stabilization by means of state space depending switching rules abstract in this paper we consider switched systems defined by a pair of linear systems x a 1 x x a 2 x such that there exists a neutrally stable linear combination of the matrices a 1 a 2 under an additional assumption we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense the result is illustrated by some simulations and examples

constrained control of siso bilinear systems relative degree and nonminimum phase difficulties limit the applicability of input output feedback linearization hence the need for approximations earlier work on predictive control of bilinear systems overcame these problems by means of interpolation between feedback linearization and state feedback the former providing optimality and the latter guaranteeing feasibility and stability through the use of invariant feasible polytopes the current work also makes use of polytopes in preference to ellipsoids but achieves distinctly different objectives first it is shown that feedback linearization can be used over particular polytopes without needing to resort to either approximation or interpolation then it is shown that invariant polytopes based on bilinear controllers can be much larger these two approaches are combined in an algorithm that guarantees stability over much larger initial condition sets and gives much improved closed loop performance

finite time stability of quantum systems governed by schrodinger s equation in this paper we investigate the finite time stability fts and finite time boundedness ftb of quantum systems which are governed by schrodinger s equation we first study the fts and fts at one target state and propose new results for the mentioned quantum systems in the form of sufficient conditions then we present sufficient conditions for the ftb and ftb at one target state in terms of matrix inequalities one numerical simulation is presented to illustrate the effectiveness of the obtained theoretical result

note on surface radiation conditions the predictions of the surface radiation condition are compared with the exact analytical answer for scattering by a soft elliptical cylinder the agreement is found to be highly satisfactory for a range of parameters which can be handled analytically numerical results are presented that substantiate the analysis the surface radiation condition is generalized to be applicable when the environment is inhomogeneous study of the particular case of a circular cylinder surrounded by an inhomogeneous medium reveals that surface boundary condition gives good results for some values of the parameters where analytic manipulation is feasible

a wide angle on surface radiation condition applied to scattering by spheroids a rational approximation of the pseudo differential dirichlet to neumann operator for a circular cylinder is made using zero placement for an acoustically hard circular cylinder this zero corresponds to the dominant creeping wave singularity in the residue series for the time harmonic free space surface green s function based on this operator a wide angle on surface radiation condition osrc is developed first for two dimensional slender convex bodies for the object scattering problem this osrc is accurate for wide scattering angles relative to the surface normal the notion of creeping waves is then used to develop a wide angle three dimensional osrc applicable to smooth convex bodies application to both hard and soft prolate and oblate spheroids is presented and excellent agreement is found in comparison with a more costly technique

some results on global and semiglobal stabilization of affine systems in this paper the relations between semiglobal stabilization and global stabilization of affine systems are investigated it is shown that for one dimensional systems the two concepts are equivalent for the n dimensional case we introduce a more restrictive concept the l semiglobal stabilization which implies global stabilization this result is applied to bilinear systems

numerical techniques for three dimensional steady state fluid structure interaction the application of a coupled finite element boundary integral approach to the analysis of vibrating elastic arbitrary shaped three dimensional structures in an infinite media is presented a feature of the methodologies implemented is the utilization of the isoparametric concept from finite element theory the same shape functions are used both to model the surface of the structure and to interpolate the acoustic variables over the radiating surface the boundary integral formulation used for the exterior acoustic field is a formulation that ensures uniqueness and existence of solutions for the entire frequency range an assessment of the accuracy was made after comparing the solutions attained for a vibrating submerged sphere for various excitation loads and frequencies with the exact solution

