that the boundary of the space p x of cp structures on x in the compactication of the grafting coordinates is the graph ix of the antipodal involution ix pml s pml s

approximation by maximal cusps in boundaries of deformation spaces of kleinian groups let m be a compact oriented irreducible atoroidal 3 manifold with nonempty boundary let cc0 m denote the space of convex cocompact kleinian groups uniformizing m we show that any kleinian group in the boundary of cc0 m whose limit set is the whole sphere can be approximated by maximal cusps density of maximal cusps on the boundary of schottky space is derived as a corollary we further show that maximal cusps are dense in the boundary of the quasiconformal deformation space of any geometrically finite hyperbolic 3 manifold with connected conformal boundary

on continuous extensions of grafting maps the definition of the grafting operation for quasifuchsian groups is extended by bromberg preprint to all b groups in this paper we show that the extended grafting maps behave as continuous maps for every sequence which converges standardly to a boundary group although the maps are not continuous in general as a consequence of this result we extend goldman s grafting theorem for quasifuchsian groups to all boundary b groups

robust static output feedback h control design for linear systems with polytopic uncertainties abstract this paper investigates the problem of robust static output feedback h control for linear systems with polytopic uncertainties a new method is proposed for robust static output feedback h controller design the proposed design method is applicable for general uncertain systems without the need to impose any constraints on system matrices the corresponding design conditions are presented in the form of linear matrix inequalities lmis one of the advantages of the new method lies in its less conservatism the proposed design method is also applicable to both continuous time and discrete time systems the performance of the method is compared with other methods based on several examples

the bounded real lemma for internally positive systems and h infinity structured static state feedback we consider the bounded real lemma for internally positive linear time invariant systems we show that the h norm of such systems can be evaluated by checking the existence of a certain diagonal quadratic storage function taking advantage of this fact the problem of designing a structured static state feedback controller achieving internal stability contractiveness and internal positivity in closed loop becomes convex and tractable

np hardness of some linear control design problems we show that some basic linear control design problems are np hard implying that unless p np they cannot be solved by polynomial time algorithms the problems that we consider include simultaneous stabilization by output feedback stabilization by state or output feedback in the presence of bounds on the elements of the gain matrix and decentralized control these results are obtained by first showing that checking the existence of a stable matrix in an interval family of matrices is np hard

a perturbation method for optimizing matrix stability we present the first practical perturbation method for optimizing matrix stability using spectral abscissa minimization using perturbation theory for a matrix with simple eigenvalues and coupling this with linear programming we successively reduce the spectral abscissa of a matrix until it reaches a local minimum optimality conditions for a local minimizer of the spectral abscissa are provided and proved for both the affine matrix problem and the output feedback control problem experiments show that this novel perturbation method is efficient especially for a matrix with the majority of whose eigenvalues are already located in the left half of the complex plane moreover unlike most available methods the method does not require the introduction of lyapunov variables the method is illustrated for a small size matrix from an affine matrix problem and is then applied to large matrices actually arising from more sophisticated control problems used in the design of the boeing 767 jet and a nuclear powered turbo generator

robust disturbance attenuation with stability for linear systems with norm bounded nonlinear uncertainties in this paper the problem of robust stabilization and robust disturbance attenuation is investigated for systems with linear nominal parts and norm bounded nonlinear uncertainties on both states and control inputs it is shown that the type of nonlinear uncertainty sets considered in this paper has an equivalent representation by linear uncertainty sets based on this key result and some standard riccati inequality approaches for robust control of linear uncertain systems a constructive design procedure is developed

slicing skinning and grafting we prove that a bers slice is never algebraic meaning that its zariski closure in the character variety has strictly larger dimension a corollary is that skinning maps are never constant the proof uses grafting and the theory of complex projective structures

