achievable performance limitations for siso plants with pole location constraints in this paper performance limitations in the linear control of general linear discrete time scalar systems are considered the performance is measured with the 2 norm of an error function which at the same time ensures that the closed loop poles lie in a prescribed region the deleterious effect of this constraint on a classical performance measurement is also quantified in such a way that the interplay between the size of the desired region and structural features of the plant is revealed

direct method for yau filtering system with nonlinear observations for all known finite dimensional filters one always assumes that the observation terms be degree one polynomials however in practice the observation terms may be nonlinear e g tracking proble

on a necessary and sufficient condition for finite dimensionality of estimation ever since the technique of the kalman bucy filter was popularized there has been an intense interest in finding new classes of finite dimensional recursive filters in the late seventies the concept of the estimation algebra of a filtering system was introduced it has proven to be an invaluable tool in the study of nonlinear filtering problems in this paper a simple algebraic necessary and sufficient condition is established for an estimation algebra of a special class of filtering systems to be finite dimensional also presented is a rigorous proof of the wei norman program which allows one to construct finite dimensional recursive filters from finite dimensional estimation algebras

robust stabilization for rectangular descriptor fractional order interval systems with order 0 α 1 abstract this paper considers the normalization and stabilization of rectangular descriptor fractional order interval systems with fractional order 0

an improved path following method for mixed h _ 2 h _ infty controller design among the few methods available to solve bilinear matrix inequalities bmis occurring in control design the path following method published some years ago appears to be one of the best ones as far as linearization methods are concerned however few details are given in the literature about its implementation and limits in this technical note this method is applied to the design of mixed h 2 h infin controllers with full details of the algorithm and some improvements over the one which has been published a few years ago the results obtained with the numerical example given in that same publication as well as with some other examples are compared with those given by other methods including a direct bmi solving program

h output feedback control design for uncertain fuzzy singularly perturbed systems an lmi approach this paper examines the problem of designing a robust h output feedback controller for a class of singularly perturbed systems described by a takagi sugeno fuzzy model based on a linear matrix inequality lmi approach lmi based sufficient conditions for the uncertain singularly perturbed nonlinear systems to have an h performance are derived to eliminate the ill conditioning caused by the interaction of slow and fast dynamic modes solutions to the problem are presented in terms of lmis which are independent of the singular perturbation the proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems a numerical example is provided to illustrate the design developed in this paper

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

unknown input observers for switched nonlinear discrete time descriptor systems in this paper a linear matrix inequality technique for the state estimation of discrete time nonlinear switched descriptor systems is developed the considered systems are composed of linear and nonlinear parts an observer giving a perfect unknown input decoupled state estimation is proposed sufficient conditions of global convergence of observers are proposed numerical examples are given to illustrate this method

fault estimation for a class of nonlinear systems based on intermediate estimator this technical note investigates the problem of fault estimation for a class of nonlinear systems with lipschitzian nonlinearities in most of the existing fault estimation approaches the observer matching condition should be satisfied however this condition is hard to meet for many systems to overcome this restriction a new fault estimation method is proposed where an intermediate variable is introduced and a specially designed intermediate estimator is proposed to estimate the state and the faults simultaneously by exploiting the properties of fault distribution matrix it is proved that the states of the error system are uniformly ultimately bounded simulation examples verify the effectiveness of the proposed method

explicit solution of dmz equation in nonlinear filtering via solution of odes in this note we develop a real time and accurate solution for nonlinear filtering problems based on the gaussian distribution specifically we present an explicit solution of the duncan mortensen zakai dmz equation of the yau filtering system which includes the linear filtering system and exact filtering system the solution is given in terms of a solution of a system of ordinary differential equations in particular our method can be implemented in hardware the complexity of our algorithms is the same as those of kalman bucy filters in the case of linear filtering systems