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

on the stabilization of the homogeneous bilinear systems abstract the problem of stabilizing the single input homogeneous bilinear systems is considered a special class of these systems is considered the matrix of the linear i e control independent term of the right hand side is semitable while the matrix of the bilinear term is skew symmetric two types of stabilization are investigated constant feedback global asymptotic stabilization and practical stabilization by a family of the linear feedbacks it will be shown for the planar case that the above system is always practically stabilizable by a family of the linear feedbacks for n 3 the solution of both stabilization problems depends on the mutual position of the expanding direction of the linear part and the direction of the infinitesimal rotation defined by the bilinear term

h state feedback control of linear systems with small state de in this note a h controller for systems with state delay is presented for a prechosen the controller is obtained by solving riccati partial differential inequalities rpdis for small time delays an asymptotic approximation of the controller is achieved by expanding the solution in powers of the delay it is shown that a higher order accuracy controller improves the performance an example is brought where the results of the new method provide a satisfactory solution for a delay length comparable with the system bandwidth the performance of the system under the zero order accuracy controller which corresponds to systems without delay is studied explicit formula for the guaranteed performance level is obtained for the delay lengths that preserve the internal stability of the system

exponential stabilization of a constrained bilinear system for a bilinear system that is open loop neutrally stable a quadratic state feedback control has been proposed to ensure global asymptotical stability of the closed loop system in this paper a new nonlinear control is proposed so that the closed loop system is not only asymptotically stable but also exponentially stable the new control results in a much faster state convergence rate than the quadratic control furthermore it can be applied to systems with tight saturation limits on the control input

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

saturated feedback stabilization of discrete time descriptor bilinear systems this note addresses global asymptotic stabilization of a class of discrete time descriptor bilinear systems via a saturated state feedback controller based on lasalle invariance principle and the implicit function theorem sufficient conditions are presented to guarantee the uniqueness and existence of solution and the global asymptotic stability of the resulting closed loop systems simultaneously it is shown that the condition is independent of the state transformation for the given descriptor systems furthermore the effectiveness of the proposed design method is illustrated by a numerical example

unconstrained and constrained stabilisation of bilinear discrete time systems using polyhedral lyapunov functions the constrained and unconstrained stabilisation problem of discrete time bilinear systems is investigated using polyhedral lyapunov functions conditions for a polyhedral set to be both positively invariant and domain of attraction for systems with second order polynomial nonlinearities are first established then systematic methods for the determination of stabilising linear feedback for both constrained and unconstrained bilinear systems are presented attention is drawn to the case where no linear control law rendering the pre specified desired domain of attraction positively invariant exists for this case an approach guaranteeing the existence of a possibly suboptimal solution is established

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

a separation principle for bilinear systems with dissipative drift input output stabilization of a class of bilinear systems using a nonlinear stabilizing feedback control law together with an observer is studied in some cases it can be proved that the result is a globally asymptotically stable system

further results for robust stability of homogeneous large scale bilinear systems with time delays and uncertainties in this paper the problem of stability analysis for homogeneous large scale time delay bilinear systems subjected to uncertainties is considered two classes of uncertainty are treated nonlinear uncertainties and parametric uncertainties by making use of the lyapunov stability approach associated with solution bounds of the lyapunov equation two delay independent criteria are presented to guarantee the robust stability of the overall systems the stability condition for the mentioned system with nonlinear uncertainties is sharper than that of a previous work the main feature of the schemes presented is that they do not involve any lyapunov equation which may be unsolvable although the lyapunov stability theorem is used

stability analysis and bang bang sliding control of a class of single input bilinear systems introduces a bang bang sliding control of a class of single input bilinear systems the sliding function is chosen via the well known pole assignment method for linear time invariant systems importantly the bang bang sliding control generates a reaching and sliding region and a stable sliding region each expressed by a set of linear inequalities both regions comprise the equilibrium point shown to be asymptotically stable however the stability analysis is processed under the limitation that the system state should be initially located in the reaching and sliding region two numeric examples are used for demonstration

stabilizability of second order bilinear systems this note states necessary and sufficient conditions for the existence of a linear state feedback controller such that a second order bilinear system has a globally asymptotically stable closed loop a suitable controller is constructed for each system which satisfies the conditions

global feedback stabilization of new class of bilinear systems abstract in this paper we consider some new classes of bilinear systems we give necessary and sufficient conditions for the asymptotic stabilization by using homogeneous feedbacks

brief output feedback stabilization of bilinear systems using dead beat observers an output feedback stabilizing controller for bilinear systems is proposed in this paper key techniques in the proposed method are periodic switching of the controller and the use of a dead beat observer the controller is proved to globally stabilize the plant both in noiseless and noisy conditions the only condition on the plant for the proposed method to be applicable is that the linear part of it is observable no condition on nonlinear observability is required

