continuous pole placement for delay equations in this paper we describe a stabilization method for linear time delay systems which extends the classical pole placement method for ordinary differential equations unlike methods based on finite spectrum assignment our method does not render the closed loop system finite dimensional but consists of controlling the rightmost eigenvalues because these are moved to the left half plane in a quasi continuous way we refer to our method as continuous pole placement we explain the method by means of the stabilization of a linear finite dimensional system in the presence of an input delay and illustrate its applicability to more general stabilization problems

global stabilization and restricted tracking with bounded feedback for multiple oscillator systems this paper is concerned with the problems of global stabilization and restricted tracking for a multiple oscillator system by bounded feedback a nonlinear feedback law consisting of nested saturation functions is proposed to achieve global stabilization to improve the transient performance of the closed loop system the parameters in this feedback law can be tuned to assign the poles of the closed loop system when none of the saturation elements in the control law is in effect the proposed feedback law is also shown to achieve restricted tracking simulation results are given to show the effectiveness of the proposed feedback law

nonlinear control of feedforward systems with bounded signals the stabilization problem for a class of nonlinear feedforward systems is solved using bounded control it is shown that when the lower subsystem of the cascade is input to state stable and the upper subsystem not exponentially unstable global asymptotic stability can be achieved via a simple static feedback having bounded amplitude that requires knowledge of the upper part of the state only this is made possible by invoking the bounded real lemma and a generalization of the small gain theorem thus stabilization is achieved with typical saturation functions saturations of constant sign or quantized control moreover the problem of asymptotic stabilization of a stable linear system with bounded outputs is solved by means of dynamic feedback finally a new class of stabilizing control laws for a chain of integrators with input saturation is proposed some robustness issues are also addressed and the theory is illustrated with examples on the stabilization of physical systems

properties of recoverable region and semi global stabilization in recoverable region for linear systems subject to constraints this paper investigates linear systems subject to input and state constraints it is shown that the recoverable region which is the largest domain of attraction that is theoretically achievable can be semiglobally stabilized by continuous nonlinear feedbacks while satisfying the constraints moreover when trying to compute the recoverable region a reduction technique shows that we only need to compute the recoverable region for a system of lower dimension which generally leads to a considerable simplification in the computational effort

global stabilization of linear discrete time systems with bounded feedback abstract this paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws the main result proved is an analog of one proved for the continuous time case by the authors and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one the proof provides in principle an algorithm for the construction of such feedback laws which can be implemented either as cascades or as parallel connections single hidden layer neural networks of simple saturation functions

dual mode predictive control algorithm for constrained hammerstein systems in the process industry there exist many systems which can be approximated by a hammerstein model moreover these systems are usually subjected to input magnitude constraints in this paper a multi channel identification algorithm mcia is proposed in which the coefficient parameters are identified by least squares estimation lse together with a singular value decomposition svd technique compared with traditional single channel identification algorithms the present method can enhance the approximation accuracy remarkably and provide consistent estimates even in the presence of coloured output noises under relatively weak assumptions on the persistent excitation pe condition of the inputs then to facilitate the following controller design this mcia is converted into a two stage single channel identification algorithm ts scia which preserves most of the advantages of mcia with this ts scia as the inner model a dual mode non linear model predictive control nmpc algorithm is developed in detail over a finite horizon an optimal input profile found by solving a open loop optimal control problem drives the non linear system state into the terminal invariant set afterwards a linear output feedback controller steers the state to the origin asymptotically in contrast to the traditional algorithms the present method has a maximal stable region a better steady state performance and a lower computational complexity finally simulation results on a heat exchanger are presented to show the efficiency of both the identification and the control algorithms

controllability and observability of systems of linear delay differential equations via the matrix lambert w function during recent decades controllability and observability of linear time delay systems have been studied including various definitions and corresponding criteria however the lack of an analytical solution approach has limited the applicability of the existing theory recently the solution to systems of linear delay differential equations has been derived in the form of an infinite series of modes written in terms of the matrix lambert w function the solution form enables one to put the results for point wise controllability and observability of systems of delay differential equations to practical use we derive the criteria for point wise controllability and observability obtain the analytical expressions for their gramians in terms of the parameters of the system and develop a method to approximate them for the first time using the matrix lambert w function based solution form