potential theory for regular and mach reflection of a shock at a wedge if a plane shock hits a wedge a self similar pattern of reflected shocks travels outward as the shock moves forward in time the nature of the pattern is explored for weak incident shocks strength b and small wedge angles 2 w through potential theory a number of different scalings some study of mixed equations and matching asymptotics for the different scalings the self similar equations are of mixed type a linearization gives a linear mixed flow valid away from a sonic curve near the sonic curve a shock solution is constructed in another scaling except near the zone of interaction between the incident shock and the wall where a special scaling is used the parameter c1 2w 1 b ranges from 0 to here is the polytropic constant and c1 is the sound speed behind the incident shock for 2 regular reflection weak or strong can occur and the whole pattern is reconstructed to lowest order in shock strength for 1 2 mach reflection occurs and the flow behind the reflection is subsonic and can be constructed in principle with an open elliptic problem and matched the case 0 can be solved for 1 2 2 or even larger the flow behind a mach reflection may be transonic and further investigation must be made to determine what happens the basic pattern of reflection is an almost semi circular shock issuing for regular reflection from the reflection point on the wedge and for mach reflection matched with a local interaction flow assuming their nature choosing the least entropy generation the weak regular reflection will occur for sufficiently large von neumann paradox an accumulation point of vorticity occurs on the wedge above the leading point 1994 john wiley sons inc

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

pole assignment for uncertain systems in a specified disk by state feedback this paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system the uncertainty being norm bounded for this the quadratic d stabilizability concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived this condition expressed as a parameter dependent discrete riccati equation enables one to design the control gain matrix by solving iteratively a discrete riccati equation

pole assignment of linear uncertain systems in a sector via a lyapunov type approach the problem of designing robust control laws in performance and in stability for uncertain linear systems is considered performances are taken into account using root clustering of the closed loop dynamic matrix in a sector of the complex plane a synthesis procedure based on a sufficient condition for quadratic stabilization and root clustering such as stabilizability is given using an auxiliary convex problem the results are illustrated by a significant example from the literature

radon measure solutions for steady compressible euler equations of hypersonic limit conical flows and newton s sine squared law abstract we formulate a mathematical problem on hypersonic limit of three dimensional steady uniform non isentropic compressible euler flows of polytropic gases passing a straight cone with arbitrary cross section and attacking angle which is to study radon measure solutions of a nonlinear hyperbolic system of conservation laws on the unit 2 sphere the construction of a measure solution with density containing dirac measures supported on the surface of the cone is reduced to find a regular periodic solution of highly nonlinear and singular ordinary differential equations ode for a circular cone with zero attacking angle we then proved the newton s sine squared law by obtaining such a measure solution this provides a mathematical foundation for the newton s theory of pressure distribution on three dimensional bodies in hypersonic flows

controller design with regional pole constraints a design procedure is developed that combines linear quadratic optimal control with regional pole placement specifically a static and dynamic output feedback control problem is addressed in which the poles of the closed loop system are constrained to lie in specified regions of the complex plane these regional pole constraints are embedded within the optimization process by replacing the covariance lyapunov equation by a modified lyapunov equation whose solution in certain cases leads to an upper bound on the quadratic cost functional the results include necessary and sufficient conditions for characterizing static output feedback controllers with bounded performance and regional pole constraints sufficient conditions are also presented for the fixed order i e full and reduced order dynamic output feedback problem with regional pole constraints circular elliptical vertical strip parabolic and section regions are considered

structure and classification theorems of finite dimensional exact estimation algebras estimation algebra turns out to be a crucial concept in the investigation of finite dimensional nonlinear filters in an earlier paper by the authors a necessary and sufficient algebraic condition was derived for an exact estimation algebra to be finite dimensional in this paper the investigation of the properties of finite dimensional exact estimation algebras is continued and some structure and partial classification theorems for such algebras are proved

a neural network for linear matrix inequality problems gradient type hopfield networks have been widely used in optimization problems solving the paper presents a novel application by developing a matrix oriented gradient approach to solve a class of linear matrix inequalities lmis which are commonly encountered in the robust control system analysis and design the solution process is parallel and distributed in neural computation the proposed networks are proven to be stable in the large representative lmis such as generalized lyapunov matrix inequalities simultaneous lyapunov matrix inequalities and algebraic riccati matrix inequalities are considered several examples are provided to demonstrate the proposed results to verify the proposed control scheme in real time applications a high speed digital signal processor is used to emulate the neural net based control scheme