optimal and suboptimal feedback controls for a class of nonlinear systems abstract in this paper we consider a class of nonlinear regulator problems in which the control appears linearly using an approach similar to that given for the classical linear quadratic regulator problem it is shown in 1 that the optimal feedback control can be expressed as a function of the solution of an algebraic riccati equation at each point in the state space more precisely it is shown that by solving a riccati equation at a given point in the state space the optimal feedback control at that particular point is readily obtained in this paper our first aim is to investigate stability of the resulting closed loop system second a simple computational scheme for constructing a suboptimal control is suggested we then consider the problem of stabilizing the system when it is subjected to bounded noise for illustration two examples are used to test the effectiveness of the proposed computational schemes

the on surface radiation condition applied to three dimensional convex objects a numerical method is described for obtaining solutions for electromagnetic scattering from convex three dimensional objects by invoking the on surface radiation condition osrc the set of objects for which the numerical method can be employed are those that are describable as bodies of revolution and have surfaces that are perfect electrical conductors the numerical method is sufficiently general to allow arbitrary angles of incident radiation in the development of the numerical method the three dimensional form of osrc was transformed from a coupled vector partial differential equation to an ordinary differential equation to ease computation issues of numerical tractability and boundary conditions also had to be addressed comparisons of the numerical solutions of osrc with accepted scattering results are provided the objects used in these comparisons are spheres spheroids disks wires and conespheres

rational square root approximations for parabolic equation algorithms in this article stable pade approximations to the function 1 z are derived by choosing a branch cut in the negative half plane the pade coefficients are complex and may be derived analytically to arbitrary order from the corresponding real coefficients associated with the principal branch defined by z 1 i z 0 i z denotes the imaginary part of z the characteristics of the corresponding square root approximation are illustrated for various segments of the complex plane in particular for waveguide problems it is shown that an increasingly accurate representation may be obtained of both the evanescent part of the mode spectrum for the acoustic case and the complex mode spectrum for the elastic case an elastic parabolic equation algorithm is used to illustrate the application of the new pade approximations to a realistic ocean environment including elasticity in the ocean bottom

stabilisation of discrete time bilinear systems by constant control inputs abstractin this paper the stabilisation problem of discrete time bilinear systems by using constant control inputs is considered it is shown that the spectrum of a matrix derived from the system

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

h filtering for a class of uncertain nonlinear systems abstract this paper investigates the problem of h filtering for a class of uncertain continuous time nonlinear systems with real time varying parameter uncertainty and unknown initial state we develop an infinite horizon h filtering methodology which provides both robust stability and a guaranteed h performance for the filtering error irrespective of the parameter uncertainty

a higher order on surface radiation condition derived from an analytic representation of a dirichlet to neumann map on surface radiation conditions are useful for obtaining approximate solutions to scattering problems involving compact obstacles an analytic representation of the dirichlet to neumann map for a circle is derived and used to construct a higher order on surface radiation condition for a generally convex perfectly conducting body in two dimensions this approach is based on a hankel function in which a tangential operator appears in the index in the high frequency limit this analytic representation approaches the square root of a differential operator which commonly arises in the application of parabolic equation techniques to propagation problems treating the scattered field propagation angle relative to the surface normal and the surface curvature as independent parameters the representation is fit to a rational function to provide an accurate and efficient on surface radiation condition that is tested for various examples

robust stability and stabilization for singular systems with state delay and parameter uncertainty considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay the parametric uncertainty is assumed to be norm bounded the purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular impulse free and stable for all admissible uncertainties while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed loop system is robustly stable these problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization respectively necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived a strict linear matrix inequality lmi design approach is developed an explicit expression for the desired robust state feedback control law is also given finally a numerical example is provided to demonstrate the application of the proposed method