pattern formation in a two component reaction diffusion system with delayed processes on a network abstract reaction diffusion systems with time delay defined on complex networks have been studied in the framework of the emergence of turing instabilities the use of the lambert w function allowed us to get explicit analytic conditions for the onset of patterns as a function of the main involved parameters the time delay the network topology and the diffusion coefficients depending on these parameters the analysis predicts whether the system will evolve towards a stationary turing pattern or rather to a wave pattern associated to a hopf bifurcation the possible outcomes of the linear analysis overcome the respective limitations of the single species case with delay and that of the classical activator inhibitor variant without delay numerical results gained from the mimura murray model support the theoretical approach

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

verified computation for the matrix lambert w function abstract two iterative algorithms are proposed for numerically computing interval matrices containing primary matrix lambert w functions the first algorithm is based on a numerical spectral decomposition and involves only cubic complexity per iteration the second algorithm is based on a numerical jordan decomposition and applicable even for defective matrices numerical results show the effectiveness and robustness of the algorithms

robust stability analysis of linear time delay systems by lambert w function some extreme point results robust stability conditions are derived for linear time delay systems using lambert w function the characteristic quasi polynomials of the systems are assumed to be factorized it is proven that if uncertainties in the coefficients of the quasi polynomial are set in appropriate regions in the complex plane we can enjoy extreme point results finite number of stability checks at some points of the boarder of the regions suffice the strength of lambert w function approach lies in the fact that the function is implemented on some standard software packages such as mathematica maple or matlab which afford to compute the function value very easily the above two points make the stability test for the class of uncertain time delay systems quite practical

global stabilization of multiple integrators with bounded controls this paper deals with the global stabilization of a chain of integrators by means of bounded feedback two nonlinear control laws made of summation of saturation of the state are proposed the first one extends that of sussmann sontag and yang 1994 ieee transactions on automatic control 39 12 2411 2425 and the second proposes variable saturation level to improve the performance both remain very simple and significantly improve the efficiency of the approach which is very competitive with respect to the other existing methods especially for its performance complexity ratio the robustness with respect to measurement delay and model uncertainty is numerically tested

a general result on the stabilization of linear systems using bounded controls we present two constructions of controllers that globally stabilize linear systems subject to control saturation we allow essentially arbitrary saturation functions the only conditions imposed on the system are the obvious necessary ones namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold one of the constructions is in terms of a neural network type one hidden layer architecture while the other one is in terms of cascades of linear maps and saturations

an exact method for the stability analysis of time delayed linear time invariant lti systems a general class of linear time invariant systems with time delay is studied recently they attracted considerable interest in the systems and control community the complexity arises due to the exponential type transcendental terms in their characteristic equation the transcendentality brings infinitely many characteristic roots which are cumbersome to elaborate as evident from the literature a number of methodologies have been suggested with limited ability to assess the stability in the parametric domain of time delay this study offers an exact structured and robust methodology to bring a closure to the question at hand ultimately we present a unique explicit analytical expression in terms of the system parameters which not only reveals the stability regions pockets in the domain of time delay but it also declares the number of unstable characteristic roots at any given pocket the method starts with the determination of all possible purely imaginary resonant characteristic roots for any positive time delay to achieve this a simplifying substitution is used for the transcendental terms in the characteristic equation it is proven that the number of such resonant roots for a given dynamics is finite each one of these roots is created by infinitely many time delays which are periodically distributed an interesting property is also claimed next that the root crossing directions at these locations are invariant with respect to the delay and dependent only on the crossing frequency these two unique findings facilitate a simple and practical stability method which is the highlight of the work