the grafting map of teichmuller space one of the underlying principles in the study of kleinian groups is that aspects of the complex projective geometry of quotients of by these groups reflect properties of the three dimensional hyperbolic geometry of the quotients ofh by these groups yet even though it has been over thirty five years since lipman bers exhibited a holomorphic embedding of the teichmuller space of riemann surfaces in terms of the projective geometry of a teichmuller space of quasi fuchsian manifolds no corresponding embedding in terms of the three dimensional hyperbolic geometry has been presented one of the goals of this paper is to give such an embedding this embedding is straightforward and has been expected for some time ta97 mc98 to each member of a bers slice of the space qf of quasi fuchsian 3manifolds we associate the bending measured lamination of the convex hull facing the fixed conformal end the geometric relationship between a boundary component of a convex hull and the projective surface at infinity for its end is given by a process known as grafting an operation on projective structures on surfaces that traces its roots back at least to klein kl33 p 230 50 with a modern history developed by many authors ma69 he75 fa83 st83 go87 gkm00 ta97 mc98 the main technical tool in our proof that bending measures give coordinates for bers slices and the second major goal of this paper is the completion of the proof of the grafting conjecture this conjecture states that for a fixed measured lamination the self map of teichmuller space induced by grafting a surface along is a homeomorphism of teichmuller space our contribution to this argument is a proof of the injectivity of the grafting map while the principal application of this result that we give is to geometric coordinates on the bers slice of qf one expects that the grafting homeomorphism might lead to other systems of geometric coordinates for other families of kleinian groups see 5 2 thus we feel that this result is of interest in its own right we now state our results and methods more precisely throughout s will denote a fixed differentiable surface which is closed orientable and of genus g 2 let tg be the corresponding teichmuller space of marked conformal structures on s and let pg denote the deformation space of complex projective structures on s see 2 for definitions

stabilizing static output feedback receding horizon controls for linear discrete time invariant systems in this paper a stabilizing static output feedback receding horizon control rhc is proposed for linear discrete time invariant systems an inequality condition on the terminal weighting matrices is presented under which the closed loop stability of static output feedback receding horizon controls is guaranteed it is shown that the stabilizing static output feedback receding horizon control problem can be represented as a non linear minimization problem based on linear matrix inequalities lmis an algorithm for solving the presented non linear minimization problem is proposed in addition this result is extended to an arbitrary reference tracking problem that is one of the main features of receding horizon control finally the efficiency of the proposed algorithm is illustrated by numerical examples

uniform stabilization of discrete time switched and markovian jump linear systems the uniform stability of discrete time switched linear systems possibly with a strongly connected switching path constraint and the existence of finite path dependent dynamic output feedback controllers uniformly stabilizing such a system are both shown to be characterized by the existence of a finite dimensional feasible system of linear matrix inequalities this characterization is based on the observation that a linear time varying system is uniformly stable only if there exists a finite path dependent quadratic lyapunov function the synthesis of a uniformly stabilizing controller is done without conservatism by solving any feasible system of linear matrix inequalities among an increasing family of systems of linear matrix inequalities the result carries over to the almost sure uniform stabilization of markovian jump linear systems

the monodromy groups of schwarzian equations on closed riemann surfaces let 1 r psl 2 be a homomorphism of the fundamental group of an oriented closed surface r of genus exceeding one we will establish the following theorem theorem necessary and sufficient for to be the monodromy representation associated with a complex projective stucture on r either unbranched or with a single branch point of order 2 is that 1 r be nonelementary a branch point is required if and only if the representation does not lift to sl 2

variational analysis of non lipschitz spectral functions we consider spectral functions f where f is any permutation invariant mapping from cn to r and is the eigenvalue map from the set of n n complex matrices to cn ordering the eigenvalues lexicographically for example if f is the function maximum real part then f is the spectral abscissa while if f is maximum modulus then f is the spectral radius both these spectral functions are continuous but they are neither convex nor lipschitz for our analysis we use the notion of subgradient extensively analyzed in variational analysis r t rockafellar and r j b wets springer 1998 we show that a necessary condition for y to be a subgradient of an eigenvalue function f at x is that y commutes with x we also give a number of other necessary conditions for y based on the schur form and the jordan form of x in the case of the spectral abscissa we refine these conditions and we precisely identify the case where subdifferential regularity holds we conclude by introducing the notion of a semistable program maximize a linear function on the set of square matrices subject to linear equality constraints together with the constraint that the real parts of the eigenvalues of the solution matrix are non positive semistable programming is a nonconvex generalization of semidefinite programming using our analysis we derive a necessary condition for a local maximizer of a semistable program and we give a generalization of the complementarity condition familiar from semidefinite programming