applying discrete time proportional integral observers for state and disturbance estimations in this note we apply the proportional integral observer to simultaneously estimate system states and unknown disturbances for discrete time nonminimum phase systems conditions for providing the existence of such observer are given when the disturbances do not vary too much between two consecutive sampling instances the proposed method can render the estimation errors of system states and disturbances to be constrained in a small bounded region simulation results support the theoretical developments

functional unknown input reconstruction of descriptor systems the problem of finding conditions for the reconstruction of a linear combination of the vector of unknown inputs is tackled appropriate definitions are given in order to address formally the analysis thus necessary and sufficient conditions are obtained for two cases when the reconstruction may be achieved in finite time and when it is possible to do it asymptotically the results are applied for the fault detection with the respective deduction of analogous conditions

linear quadratic control with stability degree constraint abstract the problem of static state feedback linear quadratic lq optimal control subject to a prescribed degree of stability for the closed loop system is considered in this paper a necessary optimality condition is given via the lagrange multiplier method a globally convergent algorithm is provided to solve the optimization problem it is shown that the algorithm recovers the standard lq feedback gain provided the desired stability degree is small enough to be within the range by the standard lq design as for other cases the optimum occurs on the boundary of the region a numerical example shows that the proposed algorithm provides a better design compared to the existing methods

a nonlinear luenberger like observer for nonlinear singular systems this paper investigates observer design problem for a large class of nonlinear singular systems with multiple outputs we firstly regularize the singular system by injecting the derivative of outputs into the system then differential geometric method is applied to transform the regularized system into a simple normal form for which a luenberger like observer is proposed

a one phase hyperbolic stefan problem in multi dimensional space the hyperbolic heat transfer model is obtained by replacing the classical fourier s law with the relaxation relation q t q k t the sufficient and necessary conditions are derived for the local existence and uniqueness of classical solutions for multi d stefan problem of hyperbolic heat transfer model where phase change is accompanied with delay of latent heat storage

the existence and stability of conic shock waves we study the existence of the nonsymmetrical conic shock wave produced by a supersonic flow past a distorted conic projectile for the weak conic shock wave we establish the existence and its linear stability using the mathematical model of an isentropic irrotational flow

an improved lmi condition for robust d stability of uncertain polytopic systems a sufficient condition for robust d stability of linear systems with polytope type uncertainties is proposed the result is based on a linear parameter dependent lyapunov function obtained from the feasibility test of a set of linear matrix inequalities lmis defined at the vertices of the polytope this improved lmi condition encompasses previous results based on additional inequalities as well as results based on extra variables

bounded amplitude performance of switched lpv systems with applications to hybrid systems this paper discusses recent results on multiple linear agent control for systems satisfying a bounded amplitude performance constraint the plant is assumed to be a linear parameter varying lpv system scheduled along a nominal parameter trajectory in this respect the control problem represents a plant operating between a prespecified set of operating conditions linear controllers are designed at setpoints along this scheduling trajectory to satisfy bounded amplitude performance constraints this paper discusses an approach to analyze the switched system behavior under practical assumptions on the structure of the switching rule the approach combines the scheduling parameter with lpv system properties to derive bounds on the switching behavior of the system these estimates are then used to construct a logical model of the switched system behavior in the form of a timed automaton in this respect this paper presents a way of extracting logical models of continuous time system behavior

on α and d negative imaginary systems this paper is concerned with and d negative imaginary systems the definition of negative imaginary transfer functions is firstly introduced then the relationship between negative imaginary and negative imaginary transfer functions is studied by means of the generalised inverse an negative imaginary lemma is proposed to test the negative imaginary property of transfer functions also a necessary and sufficient condition is provided for the stability of interconnection of negative imaginary systems a state feedback controller design condition is established such that the resulting system is negative imaginary moreover the concept of negative imaginary transfer functions is extended to that of d negative imaginary transfer functions finally the developed results are illustrated by numerical examples

impulsive modes and causality in singular systems the concepts of impulsive modes and causality in singular systems are considered their properties relations and applications are studied matrix rank criteria are presented thus all controllabilities and observabilities and related concepts have matrix rank criteria based on the original system coefficient matrices