finite spectrum assignment of unstable time delay systems with a safe implementation the instability mechanisms related to the implementation of distributed delay controllers in the context of finite spectrum assignment were studied in detail in the past few years in this note we introduce a distributed delay control law that assigns a finite closed loop spectrum and whose implementation with a sum of point wise delays is safe this property is obtained by implicitly including a low pass filter in the control loop this leads to a closed loop characteristic quasipolynomial of retarded type and not one of neutral type which was shown to be a cause of instability in previous schemes

null controllability of linear systems with constrained controls the paper considers the problem of steering the state of a linear time varying system to the origin when the control is subject to magnitude constraints necessary and sufficient conditions are given for global constrained controllability as well as a necessary and sufficient condition for the existence of a control satisfying the constraints which steers the system to the origin from a specified initial epoch x 0 t 0 the global result does not require zero to be an interior point of the control set omega and the theorem for constrained controllability at x 0 t 0 only requires that omega be compact not that it contain zero the results are compared to those available in the literature furthermore numerical aspects of the problem are discussed as is a technique for determining a steering control

controller design for a class of nonlinear systems with input saturation using convex optimization abstract in this paper we propose a new design strategy for nonlinear systems with input saturation the resulting nonlinear controllers are locally asymptotically stabilizing the origin the proposed methodology is based on exact feedback linearization which is used to reformulate the nonlinear system as a linear system having state dependent input saturation linear saturating state feedback controllers and soft variable structure controllers are developed based on this system formulation the resulting convex optimization problems can be written in terms of linear matrix inequalities and sum of squares conditions for which efficient solvers exist polynomial approximation based on legendre polynomials is used to extend the methodology to a more general class of nonlinear systems to demonstrate the benefit of this design method a stabilizing controller for a single link manipulator with flexible joint is developed

a novel nested non linear feedback law for global stabilisation of linear systems with bounded controls a novel nested non linear feedback law for global stabilisation of a chain of integrators with bounded controls is proposed which can be directly applied on the system without state transformation as soon as a so called stable polynomial is constructed then the so called state dependent saturation function is introduced into this novel nested non linear feedback law to replace the standard saturation function which can significantly improve the convergence performance of the closed loop system the results are then extended to a wider class of linear system that can be globally stabilised by bounded controls two numerical examples show the effectiveness of the proposed approach

a unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback we study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties our approach relies on well known h sub spl infin linear control tools and allows one to recover and improve in the unifying framework of a semiglobal separation result existing results on the semiglobal stabilization via output feedback in particular we discuss the case of uncorrupted outputs input and output nonlinearities or model uncertainties which may include for example practical situations such as backlash hysteresis and saturations the key feature of our design procedure is given by the choice of two continuous functions the first one is instrumental in constructing a stabilizing controller the second one arises in the candidate lyapunov function for the closed loop system relying on our main theorem we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems

semi global stabilization of linear systems with position and rate limited actuators abstract it is shown that if a linear system is asymptotically null controllable with bounded controls then when subject to both actuator position and rate saturation it is semi globally stabilizable by linear state feedback if in addition the system is also detectable then it is semi global stabilizable via linear output feedback

eigenfunctions of composite hermitian operators with application to discrete and continuous radiating systems some properties and applications of hermitian operators composed of any integral operator and its adjoint are studied such operators arise in array and aperture antenna theory and the eigenfunctions of the corresponding hermitian operators form complete sets for the expansion of sources and fields in their respective regions the eigenfunctions with the largest eigenvalue form a source and field pair which radiate the largest power under a fixed source norm constraint and can be used for example to maximize power transferred from an array to a point or from one aperture to a second aperture

a circle criterion for strong integral input to state stability abstract we present sufficient conditions for integral input to state stability iiss and strong iiss of the zero equilibrium pair of continuous time forced lur e systems where by strong iiss we mean the conjunction of iiss and small signal iss our main results are reminiscent of the complex aizerman conjecture and the well known circle criterion we derive a number of corollaries including a result on stabilisation by static feedback in the presence of input saturation in particular we identify classes of forced lur e systems with saturating nonlinearities which are strongly iiss but not iss

an algebraic approach to bounded controllability of linear systems in this paper we present an algebraic approach to the proof that a linear system with matrices a b is null controllable using bounded inputs if and only if it is null controllable with unbounde