improved sample complexity estimates for statistical learning control of uncertain systems probabilistic methods and statistical learning theory have been shown to provide approximate solutions to difficult control problems unfortunately the number of samples required in order to guarantee stringent performance levels may be prohibitively large this paper introduces bootstrap learning methods and the concept of stopping times to drastically reduce the bound on the number of samples required to achieve a performance level we then apply these results to obtain more efficient algorithms which probabilistically guarantee stability and robustness levels when designing controllers for uncertain systems

system theory for system identification abstract prediction and control problems require for their solution mathematical models in the form of dynamic systems in system theory the approach to this problem is to investigate realization problems for system identification novel in this paper is the emphasis on the realization problem for observation based realizations and on the realization problem for control a major aspect of these realization problems is computation and complexity algebraic approaches to realization problems may lead to the distinction of subclasses of systems with required finiteness properties to decompositions and to abstractions for hierarchical systems

some open problems in matrix theory arising in linear systems and control control theory has long provided a rich source of motivation for developments in matrix theory accordingly we discuss some open problems in matrix theory arising from theoretical and practical issues in linear systems theory and feedback control the problems discussed include robust stability matrix exponent induced norms stabilizability and pole assignability and nonstandard matrix equations a substantial number of references are included to acquaint matrix theorists with problems and trends in this application area feedback control theory has long provided a rich source of motivation for developments in matrix theory the purpose of this paper is to discuss several open problems in matrix theory that arise from theoretical and practical issues in feedback control theory and the associated area of linear systems theory many of these problems are remarkably simple to state are of intense interest in control theory and applications and yet remain unsolved besides leading to the resolution of these problems it is hoped that this paper will help to stimulate increased interaction between matrix and control theorists accord

robust decentralized stabilization of a class of linear discrete time systems with non linear interactions this paper deals with robust stabilization of a class of linear discrete time systems under non linear perturbations via output feedback a bound on the non linear perturbations is maximized in the design it is shown that degree of freedoms by the introduction of instrumental variables employed in this paper lead to much flexibility in obtaining both a robust output feedback controller and a maximal allowable bound of the non linear perturbations an improved method involving linear matrix inequalities are suggested to solve the matrix inequalities characterizing a solution of the robust stabilization problem consequently the proposed method can yield a much less conservative result than that of earlier methods of major interest is an extension to a class of interconnected systems composed of linear subsystems with non linear interactions a robust decentralized controller is presented such that the closed loop systems are maximally tolerant to interconnected non linear couplings numerical examples i

simultaneous control of linear systems by state feedback in this paper a new method for finding a state feedback matrix in order to control simultaneously a collection of linear systems of the same size by using similarity operations is presented for stabilization of all the systems it is necessary that the eigenvalues of the closed loop systems lie inside a specified region in the left hand side of the complex plane this aim is achieved by solving linear and nonlinear parametric systems of equations using nonlinear programming the presented method is implemented in two examples and the results are verified in view of the norm of the state feedback matrix and stabilizability

distributed mpc of constrained linear systems with time varying terminal sets abstract this paper proposes a decoupling strategy for the distributed model predictive control dmpc for a network of dynamically coupled linear systems like most dmpc approaches the proposed approach has a terminal set and uses a lyapunov matrix for the terminal cost in the online optimization problem for each system unlike them the terminal set changes at every time step and the lyapunov matrix is not block diagonal these features result in a less conservative dmpc formulation the proposed method is easy to implement when the network is strongly connected or when a central collector is used otherwise the computations of the terminal set require the online solutions of a series of linear programming problems but can be speeded up significantly by preprocessing numerical examples showing these results are provided