a new scheme of fault detection for linear discrete time varying systems in this note a new scheme of fault detection fd is proposed for linear discrete time varying ldtv systems subject to l 2 norm bounded unknown inputs the basic idea is to find an optimal estimation of the l 2 norm of the unknown inputs including the unknown initial state variables this leads to a natural design of the fd system with the l 2 norm boundedness of the unknown inputs as a threshold and the l 2 norm of the unknown input estimate as the evaluation function to avoid heavy computational burden projection technique in krein space is applied which allows a recursive computation of the evaluation function it is shown that the achieved fd system satisfies both the worst case and best case sensitivity robustness ratio criteria and further applications to observer based fd lead to an alternative design of h infty h infty and or h h infty fault detection filter

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

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

nonfragile h state estimation for recurrent neural networks with time varying delays on proportional integral observer design in this article a novel proportional integral observer pio design approach is proposed for the nonfragile h state estimation problem for a class of discrete time recurrent neural networks with time varying delays the developed pio is equipped with more design freedom leading to better steady state accuracy compared with the conventional luenberger observer the phenomena of randomly occurring gain variations which are characterized by the bernoulli distributed random variables with certain probabilities are taken into consideration in the implementation of the addressed pio attention is focused on the design of a nonfragile pio such that the error dynamics of the state estimation is exponentially stable in a mean square sense and the prescribed h performance index is also achieved sufficient conditions for the existence of the desired pio are established by virtue of the lyapunov krasovskii functional approach and the matrix inequality technique finally a simulation example is provided to demonstrate the effectiveness of the proposed pio design scheme

interval stability and stabilization of linear stochastic systems this technical note applies the spectrum technique to deal with the interval stability and stabilization of linear stochastic time invariant systems first the notion of beta alpha stability of stochastic systems is defined and some relationships among the beta alpha stability the decay rate of system state response and the second order moment lyapunov exponent are revealed we then address the beta alpha stabilization problem and give a sufficient condition via a linear matrix inequality approach

disturbance attenuation using proportional integral observers in this paper we first propose a proportional integral observer design for single output uncertain linear systems which permit us to attenuate either measurement noise or modelling errors we show that when only sensor noise is present in the system an integral observer alone suffices to achieve good convergence and filtering properties on the other hand when modelling errors and sensor noise are present we show that for some classes of linear systems the proportional integral observer allows us to decouple completely the modelling uncertainties while keeping satisfactory convergence properties a comparison of the classical proportional observer to the proposed observers are given via academic simulation examples we next extend the design to the class of single output uniformly observable non linear systems we show through a practical simulation example dealing with a flexible joint robot that the non linear proportional integral has very satisfactory disturbance attenuating properties

robust matrix root clustering analysis through extended kyp lemma this paper is dedicated to robust matrix eigenvalue clustering in a subregion mathcal d of the complex plane a norm bounded uncertainty is considered cd is any intersection and or union of half planes discs and outsides of discs this work aims at computing the associated complex cd stability radius this challenge was already tackled in a recent paper but the technique therein may fail or lead to conservative results when the subregions overlap the present paper proposes to circumvent those limits thanks to an extended version of the kalman yakubovich popov kyp lemma which is deduced from the so called generalized s procedure

unknown input proportional multiple integral observer design for linear descriptor systems application to state and fault estimation in this note the problem of observer design for linear descriptor systems with faults and unknown inputs is considered first it is considered that the fault vector function f is s times piecewise continuously differentiable if the s th time derivative of f is null then s integral actions are included into a luenberger observer which is designed such that it estimates simultaneously the state the fault and its finite derivatives face to unknown inputs second when the fault is not time piecewise continuously differentiable but bounded like actuator noise or s th time derivative of fault is not null but bounded too a high gain observer is derived to attenuate the fault impact in estimation errors the considered faults may be unbounded may not be determinist and faults and unknown inputs may affect the state dynamic and plant outputs sufficient conditions for the existence of such observer are given results are illustrated with a differential algebraic power system