on finite gain stabilizability of linear systems subject to input saturation this paper deals with global finite gain input output stabilization of linear systems with saturated controls for neutrally stable systems it is shown that the linear feedback law suggested by the passivity approach indeed provides stability with respect to every l p norm explicit bounds on closed loop gains are obtained and they are related to the norms for the respective systems without saturation these results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple size 1 jordan blocks contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state space sense this is shown in particular for the double integrator

an are approach to semi global stabilization of discrete time descriptor linear systems with input saturation the semi global stabilization problem of discrete time descriptor linear systems with input saturation is considered by exploring the properties of the solutions to a class of parametric discrete time riccati equations for discrete time descriptor linear system and their associated feedback gains both the state feedback and output feedback semi global stabilization problem are solved by linear feedback without any system decomposition on the original descriptor linear system a numerical example is used to show the effectiveness of the proposed approach

saturated stabilization for an uncertain cascaded system subject to an oscillator abstract this paper investigates saturated stabilization of an uncertain cascaded system that consists of an uncertain double integrator and an uncertain oscillator the saturation reduction analysis is carried out by using the time interval based contradiction approach while the exponential stability analysis of the corresponding reduced system is conducted by using the hurwitz lemma in doing the saturation reduction analysis an intractable problem is how to estimate the states of the oscillator fully using the property of saturation functions as well as the technique of lyapunov inequalities we can first estimate the states of the oscillator and then achieve the time derivative bounds that some saturated terms possess in a finite time this has helped to carry out the saturation reduction analysis as the applications of the suggested algorithm the stabilizing controllers have been provided for two benchmark systems the uncertain two mass spring and the translational oscillator with a rotational actuator tora

exact characterization of invariant ellipsoids for single input linear systems subject to actuator saturation we present a necessary and sufficient condition for an ellipsoid to be an invariant set of a linear system under a saturated linear feedback the condition is given in terms of linear matrix inequalities lmis and can be easily used for optimization based analysis and design

antenna synthesis and optimization using generalized characteristic modes a set of modes called generalized characteristic modes is described previously developed characteristic modes exhibit orthogonality properties over an obstacle surface as well as the complete sphere at infinity the generalized characteristic modes described here also exhibit orthogonality properties over the obstacle surface but rather than showing orthogonality over the sphere at infinity they are orthogonal over any region of space similar to generalized inagaki modes theories developed for antenna pattern synthesis and directivity optimization using generalized inagaki modes can be applied in an entirely parallel fashion using generalized characteristic modes comparisons are made between generalized characteristic modes and generalized inagaki modes through three examples

brief stability region for a class of open loop unstable linear systems theory and application a new method to calculate the stability region of scalar systems with one unstable pole subject to control limitations is derived and used to determine the conditions for a maximum stabilizer controller the results are illustrated by means of two numerical examples and experiments on the real compass d tokamak

output feedback stabilization and approximate and restricted tracking for a class of cascaded systems in this note we discuss the problems of output feedback stabilization for a class of cascaded systems and of approximate and restricted output regulation for general nonlinear systems it is shown that global output feedback stabilization for a class of systems in feedforward form can be achieved with a dynamic feedback law yielding bounded control and relying on the introduction of a reduced order observer the above result together with standard tools borrowed from the output regulator theory is instrumental to construct dynamic control laws achieving approximate disturbance rejection and output tracking in the presence of small disturbance reference signals generated by a known exosystem

guaranteed stability regions of linear systems with actuator saturation using the low and high gain technique the stability regions of input saturated linear systems are examined with attention focused on state feedback lq control the results describe hyper ellipsoidal domains which are subsets of the actual domain of attraction for the system this is not new the novelty is in the use of the low and high gain technique to reduce conservatism in the results in addition to the standard regulator the tracking case is treated and some comments are made regarding other extensions