decentralized adaptive tracking control of nonaffine nonlinear large scale systems with time delays this paper addresses the problem of decentralized tracking control of large scale systems with uncertain nonaffine nonlinear isolated subsystems and nonlinear interconnections with time varying delays based on lyapunov krasovskii functional approach and implicit function theorem a delay independent decentralized tracking controller is proposed due to functional approximation capability of fuzzy logic systems fls neither strict structure restrictions on the isolated subsystems nor a priori knowledge of the strong interconnections with time varying delays is required in our control design furthermore transient performance of the resulting closed loop system is also addressed under an analytical framework finally two numerical examples are provided to show the effectiveness of the proposed controller

suboptimal control for nonlinear systems a successive approximation approach abstract this paper presents a successive approximation approach saa designing optimal controllers for a class of nonlinear systems with a quadratic performance index by using the saa the nonlinear optimal control problem is transformed into a sequence of nonhomogeneous linear two point boundary value tpbv problems the optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence by using the finite step iteration of the nonlinear compensation sequence we can obtain a suboptimal control law simulation examples are employed to test the validity of the saa

two single shot methods for locating multiple electromagnetic scatterers we develop two inverse scattering schemes for locating multiple electromagnetic em scatterers by the electric far field measurement corresponding to a single incident detecting plane wave the first scheme is for locating scatterers of small size compared to the wavelength of the detecting plane wave the multiple scatterers could be extremely general with an unknown number of components and each scatterer component could be either an impenetrable perfectly conducting obstacle or a penetrable inhomogeneous medium with an unknown content the second scheme is for locating multiple perfectly conducting obstacles of regular size compared to the detecting em wavelength the number of the obstacle components is not required to be known in advance but the shape of each component must be from a certain known admissible class the admissible class may consist of multiple different reference obstacles the second scheme could also be extended to include the medium components if a certain generic condition is s

local absorbing boundary conditions for elliptical shaped boundaries we compare several local absorbing boundary conditions for solving the helmholtz equation by a finite difference or finite element method exterior to a general scatterer these boundary conditions are imposed on an artificial elliptical or prolate spheroid outer surface in order to compare the computational solution with an analytical solution we consider as an example scattering about an ellipse we solve the helmholtz equation with both finite differences and finite elements we also introduce a new boundary condition for an ellipse based on a modal expansion

output feedback control of bilinear systems via a bilinear ltr observer in the literature most observer based output feedback controls for bilinear systems are only applicable to open loop neutrally stable systems this paper proposes a new observer based output feedback control that can be applied to open loop unstable systems the key component of the new control is an exponentially stable bilinear loop transfer recovery ltr observer that derives from the linear ltr observer

reduced order filtering for networks with markovian jumping parameters and missing measurements abstractthe problem of reduced order h filters design for markovian jumping complex networks with polytopic time varying transition probability matrices is first addressed in this paper where th

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

division controllers for homogeneous dyadic bilinear systems when a homogeneous bilinear system is dyadic it permits the use of the so called division controller for global stabilization however due to singularities in the control law a dead zone must be cascaded with the division controller in practical implementation the contribution of this note is to show that the division controller when cascaded with a dead zone can asymptotically drive the bilinear system state into a bounded set around the origin with the size of the bounded set proportional to the size of dead zone this note further proposes a c sup 0 modification and a c sup spl infin modification of the conventional discontinuous dead zone so that the control signals from the modified division controllers are continuous and smooth respectively

exponential stabilization of a class of unstable bilinear systems considers the control design of bilinear systems with multiplicative control inputs previous control designs for such systems normally assume that the open loop bilinear system is neutrally stable in this paper a nonlinear control design is proposed for open loop unstable bilinear systems the new control stabilizes the bilinear system globally and exponentially if a sufficient stability condition which can be checked by off line computer simulations in advance of the control is satisfied