disturbance decoupled observer design a unified viewpoint this paper is concerned with the observer design for linear systems with unknown inputs an equivalent system which is free of unknown inputs is derived for the purpose of the observer design based on the equivalent system description one can design an observer full order reduced order minimal order or functional for linear systems with unknown inputs using well known techniques it is shown that the equivalent system exists as long as there exists a disturbance decoupled observer two sets of the known existence conditions of disturbance decoupled observers are proved to be equivalent

robust control with pole shifting via performance index modification robust controllers that ensure closed loop eigenvalue placement are designed for linear systems with parametric uncertainties by using an appropriate state weighting matrix choice and a relative stability degree an lmi based algorithm is proposed to provide guaranteed cost controllers that ensure i the closed loop nominal eigenvalues shifting by a pre specified amount ii a prescribed degree of stability for all system uncertainties of a given class a certain level of closed loop performance is also ensured by minimizing the associated guaranteed cost

design of proportional integral observer for unknown input descriptor systems this note presents simple methods to design full and reduced order proportional integral observer for unknown inputs ui descriptor systems sufficient conditions for the existence of the observer are given and proven the observer is solvable by any pole placement algorithm it achieves a posteriori robustness state and ui estimation versus to time varying parameters and bounded nonlinear ui an illustrative example is included

double shock fronts for hyperbolic systems of conservation laws in multidimensional space the existence of a unique double shock front for hyperbolic systems of conservation laws in several space variables is established extending an earlier result of metivier an example of a double shock wave arising from physical applications is given the purpose of this paper is to show the existence of a unique double shock front for hyperbolic systems of conservation laws in several space variables describing physical phenomena unlike the one dimensional case it is only recently that majda 7 using microlocal analysis established the existence of a unique stable shock front for hyperbolic systems for double shock fronts the only known result is due to metivier 8 9 where 2 x 2 systems of conservation laws in two dimensional space are considered in this paper the existence of a double shock front for hyperbolic systems of conservation laws in several space variables is established when restricted to 2 x 2 systems in two dimensional space our result is similar to that of metivier but our approach is somewhat different and perhaps simpler the notation and the basic assumptions are given in 1 the free boundary problem is transformed in 2 into one with fixed boundaries the linearized problem is considered in 3 and the nonlinear one is studied in 4 using the iteration method finally in 5 an application to isentropic gas in two dimensional space is given let g be an open subset of rn with a smooth boundary ag and let x xi xn be the generic point of g for each n tuple a a n of nonnegative integers we write n n d f dj dj 0 x la zaj j l j l received by the editors january 17 1987 and in revised form april 15 1988 1980 mathematics subject classification 1985 revision primary 35l65 35l50 secondary 76l05 work supported by nserc canada 1989 american mathematical society 0002 9947 89 1 00 25 per page

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

disturbance decoupled observer design for descriptor systems in this paper we study the observer design problem for descriptor systems with partly unknown inputs we give necessary and sufficient conditions for the existence of a solution to the disturbance decoupled estimation problem with or without stable error spectrum requiring at the same time that the resulting combined system is regular and of index at most one all results are proved based on a condensed form that can be computed using orthogonal matrix transformations i e transformations that can be implemented in a numerically stable way

reduced order observer design for descriptor systems with unknown inputs a new method for the design of reduced order observers for descriptor systems with unknown inputs is presented the approach is based on the generalized constrained sylvester equation sufficient conditions for the existence of the observer are given

luenberger like interval observer design for discrete time descriptor linear system abstract in this paper the problem of luenberger like interval observer design for discrete time descriptor linear system is investigated in the first place two ways in which the original descriptor system is transformed into general systems are given and the detectability of the equivalent general systems is discussed in detail a new equivalent general system construction is developed and we prove that the detectability can be kept under this new equivalent transformation after this based on the new equivalent general system a luenberger like interval observer is proposed finally two simulation examples are given to demonstrate the correctness and the effectiveness of the proposed interval observer

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

finite dimensional filters with nonlinear drift x explicit solution of dmz equation in this note we consider the explicit solution of duncan mortensen zakai dmz equation for the finite dimensional filtering system we show that yau s 1990 1994 filtering system spl delta f sub j spl delta x sub i spl delta f sub i spl delta x sub i c sub ij constant for all i j can be solved explicitly with an arbitrary initial condition by solving a system of ordinary differential equations and a kolmogorov type equation let n be the dimension of state space we show that we need only n sufficient statistics in order to solve the dmz equation