on the stabilization of feedforward systems with bounded control abstract for the global asymptotic stabilization of nonlinear controllable in the first approximation cascades consisting of a globally asymptotically locally exponentially stable system driving a stable system a lyapunov like design is proposed this yields bounded control laws where the control magnitude can be chosen arbitrarily large this result provides an alternative to classical forwarding

semi global exponential stabilization of linear systems subject to input saturation via linear feedbacks abstract it is known that a linear time invariant system subject to input saturation can be globally asymptotically stabilized if it has no eigenvalues with positive real parts it is also shown by fuller 1997 and sussmann and yang 1991 that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws in this paper we show the existence of linear state feedback and or output feedback control laws for semi global exponential stabilization rather than global asymptotic stabilization of such systems we explicitly construct linear static state feedback laws and or linear dynamic output feedback laws that semi globally exponentially stabilize the given system our results complement the negative result of fuller 1977 and sussmann and yang 1991

robust global stabilization of a class of uncertain feedforward nonlinear systems abstract the problem of global asymptotically stabilizing a certain class of uncertain feedforward nonlinear systems is considered the control law is obtained by nesting saturation functions whose amplitude can be rendered arbitrarily small with respect to previous works on the subject the design procedure is able to deal with uncertain possibly time varying parameters ranging within the prescribed compact sets which can affect also the linear approximation of the system the small gain theorem for nonlinear systems which are input to state stable with restrictions is shown to be a key tool for designing a state feedback saturated control law

numerical bifurcation analysis of delay differential equations numerical methods for the bifurcation analysis of delay differential equations ddes have only recently received much attention partially because the theory of ddes smoothness boundedness stability of solutions is more complicated and less established than the corresponding theory of ordinary differential equations as a consequence no established software packages exist at present for the bifurcation analysis of ddes we outline existing numerical methods for the computation and stability analysis of steady state solutions and periodic solutions of systems of ddes with several constant delays

the almost disturbance decoupling problem with internal stability for linear systems subject to input saturation state feedback case abstract we consider the almost disturbance decoupling problem addp and or almost d bounded disturbance decoupling problem addp d with internal stability for linear systems subject to input saturation and input additive disturbance via linear static state feedback we show that the almost d bounded disturbance decoupling problem with local asymptotic stability addp las d is always solvable via linear static state feedback as long as the system in the absence of input saturation is stabilizable no matter where the poles of the open loop system are and the locations of these poles play a role only in the solution of addp gas d addp sgas d or addp gas where semi global or global asymptotic stability is required

a parametric lyapunov equation approach to the design of low gain feedback low gain feedback has found several applications in constrained control systems robust control and nonlinear control low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero such feedback gains can be constructed either by an eigenstructure assignment algorithm or through the solution of a parametric algebraic riccati equation are the eigenstructure assignment approach leads to feedback gains in the form of a matrix polynomial in the parameter while the are approach requires the solution of an are for each value of the parameter this note proposes an alternative approach to low gain feedback design based on the solution of a parametric lyapunov equation such an approach possesses the advantages of both the eigenstructure assignment approach and the are based approach it also avoids the possible numerical stiffness in solving a parametric are and the structural decomposition of the open loop system that is required by the eigenstructure assignment approach

simple saturated designs for ancbc systems and extension to feedforward nonlinear systems this article re examines the robust stabilisation of the asymptotically null controllable with bounded controls ancbc systems and extends the established algorithm to a wide class of feedforward nonlinear systems whose nominal dynamics contains both multiple integrators and multiple oscillators based on the notion of converging input bounded state cibs rather than small input small state siss the computation burden in sussmann et al sussmann h j sontag e d and yang y 1994 a general result on the stabilization of linear systems using bounded controls ieee transactions on automatic control 39 2411 2425 is reduced and a class of simple saturated control laws is presented for the cibs stabilisation of ancbc systems then by combining the technique of dealing with higher order terms the algorithm for ancbc systems is extended to feedforward nonlinear systems