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

a decoupled approach to filter design for stochastic systems abstractthis paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems this result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept two kinds of observers are treated the full order and reduced order cases

global asymptotic stabilization for a class of bilinear systems by hybrid output feedback this technical note deals with the global asymptotic stabilization problem for a class of bilinear systems a state feedback controller solving this problem is obtained uniting a local controller having an interesting behavior in a neighborhood of the origin and a constant controller valid outside this neighborhood the approach developed is based on the use of a hybrid loop and more precisely a hybrid state feedback this result is extended to the case where the state of the plant is not fully available and only the measured output can be used for control purposes in this case a dynamical controller constituted by an observer and a state feedback is built by means of hybrid output feedback framework in both cases the conditions are expressed by a set of linear matrix inequalities

stabilizability conditions for strictly bilinear systems with purely imaginary spectra this paper presents simple sufficient conditions for the stabilizability of single input strictly bilinear systems with purely imaginary spectra if the state matrix eigenvalues are distinct and a matrix function of the bilinear input and eigenvector matrices has nonzero diagonal elements then the system is globally asymptotically stabilizable

robust h control for descriptor systems with non linear uncertainties this paper considers robust performance analysis and robust h x control for a class of descriptor systems with time varying and non linear uncertainties these uncertainties exist not only in the state the control input and exogenous input but also in the derivative of the state a sufficient condition is firstly proposed to analyse the robust h x performance problem of the unforced systems feasible design procedures are presented to construct both the robust state feedback and output feedback controllers such that the closed loop system has a unique non impulsive and asymptotically stable solution and satisfies a robust h x performance criterion a numerical example is provided to show the efficiency of the approach

optimal control of nonlinear systems a recursive approach abstract in this paper we shall generalize our result 1 on the optimal control of bilinear systems to nonlinear systems adomian s decomposition is used to derive series expansions of the optimal control and state

technical communique a note on the existence of a solution and stability for lipschitz discrete time descriptor systems this paper addresses the existence and uniqueness of a solution and stability for lipschitz discrete time descriptor systems by means of the fixed point principle a criterion is presented via a matrix inequality and the criterion guarantees the existence and uniqueness of a solution in addition a sufficient condition is also presented to ensure that the solution exists for any compatible initial condition and the system is globally exponentially stable simultaneously it is shown that the criterion presented in this paper is easy to verify and independent of the choices of decomposition matrices for the given system finally the approach is illustrated by a numerical example

a framework for state space estimation with uncertain models develops a framework for state space estimation when the parameters of the underlying linear model are subject to uncertainties compared with existing robust filters the proposed filters perform regularization rather than deregularization it is shown that under certain stabilizability and detectability conditions the steady state filters are stable and that for quadratically stable models the filters guarantee a bounded error variance moreover the resulting filter structures are similar to various time and measurement update prediction and information forms of the kalman filter albeit ones that operate on corrected parameters rather than on the given nominal parameters simulation results and comparisons with spl hscr sub spl infin guaranteed cost and set valued state estimation filters are provided

nonlinear state observation using h sub spl infin filtering riccati design the authors propose an observer for continuous time nonlinear systems the observer gain is computed by a riccati differential equation similar to the extended kalman filter they prove that under certain conditions the proposed observer is an exponential observer by choosing an appropriate lyapunov function furthermore the authors explore some important relations of the proposed observer to robust control theory and h sub spl infin filtering to examine the practical usefulness of the proposed observer they applied it to an induction motor for the estimation of the rotor flux and the angular velocity

observers for a special class of bilinear systems design and application this note presents full and reduced order observation strategies for a subclass of systems that are bilinear in the immeasurable states lyapunov analysis is carried out to derive the conditions for convergence of the observed states for all strategies the full order observer is then utilized in the problem of bus voltage regulation effected by a static compensator statcom acting as a controlled reactive current source

numerical design of fshl based approximate cloaks with arbitrary shapes this paper considers numerical design of finite sound hard lining fshl based approximate cloaks with arbitrary shapes regarding the complexity of the shape two new approaches are proposed to design the transformation map from the virtual space to the physical space via transformation optics for star shaped geometry we propose an explicit global transformation map which can be easily differentiated and inverted for more general shapes an initialize untangle extend iue approach is initiated to build locally piecewise differentiable deformations which can be locally inverted with the help of an approximate triangulation with the locally piecewise constructed transformation the parameters of acoustic scattering models in physical space can be determined in both approaches based on the transformation invariance of the helmholtz system then the cloaking effects for an arbitrary shape fshl based cloak can be realized following li et al 2012 5 extensive numerical experiments are presented to illustrate both the effectiveness of cloak design and the efficiency of the proposed fshl based cloaks with arbitrary shapes