a characterization of all the static stabilizing controllers for lti systems abstract in this article we give a complete characterization geared towards a parametrization of all the static feedbacks of a given lti system triplet in terms of the coefficients of some reduced order riccati equation with simultaneously stabilizing solutions and structural constraints on the coefficients

combining convex concave decompositions and linearization approaches for solving bmis with application to static output feedback a novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality bmi constraints the key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings at each iteration of the algorithm the concave part is linearized leading to a convex subproblem applications to various output feedback controller synthesis problems are presented in these applications the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality lmi constraints the performance of the algorithm has been benchmarked on the data from the compleib library

minimal interconnection topology in distributed control design in this paper we consider a distributed control design problem multiple agents or subsystems that are dynamically uncoupled need to be controlled to optimize a joint cost function an interconnection graph specifies the topology according to which the agents can access information about each others state we propose and partially analyze a new model for determining the influence of the topology of the interconnection graph on the performance achieved by the subsystems we consider the classical linear quadratic regulator lqr cost function and propose making one of the weight matrices to be topology dependent to capture the extra cost incurred when more communication between the agents is allowed we present results about optimal topologies for some models of the dependence of the weight matrix on the communication graph we also give some results about the existence of critical prices at which adding supplementary edges becomes detrimental to closed loop performance one conclusion of the work is that if the communication between the agents comes at a cost then adding communication edges may be harmful for the system performance

index information algorithm with local tuning for solving multidimensional global optimization problems with multiextremal constraints multidimensional optimization problems where the objective function and the constraints are multiextremal non differentiable lipschitz functions with unknown lipschitz constants and the feasible region is a finite collection of robust nonconvex subregions are considered both the objective function and the constraints may be partially defined to solve such problems an algorithm is proposed that uses peano space filling curves and the index scheme to reduce the original problem to a holder one dimensional one local tuning on the behaviour of the objective function and constraints is used during the work of the global optimization procedure in order to accelerate the search the method neither uses penalty coefficients nor additional variables convergence conditions are established numerical experiments confirm the good performance of the technique

a convex approach to robust stability for linear systems with uncertain scalar parameters in this paper robust stability for linear systems with several uncertain complex and or real scalar parameters is studied a countable family of conditions sufficient for robust stability is given in terms of solvability of some simple linear matrix inequalities lmis these conditions are of increasing precision and it is shown conversely that robust stability implies solvability of these lmis from a certain rank and beyond this result constitutes an extension of the characterization by solvability of lyapunov inequality of the asymptotic stability for usual linear systems it is based on the search of parameter dependent quadratic lyapunov functions polynomial of increasing degree in the parameters

discrete time positive periodic systems with state and control constraints the aim of this technical note is to provide an efficient control design technique for discrete time positive periodic systems in particular stability positivity and periodic invariance of such systems are studied moreover the concept of periodic invariance with respect to a collection of boxes is introduced and investigated with connection to stability it is shown how such concept can be used for deriving a stabilizing state feedback control that maintains the positivity of the closed loop system and respects states and control signals constraints in addition all the proposed results can be efficiently solved in terms of linear programming

on the complexity of detecting convexity over a box it has recently been shown that the problem of testing global convexity of polynomials of degree four is strongly np hard answering an open question of n z shor this result is minimal in the degree of the polynomial when global convexity is of concern in a number of applications however one is interested in testing convexity only over a compact region most commonly a box i e a hyper rectangle in this paper we show that this problem is also strongly np hard in fact for polynomials of degree as low as three this result is minimal in the degree of the polynomial and in some sense justifies why convexity detection in nonlinear optimization solvers is limited to quadratic functions or functions with special structure as a byproduct our proof shows that the problem of testing whether all matrices in an interval family are positive semidefinite is strongly np hard this problem which was previously shown to be weakly np hard by nemirovski is of independent interest in the theory of robust control