continuation of eigenvalues and invariant pairs for parameterized nonlinear eigenvalue problems invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding generalized eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter in this work we consider nonlinear eigenvalue problems that depend on an additional parameter and our interest is to track several eigenvalues as this parameter varies based on the concept of invariant pairs a theoretically sound and reliable numerical continuation procedure is developed particular attention is paid to the situation when the procedure approaches a singularity that is when eigenvalues included in the invariant pair collide with other eigenvalues for the real generic case it is proven that such a singularity only occurs when two eigenvalues collide on the real axis it is shown how this situation can be handled numerically by an appropriate expansion of the invariant pair the viability of our continuation procedure is illustrated by a numerical example

reliably computing all characteristic roots of delay differential equations in a given right half plane using a spectral method spectral discretization methods are well established methods for the computation of characteristic roots of time delay systems in this paper a method is presented for computing all characteristic roots in a given right half plane in particular a procedure for the automatic selection of the number of discretization points is described this procedure is grounded in the connection between a spectral discretization and a rational approximation of exponential functions first a region that contains all desired characteristic roots is estimated second the number of discretization points is selected in such a way that in this region the rational approximation of the exponential functions is accurate finally the characteristic roots approximations obtained from solving the discretized eigenvalue problem are corrected up to the desired precision by a local method the effectiveness and robustness of the procedure are illustrated with several examples and compared with dde biftool

exponential stabilization of singularly perturbed switched systems subject to actuator saturation this paper considers the problem of exponential stabilization for a class of singularly perturbed switched systems subject to actuator saturation a time dependent switching law is designed to obtain the exponential stabilization conditions of the switched systems with unstabilizable subsystems based on the multiple lyapunov functions method depending on singular perturbation parameters a domain of attraction is constructed furthermore in order to maximize an estimate of the domain of attraction convex optimization problems are formulated finally a numerical example is presented in order to illustrate the effectiveness of the established results

technical communique the lambert w function and the spectrum of some multidimensional time delay systems in this note we find an explicit expression for the eigenvalues of a retarded time delay system with one delay for the special case that the system matrices are simultaneously triangularizable which includes the case where they commute using matrix function definitions we define a matrix version of the lambert w function from which we form the expression we prove by counter example that some expressions in other publications on lambert w for time delay systems do not always hold

mapping based algorithm for large scale computation of quasi polynomial zeros a method for computing all zeros of a retarded quasi polynomial that are located in a large region of the complex plane is presented the method is based on mapping the quasi polynomial and on utilizing asymptotic properties of the chains of zeros first the asymptotic exponentials of the chains are determined based on the distribution diagram of the quasi polynomial secondly large regions free of zeros are defined finally the zeros are located as the intersection points of the zero level curves of the real and imaginary parts of the quasi polynomial which are evaluated over the areas of the region outside those free of zeros

stability analysis of time delay systems using a contour integral method in this paper we propose a contour integral method for computing the rightmost characteristic roots of systems of linear time delay differential equations ddes these roots are very important in the context of stability analysis of the time delay systems the effectiveness of the proposed method is illustrated by some numerical experiments

global stabilization with low computational cost of the discrete time chain of integrators by means of bounded controls this note proposes a bounded nonlinear control law composed of saturation functions for the discrete time chain of integrators a dynamical adaptation rule of the saturation levels involved in the control law is proposed to improve the closed loop performances the note unifies the original work of yang 1997 with static saturation level and convergence improvements that recently appeared in the continuous time case the possible ranges for the controller s parameters are extended with respect to existing results

discrete time l and l2 norm vanishment and low gain feedback with their applications in constrained control the existing low gain feedback which is a parameterized family of stabilizing state feedback gains whose magnitudes approach zero as the parameter decreases to zero has been designed in very specific ways in this paper by recognizing the l and l 2 slow peaking phenomenon that exists in discrete time systems under low gain feedback more general notions of l and l 2 norm vanishment are considered so as to provide a full characterization of the nonexistence of slow peaking phenomenon in some measured signals low gain feedback that does not lead to l and l 2 slow peaking in the control input are respectively referred to as l and l 2 low gain feedback based on the notions of l and l 2 vanishment not only can the existing low gain feedback be recognized as an l low gain feedback but also a new design approach referred to as the l 2 low gain feedback approach is developed for discrete time linear systems parallel to the effectiveness of l low gain feedback in magnitude constrained control the l 2 low gain feedback is instrumental in the control of discrete time systems with control energy constraints the notions of l and l 2 vanishment also result in a systematic approach to the design of l and l 2 low gain feedback by providing a family of solutions including those resulting from the existing design methods