finite time stability of linear time varying singular systems with impulsive effects in this paper we introduce a new concept of finite time stability of linear time varying singular systems with impulses at fixed times and present new results for the above mentioned class of system in the form of sufficient conditions a sufficient condition is given in terms of matrix inequalities which gives the opportunity of fitting the finite time control problem in the general framework via impulsive control a numerical example is presented to illustrate the efficiency of the proposed result

remark on local and global stabilization of homogeneous bilinear systems in this paper we deal with the problem of stabilization of homogeneous bilinear systems the aim is to clarify some results on stabilizability of these systems

brief paper h functional filtering for stochastic bilinear systems with multiplicative noises this paper deals with the design of a reduced order h filter for a stochastic bilinear system with a prescribed h norm criterion the considered system is bilinear in control and with multiplicative noises in the dynamics and in the measurement equations the problem is transformed into the search of a unique gain matrix by using sylvester like constraints the approach is based on the resolution of lmi and is then easily implementable

brief residual generator design for singular bilinear systems subjected to unmeasurable disturbances an lmi approach in this paper a method to design a bank of unknown input residual generator for fault detection and isolation is investigated the plant model is assumed to be a bounded control inputs singular bilinear systems subjected to unknown disturbances the measurements can be bilinear

continuous stabilization controllers for singular bilinear systems the state feedback case global asymptotic stabilization for a class of singular bilinear systems is first studied in this paper new approaches are developed by means of the lasalle invariant principle for nonlinear systems a new set of sufficient condition is first derived via the continuous static state feedback the feedback not only guarantees the existence of solution but also the global asymptotical stabilization for the closed loop system

algebraic and topological classification of the homogeneous cubic vector fields in the plane tsutomu date and masao iri in di gave an algebraic classification of systems i p x y i q x y where p and q are homogeneous polynomials of degree 2 for this they used the classification of the binary cubic forms and also the simultaneous classification of a linear binary form and a cubic binary form given by the algebraic invariant theory we begin by doing a similar study for systems p x y q x y where p and q are homogeneous polynomials of degree three i e cubic systems the classification s theorem of such systems is based on the classification of fourth order binary forms gurevich in gu did the classification of fourth order binary forms on the field of complex numbers since we did not find the classification on the real domain we adapt gurevich s proof to obtain it in section 1 we give some definitions and preliminary results while in section 2 we give the theorem of classification of fourth order binary forms on the real domain the method used in the proof caley s method let us obtain canonical forms of the fourth order binary forms and the algebraic characteristics section 3 is devoted to obtaining the algebraic classification of systems p x y j q x y where p and q are homogeneous polynomials of degree 3 given an arbitrary system x p q with p and q homogeneous polynomials of degree 3 we can know the equivalence class at which it belongs through the algebraic characteristics in section 4 we study the phase portraits of systems 1 p x y j q x y where p and q are homogeneous polynomials of degree n and p and q have no common factor such systems have been studied by j argemi in a here we give a shorter new proof of his results by using

cal h _ infty filter for bilinear systems using lpv approach the aim of this technical note is to present a linear paramater varying lpv approach for the design of a functional filter for bilinear systems with a disturbance attenuation specification the unbiasedness requirement on the observation error is guaranteed by the solution of sylvester equations obtained by parametrizing the filter gain matrix this parametrization leads to a non convex optimization problem which is overcome by introducing a constraint on the gain matrix to take into account the whole set of the inputs in the filter design an lpv approach is used to obtain the gain matrix guaranteeing the quadratic stability of the observation error and a given level of disturbance attenuation this approach is then applied to the high gain observer design in order to consider the level of disturbance attenuation

high order surface radiation conditions for time harmonic waves in exterior domains abstract we formulate a new family of high order on surface radiation conditions to approximate the outgoing solution to the helmholtz equation in exterior domains motivated by the pseudo differential expansion of the dirichlet to neumann operator developed by antoine et al 1999 we design a systematic procedure to apply pseudo differential symbols of arbitrarily high order numerical results are presented to illustrate the performance of the proposed method for solving both the dirichlet and the neumann boundary value problems possible improvements and extensions are also discussed