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

brief positive polynomial matrices and improved lmi robustness conditions recently several new lmi conditions for stability of linear systems have been proposed introducing additional slack variables to reduce the gap between conservative convex quadratic stability conditions and intractable non convex robust stability conditions in this paper we show that these improved lmi conditions can be derived with the help of some basic results on positive polynomial matrices the approach allows us to derive in a unifying way results in the state space and polynomial frameworks applications to robust stability analysis and robust stabilization of systems with multi linear parametric uncertainty are fully described

output feedback decentralized control of large scale systems using weighted sensitivity functions minimization this paper considers the problem of achieving stability and desired dynamical transient behavior for linear large scale systems by decentralized control it can be done by making the effects of the interconnections between the subsystems arbitrarily small sufficient conditions for stability and diagonal dominance of the closed loop system are introduced these conditions are in terms of decentralized subsystems and directly make a constructive h control design possible a mixed h pole region placement is suggested such that by assigning the closed loop eigenvalues of the isolated subsystems appropriately the eigenvalues of the overall closed loop system are assigned in desirable range the designs are illustrated by an example

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

global supersonic conic shock wave for the steady supersonic flow past a cone polytropic gas abstract in this paper we establish the global existence and stability of a steady conic shock wave for the symmetrically perturbed supersonic flow past an infinitely long conic body as long as the vertex angle is less than a critical value the flow is assumed to be polytropic isentropic and described by a steady potential equation based on the delicate asymptotic expansion of the background solution one can verify that the boundary conditions on the shock and the conic surface satisfy the dissipative property from this property by use of the reflected characteristics method and the special form of the shock equation we show that the conic shock attached at the vertex of the cone exists globally in the whole space when the speed of the supersonic coming flow is appropriately large on the other hand we remove the smallness restriction on the sharp vertex angle in order to establish the global existence of a shock or a global weak solution moreover our proof approach is different from that in shuxing chen zhouping xin huicheng yin global shock wave for the supersonic flow past a perturbed cone comm math phys 228 2002 47 84 and zhouping xin huicheng yin global multidimensional shock wave for the steady supersonic flow past a three dimensional curved cone anal appl 4 2 2006 101 132

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

observability and detectability of singular linear systems with unknown inputs in this paper the strong observability and strong detectability of a general class of singular linear systems with unknown inputs are tackled the case when the matrix pencil is non regular is comprised i e more than one solution for the differential equation is allowed it is shown that under suitable assumptions the original problem can be studied by means of a regular non singular linear system with unknown inputs and algebraic constraints thus it is shown that for purposes of analysis the algebraic equations can be included as part of an extended system output based on this analysis we obtain necessary and sufficient conditions guaranteeing the observability or detectability of the system in terms of the zeros of the system matrix corresponding algebraic conditions are given in order to test the observability and detectability a formula is provided that expresses the state as high order derivative of a function of the output which allows for the reconstruction of the actual state vector it is shown that the unknown inputs may be reconstructed also

brief paper state and input observability for structured linear systems a graph theoretic approach this paper deals with the state and input observability analysis for structured linear systems with unknown inputs the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure using a particular decomposition of the systems into two subsystems we express in simple graphic terms necessary and sufficient conditions for the generic state and input observability these conditions are easy to check because they are based on comparison of integers and on finding particular subgraphs in a digraph therefore our approach is suited to study large scale systems

robust fuzzy observer based fuzzy control design for nonlinear systems with persistent bounded disturbances a novel decoupled approach unlike the l 2 gain h control case the l gain control problem is dealing with persistent bounded disturbances this study introduces l gain fuzzy observer based fuzzy control design where the premise variables depend on the state variables estimated by a fuzzy observer for nonlinear systems via t s fuzzy models the fuzzy control design for this case is more flexible but much more complex than that for the case where the premise variables do not depend on the state variables estimated by a fuzzy observer a novel decoupled method is proposed in this study to transform the non lmi conditions into some lmi forms by the proposed decoupled method and the genetic algorithm the l gain fuzzy observer based fuzzy control problem can be easily solved by an lmi based method