stability analysis and h controller synthesis of discrete time switched systems with time delay abstract this paper studies the problems of stability analysis and h controller synthesis of switched systems with time varying delay based on an input output approach the attention is focused on developing a new method to further reduce the conservatism of the existing results the system under consideration is transformed into an interconnection system and the scaled small gain condition for the interconnection systems is introduced based on the system transformation and the scaled small gain theorem an improved delay dependent stability criterion is proposed such that the interconnection system is asymptotically stable which is also proved to guarantee the asymptotic stability of the system based on the direct lyapunov method in another perspective the proposed stability condition is demonstrated to be less conservative than most existing results moreover an admissible controller which solves the problem of h controller synthesis is formulated into a convex optimization problem illustrative examples are provided to show the advantage and the effectiveness of the proposed method

ellipsoidal sets for resilient and robust static output feedback the implementation of a controller if not exact may lead to the so called fragility problem i e the loss of expected closed loop properties in the present note this difficult problem is dealt with considering robust static output feedback sof control for uncertain linear time invariant systems by analogy with robust analysis theory based on quadratic separation a new formulation for the sof design is shown to be a valuable way to tackle fragility issues indeed the use of a quadratic separator for design purpose allows to define a whole resilient nonfragile set of sof control laws results are formulated as matrix inequalities one of which is nonlinear a numerical algorithm based on nonconvex optimization is provided ant its running is illustrated on classical examples from literature

on the combinatorial and algebraic complexity of quantifier elimination in this paper a new algorithm for performing quantifier elimination from first order formulas over real closed fields in given this algorithm improves the complexity of the asymptotically fastest algorithm for this problem known to this data a new feature of this algorithm is that the role of the algebraic part the dependence on the degrees of the imput polynomials and the combinatorial part the dependence on the number of polynomials are sparated another new feature is that the degrees of the polynomials in the equivalent quantifier free formula that is output are independent of the number of input polynomials as special cases of this algorithm new and improved algorithms for deciding a sentence in the first order theory over real closed fields and also for solving the existential problem in the first order theory over real closed fields are obtained

a randomized approximation algorithm for the minimal norm static output feedback problem a new randomized algorithm is suggested for extracting static output stabilizing feedbacks with approximately minimal norm for lti systems the algorithm has two similar stages where in the first one the feasibility problem is solved and in the second one the optimization problem is solved the formulation is unified for the feasibility and for the optimization problems as well as for continuous time or discrete time systems the method is demonstrated by applying it to the hard conjectured to be np hard problem of the minimal gain static output stabilizing feedback and to the hard conjectured to be np hard problem of regional pole placement via static output feedback in non convex or unconnected regions a proof of convergence in probability that captures the two rounds of the algorithm is given and complexity analysis is provided under some mild assumptions

randomized methods for design of uncertain systems in this paper we study randomized methods for feedback design of uncertain systems the first contribution is to derive the sample complexity of various constrained control problems in particular we show the key role played by the binomial distribution and related tail inequalities and compute the sample complexity this contribution significantly improves the existing results by reducing the number of required samples in the randomized algorithm these results are then applied to the analysis of worst case performance and design with robust optimization the second contribution of the paper is to introduce a general class of sequential algorithms denoted as sequential probabilistic validation spv in these sequential algorithms at each iteration a candidate solution is probabilistically validated and corrected if necessary to meet the required specifications the results we derive provide the sample complexity which guarantees that the solutions obtained with spv algorithms meet some pre specified probabilistic accuracy and confidence the performance of these algorithms is illustrated and compared with other existing methods using a numerical example dealing with robust system identification

a new exclusion test for finding the global minimum exclusion algorithms have been used recently to find all solutions of a system of nonlinear equations or to find the global minimum of a function over a compact domain these algorithms are based on a minimization condition that can be applied to each cell in the domain in this paper we consider lipschitz functions of order a and give a new minimization condition for the exclusion algorithm furthermore convergence and complexity results are presented for such algorithm