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

exponentially stabilizing division controllers for dyadic bilinear systems it is difficult to asymptotically stabilize a dyadic bilinear system with only multiplicative control inputs when the open loop dynamics are unstable the previous approach of cascading a division controller with a constant size dead zone can only stabilize but not asymptotically stabilize the system this note proposes a new control design which cascades a division controller with a modified dead zone whose size is proportional to the modulus of the system state it is shown that this new division controller can globally and exponentially stabilize any open loop unstable dyadic bilinear system as long as it is controllable

optimal unbiased filtering via linear matrix inequalities abstract solutions to the optimal h and l2 l unbiased reduced order filtering problems are obtained in terms of linear matrix inequalities lmis the order of the optimal filter is equal to the number of measurements both continuous and discrete time results are presented an explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix

a frequency domain approach to the problems of h sub infinity minimum error state estimation and deconvolution the properties of the minimum h sub infinity norm filtering estimation error are investigated and the relation between the optimal estimator and the equalizing solution to the standard h sub infinity minimization problem is discussed the optimal estimation method is applied in the multivariable deconvolution problem a simple deconvolution filter of minimum order which minimizes the h sub infinity norm of the deconvolution error is obtained the proposed methods of optimal estimation and deconvolution are useful in cases where the statistics of the disturbance and the noise signals is not completely known or in cases where it is required to minimize the maximum singular value of the estimation or the deconvolution error problem

galerkin approximations of the generalized hamilton jacobi bellman equation in this paper we study the convergence of the galerkin approximation method applied to the generalized hamilton jacobi bellman ghjb equation over a compact set containing the origin the ghjb equation gives the cost of an arbitrary control law and can be used to improve the performance of this control the ghjb equation can also be used to successively approximate the hamilton jacobi bellman equation we state sufficient conditions that guarantee that the galerkin approximation converges to the solution of the ghjb equation and that the resulting approximate control is stabilizing on the same region as the initial control the method is demonstrated on a simple nonlinear system and is compared to a result obtained by using exact feedback linearization in conjunction with the lqr design method

reconstruction procedures for two inverse scattering problems without the phase information this is a continuation of two recent publications of the authors j inverse ill posed probl 23 2015 pp 415 426 j inverse ill posed probl 23 2015 pp 187 193 about reconstruction pr

recovering a polyhedral obstacle by a few backscattering measurements abstract we propose an inverse scattering scheme of recovering a polyhedral obstacle in r n n 2 3 by only a few high frequency acoustic backscattering measurements the obstacle could be sound soft or sound hard it is shown that the modulus of the far field pattern in the backscattering aperture possesses a certain local maximum behavior from which one can determine the exterior normal directions of the front sides faces then by using the phaseless backscattering data corresponding to a few incident plane waves with suitably chosen incident directions one can determine the exterior unit normal vector of each side face of the obstacle after the determination of the exterior unit normals the recovery is reduced to a finite dimensional problem of determining a location point of the obstacle and the distance of each side face away from the location point for the latter reconstruction we need to make use of the far field data with phases numerical experiments are also presented to illustrate the effectiveness of the proposed scheme

control of a driftless bilinear vector field on n sphere in this paper we consider a multi input driftless bilinear system evolving on the n dimensional sphere s n we first provide examples drawn from rigid body mechanics that provide the motivation for the control of bilinear systems on s n for the general framework we establish the global controllability on s n and propose two linear control laws on s n that achieve asymptotic stabilization of an equilibrium point with an almost global domain of attraction further the asymptotically stable closed loop system trajectories are shown to be arcs on the geodesics of s n for a particular choice of the equilibrium point next we propose two linear time varying control laws to achieve trajectory tracking on s n and show the asymptotic stability of the tracking error a distributed control is designed for the consensus of multiagent bilinear systems on s n with an undirected tree as the communication graph the consensus manifold is shown to have an almost global domain of attraction