solution of filtering problem with nonlinear observations for all known finite dimensional filters one always needs the conditon that the observation terms are degree one polynomial on the other hand in many practical examples e g tracking problem the observation terms may be nonlinear our new method in this paper can treat filtering problems with nonlinear observation terms in the first time which includes kalman bucy filter as a special case

sliding mode design via quadratic performance optimization with pole clustering constraint we consider a novel method for designing the sliding mode that minimizes the quadratic performance while keeping a pole clustering constraint our approach is based on the manipulations of linear matrix inequalities lmis imposed by the design objectives for this purpose we newly propose lmi conditions for the quadratic performance optimization and the pole clustering problem respectively in a full order state then they are combined in the lmi framework that is typically devised for the sliding mode design in the convex form an effort is made to reduce the generic conservatism by allowing different lyapunov matrices in addition a class of polytope uncertain systems is addressed to illustrate the advantages of the proposed method

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

pole assignment in a specified disk the problem of assigning all poles of a closed loop system in a specified disk by state feedback is considered for both continuous and discrete systems a state feedback control law is determined by using a discrete riccati equation this kind of pole assignment problem is named d pole assignment and its relation to the optimal control problem and its robustness properties are discussed the gain and phase margins for all closed loop poles to stay inside the specified disk d are determined for the proposed control

unknown input functional observability of descriptor systems with neutral and distributed delay effects in this paper a general class of linear systems with time delays is considered which includes linear classical systems linear systems with commensurate delays neutral systems and singular systems with delays after given a formal definition of functional backward observability bo an easily testable condition is found the fulfillment of the obtained condition allows for the reconstruction of the trajectories of the system under consideration using the actual and past values of the system output and some of its derivatives the methodology we follow consists in an iterative algorithm based upon the classical silverman algorithm used for inversion of linear systems by using basic module theory we manage to prove that the proposed algorithm is convergent a direct application of studying functional observability is that a condition can be derived for systems with distributed delays also we do this as a case of study the obtained results are illustrated by two examples one is merely academic but illustrates clearly the kind of systems which the proposed methodology works for and the other is a practical system with distributed delays

a general theory for matrix root clustering in subregions of the complex plane we consider the general problem of root clustering of a matrix in the complex plane let a in c n times n and s subset c find the largest class of s and an algebraic criterion which is necessary and sufficient for lambda i a in s i 1 2 n we introduce two types of regions which constitute the largest class of s known to date the criterion is presented both for open regions and closed ones the results are used to define a design methodology for control systems moreover all classical results are shown to be special cases of the present theory

h consensus control with spectrum constraints for stochastic multi agent systems subject to x u v dependent noises abstract this paper is concerned with the problem of h consensus control with spectrum constraints for continuous time multi agent systems mass with x u v dependent noises by means of the spectrum technique the definition of stability is introduced and the relationship between the convergence rate of state responses and the stability is discussed for the closed loop system the aim of the addressed problem is to design a static output feedback controller such that the closed loop system is stable and the prescribed h performance requirement is satisfied in virtue of the stochastic analysis method and kronecker product sufficient conditions are obtained for the existence of h consensus controller two examples are provided to illustrate the availability of the proposed techniques

brief an lmi condition for robust stability of polynomial matrix polytopes a sufficient lmi condition is proposed for checking robust stability of a polytope of polynomial matrices it hinges upon two recent results a new approach to polynomial matrix stability analysis and a new robust stability condition for convex polytopic uncertainty numerical experiments illustrate that the condition narrows significantly the unavoidable gap between conservative tractable quadratic stability results and exact np hard robust stability results

real time solution of the nonlinear filtering problem without memory ii it is well known that the nonlinear filtering problem has important applications in both military and commercial industries the central problem of nonlinear filtering is to solve the duncan mortensen zakai dmz equation in real time and in a memoryless manner the purpose of this paper is to show that under very mild conditions which essentially say that the growth of the observation h is greater than the growth of the drift f the dmz equation admits a unique nonnegative weak solution u which can be approximated by a solution u r of the dmz equation on the ball b r with u r pat b r 0 the error of this approximation is bounded by a function of r which tends to zero as r goes to infinity the solution u r can in turn be approximated efficiently by an algorithm depending only on solving the observation independent kolmogorov equation on b r in theory our algorithm can solve basically all engineering problems in real time specifically we show that the solution obtained from ou