antenna synthesis and optimization using weighted inagaki modes inagaki modes represent a new modal formalism for problems of radiation and scattering from arbitrary discrete and continuous structures these modes can be generalized to be orthogonal over any sector of the sphere at infinity as well as the source region itself theory and application of these modes to problems of pattern synthesis and array optimization including constraints are presented examples are given for a line source an array of printed dipoles and a dipole array in free space

some special cases in the stability analysis of multi dimensional time delay systems using the matrix lambert w function this paper revisits a recently developed methodology based on the matrix lambert w function for the stability analysis of linear time invariant time delay systems by studying a particular yet common second order system we show that in general there is no one to one correspondence between the branches of the matrix lambert w function and the characteristic roots of the system furthermore it is shown that under mild conditions only two branches suffice to find the complete spectrum of the system and that the principal branch can be used to find several roots and not the dominant root only as stated in previous works the results are first presented analytically and then verified by numerical experiments

control of linear systems subject to time domain constraints with polynomial pole placement and lmis this note focuses on the control of continuous time linear systems subject to time domain constraints input amplitude limitation output overshoot on closed loop signals using recent results on positive polynomials it is shown that finding a youla kuc spl breve era polynomial parameter of fixed degree hence a controller of fixed order such that time domain constraints are satisfied amounts to solving a convex linear matrix inequality lmi optimization problem as soon as distinct strictly negative closed loop poles are assigned by pole placement proceeding this way time domain constraints are handled by an appropriate choice of the closed loop zeros

a unique methodology for the stability robustness of multiple time delay systems abstract the stability robustness is considered for linear time invariant lti systems with rationally independent multiple time delays against delay uncertainties the problem is known to be notoriously complex primarily because the systems are infinite dimensional due to delays multiplicity of the delays in this study complicates the analysis even further and rationally independent feature of the delays makes the problem prohibitively challenging as opposed to the tds with commensurate time delays where time delays are rationally related a unique framework is described for this broadly studied problem and the enabling propositions are proven we show that this procedure analytically reveals all possible stability regions exclusively in the space of the delays as an added strength it does not require the delay free system under consideration to be stable our methodology offers a resolution to this question which has been studied from variety of directions in the past four decades none of these respectable investigations can however deliver an exact and exhaustive robustness declaration from this stand point the new method has a unique contribution

properties of the parametric lyapunov equation based low gain design with applications in stabilization of time delay systems this technical note studies some properties of the recently developed parametric lyapunov equation based low gain feedback design method as applications of these new properties alternative and simpler solutions are proposed to the global stabilization problem for a class of linear systems with input delay and the semi global stabilization problem when the systems are in addition subject to actuator saturation besides the simplicity in their construction the new solutions can also be easily scheduled online to achieve global result in the presence of input saturation

semi global exponential stabilization of linear discrete time systems subject to input saturation via linear feedbacks abstract in this paper we show that a linear discrete time system subject to input saturation is semi globally exponentially stabilizable via linear state and or output feedback laws as long as the system in the absence of input saturation is stabilizable and detectable and has all its poles located inside or on the unit circle furthermore the semi globally stabilizing feedback laws are explicitly constructed the results presented here are parallel to our earlier results on the continuous time counterpart lin and saberi 1993

on antenna array design using orthogonal modes antenna array design using orthogonal modes has been extensively studied in the past the design procedure is based on the projection of an arbitrary array factor on a basis defined by a set of orthogonal modes on the array structure a design method is presented that relies on the construction of an orthogonal basis using the gram schmidt orthonormalization method moreover simplifications of the orthogonal projection are provided reducing the computational complexity of the design procedure finally the validity of the method is displayed with a design example