a split step pade solution for the parabolic equation method a split step pade solution is derived for the parabolic equation pe method higher order pade approximations are used to reduce both numerical errors and asymptotic errors e g phase errors due to wide angle propagation this approach is approximately two orders of magnitude faster than solutions based on pade approximations that account for asymptotic errors but not numerical errors in contrast to the split step fourier solution which achieves similar efficiency for some problems the split step pade solution is valid for problems involving very wide propagation angles large depth variations in the properties of the waveguide and elastic ocean bottoms the split step pade solution is practical for global scale problems

robust h reduced order filtering for uncertain bilinear systems this paper investigates both the h and robust h reduced order unbiased filtering problems for respectively a nominal bilinear system and a bilinear system affected by norm bounded structured uncertainties in all the system matrices first an algebraic framework is used to solve the unbiasedness condition and second a change of variable is introduced on the inputs of the system to reduce the conservatism inherent to the requirement of exponential convergence of the filter then the reduced order filtering solution is obtained through lmi with an equality constraint by transforming the problem into a robust state feedback in the nominal case and a robust static output feedback in the presence of uncertainties in the last case an additional bilinear matrix equality must also be solved

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

a self starter for the parabolic equation method an efficient method is developed for generating accurate starting fields for the parabolic equation pe method for both fluid and solid media the self starter which is constructed by solving a one dimensional boundary value problem bvp involving the pe operator is more efficient than the normal mode starter which requires the solution of a large number of similar bvps the self starter depends on the depth dependent properties of the medium and satisfies all interface and boundary conditions since the self starter is based on higher order parabolic approximations it is accurate for problems involving wide propagation angles large depth variations in the properties of the medium low frequencies interface waves and the continuous spectrum

continuous time model reference adaptive control based on weighting functions this note presents a model reference adaptive control for a plant with unknown system degree a continuous time observer based on the weighting function is introduced instead of a finite dimensional state variable filter which needs an upper bound of the plant degree the state is reconstructed by a sum of convolution integrals in a finite span of time

the successive approximation procedure for finite time optimal control of bilinear systems it is shown that the successive approximation procedure simplifies computations of the optimal solution of a bilinear quadratic optimal control problem on the contrary to the results of hofer and tibken 1985 where the optimal solution has been obtained in terms of a sequence of the differential riccati equations in the presented method only solutions of a sequence of the differential lyapunov equations are required a chemical reactor example is used to demonstrate the efficiency of the new method

optimal tracking control for large scale interconnected systems with time delays this paper considers an infinite horizon optimal tracking control problem for a class of large scale interconnected systems with state time delays by using the successive approximation approach two iteration sequences of vector differential equations are constructed meanwhile the large scale interconnected system is decomposed into finite decoupled subsystems the existence and uniqueness of the optimal solution is proved as well as the convergence of the solution sequence by finite iterations of the solution sequence a suboptimal tracking control law is obtained a reduced order reference input observer is designed to make the feedforward term of the optimal tracking control law physically realizable a numerical example shows that the presented algorithm is effective and easy to implement

technical communique robust stability of uncertain delay differential systems of neutral type this paper focuses on the stability problem for neutral delay differential systems with norm bounded and possibly time varying uncertainty the time delay is assumed constant and known a stability criterion that is formulated in a linear matrix inequality lmi form is derived numerical examples show that the results obtained by this new criterion significantly improve the estimate of stability limit over some existing results in the literature

factored forms for solutions of ax xb c and x axb c in companion matrices abstract the main concern of this paper is linear matrix equations with block companion matrix coefficients it is shown that general matrix equations ax xb c and x axb c can be transformed to equations whose coefficients are block companion matrices c l x xc m diag i 0 0 and x c l xc m diag i 0 0 respectively where l and cm stand for the first and second block companion matrices of some monic r r matrix polynomials l si s 1j 0 jlj and m ti t7minus 1j 0 jmj the solution of the equat with block companion coefficients is reduced to solving vector equations sx where the matrix s is r2l r2l l max s t and enjoys some symmetry properties

on asymptotically stabilizing feedback control of bilinear systems asymptotically stabilizing feedback controls for a class of bilinear systems are discussed a simple modification which strengthens a result of slemrod 1 is noted and illustrated by example