on a conservative concept for output static stabilizability analysis consequences and related problems this communication is concerned with the problem of stabilization via output static feedback of linear time invariant finite dimensional systems a new output static stabilization concept is introduced output static stabilization in the relaxed sense this conservative stabilization concept is the result of imposing an additional condition to a set of necessary and sufficient conditions for output static stabilization this paper is devoted to exhaustively study the introduced new stabilization concept i it is shown that for a particular class of plants the stabilization problem in the above sense can be cast as a convex programming problem ii a full characterization of the class of plants that are stabilizable in the above new sense is presented some of the important consequences of that study are as follows 1 the identification of a class of plants stabilizable via output static feedback for which stabilizing feedback matrices can be almost expressed in analytic closed form 2 it is

holonomy limits of complex projective structures abstract we study the limits of holonomy representations of complex projective structures on a compact riemann surface in the morgan shalen compactification of the character variety we show that the dual r trees of the quadratic differentials associated to a divergent sequence of projective structures determine the morgan shalen limit points up to a natural folding operation for quadratic differentials with simple zeros no folding is possible and the limit of holonomy representations is isometric to the dual tree we also derive an estimate for the growth rate of the holonomy map in terms of a norm on the space of quadratic differentials

the schwarzian derivative and measured laminations on riemann surfaces a holomorphic quadratic differential on a hyperbolic rie mann surface has an associated measured foliation which can be straight ened to yield a measured geodesic lamination on the other hand a quadratic differential can be considered as the schwarzian derivative of a 1 structure to which one can naturally associate another measured geodesic lamination using grafting we compare these two relationships between quadratic differentials and measured geodesic laminations each of which yields a homeomor phism ml s q x for each conformal structure x on a compact surface s we show that these maps are nearly the same differing by a multiplicative factor of 2 and an error term of lower order than the maps themselves which we bound explicitly as an application we show that the schwarzian derivative of a 1 structure with fuchsian holonomy is close to a 2 integral jenkins strebel differential we also study compactifications of the space of 1 structures using the schwarzian derivative and grafting coordinates we show that the natural map between these extends to the boundary of each fiber over teichmuller space and we describe this extension

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

implementation of fir control for h output feedback stabilisation of linear systems in this article finite impulse response fir control is addressed for h output feedback stabilisation of linear systems the problem we deal with is the construction of an output feedback controller with a certain fir structure such that the resulting closed loop system is asymptotically stable and a prescribed h norm bound constraint is guaranteed some solvability conditions are suggested in this article sufficient conditions are derived to obtain a suboptimal solution of the h fir control problem via convex optimisation also an equivalent condition for the existence of h fir control is presented in the set of linear matrix inequalities lmis and a reciprocal matrices equality constraint an effective computational algorithm involving lmis is suggested to solve a concave minimisation problem characterising a local optimal solution of the h fir control problem numerical examples demonstrate the validity of the proposed h fir control and the numerical efficiency of the proposed algorith

an existence result for polynomial solutions of parameter dependent lmis we show in this paper that any system of linear matrix inequalities depending continuously upon scalar parameters and solvable for any value of the latter in a fixed compact set admits a branch of solutions polynomial with respect to the parameters this result is useful for studying e g parametric robustness or gain scheduling issues

guaranteed properties of gain scheduled control for linear parameter varying plants abstract gain scheduling has proven to be a successful design methodology in many engineering applications however in the absence of a sound theoretical analysis these designs come with no guarantees on the robustness performance or even nominal stability of the overall gain scheduled design this paper presents such an analysis for one type of gain scheduled system namely a linear parameter varying plant scheduling on its exogenous parameters conditions are given which guarantee that the stability robustness and performance properties of the fixed operating point designs carry over to the global gain scheduled design these conditions confirm and formalize popular notions regarding gain scheduled design such as the scheduling variable should vary slowly

twisted harmonic maps and the self duality equations si m est une surface de riemann compacte on utilise des resultats de la theorie des applications harmoniques pour trouver une solution aux equations d auto dualite associees a une representation irreductible p 1 m psl 2 c