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

robust observer design for unknown inputs takagi sugeno models this paper deals with the observer design for takagi sugeno t s fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system sufficient conditions to design an unknown input t s observer are given in linear matrix inequality lmi terms both continuous time and discrete time cases are studied relaxations are introduced by using intermediate variables extension to the case of unmeasured decision variables is also given a numerical example is given to illustrate the effectiveness of the given results

a less conservative lmi condition for robust cal d stability of polynomial matrix polytopes a projection approach this technical note investigates the problem of checking robust d stability of a polytope of polynomial matrices finsler s projection lemma is taken to derive a new sufficient condition in terms of a linear matrix inequality lmi feasibility problem the basic idea behind this condition is to lift the existing stability condition into the one of larger space by means of finsler s lemma and based on it to introduce additional decision variables examples are given to show that the proposed condition can yield less conservative results than the previous one

interval observer for a class of uncertain nonlinear singular systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantee the existence of a luenberger like observer for the general system

fundamental connections among the stability conditions using higher order time derivatives of lyapunov functions for the case of linear time invariant systems abstract it has already been recognized that looking for a positive definite lyapunov function such that a high order linear differential inequality with respect to the lyapunov function holds along the trajectories of a nonlinear system can be utilized to assess asymptotic stability when the standard lyapunov approach examining only the first derivative fails in this context the main purpose of this paper is on one hand to theoretically unveil deeper connections among existing stability conditions especially for linear time invariant lti systems and from the other hand to examine the effect of the higher order time derivatives approach on the stability results for uncertain polytopic lti systems in terms of conservativeness to this end new linear matrix inequality lmi stability conditions are derived by generalizing the concept mentioned above and through the development relations among some existing stability conditions are revealed examples illustrate the improvement over the quadratic approach

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

filtering and fault estimation of descriptor switched systems in this paper the problems of state and fault estimation are addressed for a class of switched descriptor systems subject to lipschitz nonlinearities and unknown inputs ui the ui appear both on the dynamic and on the measurement equations two problems are addressed by l 2 gain minimization with the use of switched lyapunov functions and formulated by lmi first a functional observer for switched lipschitz nonlinear descriptor system is proposed for robust state estimation second fault estimation is performed by filtering the output estimation error as usually done in the residual generation framework moreover frequency weighting functions can be used to shape the response to the fault and thus improve the estimation

technical communique on the existence of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties recently choi 1998 automatica 34 8 1015 1020 has considered the problem of designing a variable structure control vsc law for uncertain systems where the uncertainty in the state model does not satisfy the matching condition he has given a sufficient condition for the existence of linear sliding surfaces in terms of lmis in this note we show that the lmi existence condition given in the above paper is a necessary and sufficient one and we give lmi existence conditions of a sliding surface guaranteeing general lmi regional pole placement constraints while in the above paper pole placement only in a vertical half plane and a disk has been considered finally we give simulation results for controlling an inverted pendulum mounted on a cart

on the dissipativity of nonlinear systems fuzzy control approach a controller with large dissipativity is designed and implemented the stability margin is increased in order to tolerate the uncertainties and the disturbance in the nonlinear system in this study the dissipativity of a nonlinear system is facilitated via fuzzy control method first the nonlinear system is represented by an takagi and sugeno fuzzy model if the state variables of the nonlinear system are available then a state feedback fuzzy control is developed to guarantee that the nonlinear control system is dissipative this design problem becomes a linear matrix inequality lmi problem the maximum dissipativity design is obtained by solving an eigenvalue problem evp if the state variables are not available a fuzzy observer based state feedback controller will be used to solve the dissipative problem of the nonlinear system simulation examples are given to illustrate the design procedures and performances of the proposed method