mild solutions of non autonomous second order problems with nonlocal initial conditions abstract in this paper we establish the existence of mild solutions for a non autonomous abstract semi linear second order differential equation submitted to nonlocal initial conditions our approach relies on the existence of an evolution operator for the corresponding linear equation and the properties of the hausdorff measure of non compactness

l_ infty and l_ 2 low gain feedback their properties characterizations and applications in constrained control low gain feedback has found several applications in constrained control robust control and nonlinear control in this paper we first generalize the existing low gain design methods by introducing the notion of l vanishment and by providing a full characterization of feedback gains that achieve such a property we observe that l low gain feedback can lead to energy peaking namely the control energy required by l low gain feedback increases toward infinity as the low gain parameter decreases to zero motivated by this observation we consider the notion of l2 vanishment and establish several of its characterizations based on which a new design approach referred to as the l2 low gain feedback approach for linear systems is developed different from the l low gain feedback the l2 low gain feedback is instrumental in the control of systems with control energy constraints as an application of l2 low gain feedback the problem of semiglobal stabilization of linear systems with control energy constraints is solved in this paper the notions of l and l2 vanishment also allow us to establish a systematic approach to the design of l and l2 low gain feedback the advantage of this new design approach is that it results in a family of control laws including those resulting from the existing design methods

stabilization of nonlinear systems via forwarding mod l sub g v forwarding is a tool for constructing stabilizers for nonlinear systems a key step in this design technique is to find an explicit solution to a partial differential equation pde which may be hard to find actually the pde may even not be solvable at all in this paper we show that it is possible to provide an additional degree of freedom for the solution of the aforementioned pde hence effectively extending the realm of application of the forwarding methodology our contribution is illustrated with the example of an inverted pendulum with a disk inertia

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

stabilization of linear systems in the presence of output measurement saturation this note considers siso nonlinear systems which have a linear controllable and observable part followed by a measurement saturation nonlinearity a controller is presented which feeds back only the saturating output measurements and nevertheless globally asymptotically stabilizes the system the equilibrium is actually reached in finite time i e the controller is dead beat

technical communique semi global stabilization of linear time delay systems with control energy constraint this note is concerned with the problem of semi globally stabilizing a linear system with an input delay and a constraint on the energy of its input under the condition of null controllability with vanishing energy the parametric lyapunov equation based l 2 low gain feedback is adopted to solve the problem the proposed approach is applied to the linearized model of the relative motion in the orbit plane of a spacecraft with respect to another spacecraft in a circular orbit around the earth to validate its effectiveness

further facts about input to state stabilization previously published results about input to state stabilizability are shown to hold even for systems which are not linear in controls provided that a more general type of feedback is allowed applications to certain stabilization problems and coprime factorizations as well as comparisons to other results on input to state stability are briefly discussed

surfaces of general type with p_g q 1 k 2 8 and bicanonical map of degree 2 we classify the minimal algebraic surfaces of general type with pg q 1 k 2 8 and bicanonical map of degree 2 it will turn out that they are isogenous to a product of curves i e if s is such a surface then there exist two smooth curves c f and a finite group g acting freely on c x f such that s c x f g we describe the c f and g that occur in particular the curve c is a hyperelliptic bielliptic curve of genus 3 and the bicanonical map of s is composed with the involution induced on s by r x id c x f c x f where is the hyperelliptic involution of c in this way we obtain three families of surfaces with pg q 1 k 2 8 which yield the first known examples of surfaces with these invariants we compute their dimension and we show that they are three generically smooth irreducible components of the moduli space m of surfaces with p g q 1 k 2 8 moreover we give an alternative description of these surfaces as double covers of the plane recovering a construction proposed by du val

semi global stabilization of linear systems subject to output saturation abstract it is established that a siso linear stabilizable and detectable system subject to output saturation can be semi globally stabilized by linear output feedback if all its invariant zeros are in the closed left half plane no matter where the open loop poles are this result complements a recent result that such systems can always be globally stabilized by discontinuous nonlinear feedback laws and can be viewed as dual to a well known result a linear stabilizable and detectable system subject to input saturation can be semi globally stabilized by linear output feedback if all its poles are in the open left half plane no matter where the invariant zeros are

towards a generic constructive nonlinear control design tool using relaxed control in this technical note we revisit a control design approach for general non affine nonlinear systems using relaxed control using the notion of relaxed input where the ordinary real valued control input is replaced by a measure valued control input we are able to manipulate the original system such that the resulting relaxed system is amenable to control we show the applicability of using relaxed input for transforming a non affine nonlinear system into an affine one such that the relaxed system has desirable control properties finally we present a practical implementation of relaxed input via ordinary control input which is based on the sampled data of the relaxed input

the tate conjecture for a family of surfaces of general type with p g q 1 and k 2 3 we prove a big monodromy result for a smooth family of complex algebraic surfaces of general type with invariants p g q 1 and k 2 3 that has been introduced by catanese and ciliberto this is accomplished via a careful study of degenerations as corollaries when a surface in this family is defined over a finitely generated extension of bbb q we verify the semisimplicity and tate conjectures for the galois representation on the middle ell adic cohomology of the surface

resolvent positive operators resolvent positive operators on an ordered banach space with generating and normal positive cone are by definition linear possibly unbounded operators whose resolvent exists and is positive on a right half line even though these operators are defined by a simple purely algebraic condition analogues of the basic results of the theory of q semigroups can be proved for them in fact if a is resolvent positive and has a dense domain then the cauchy problem associated with a has a unique solution for every initial value in the domain of a and the solution is positive if the initial value is positive also the converse is true if we assume that a has a non empty resolvent set and d a n e is dense in moreover every positive resolvent is a laplace stieltjes transform of a so called integrated semigroup and conversely every such increasing non degenerate integrated semigroup defines a unique resolvent positive operator

on impulsive functional differential inclusions with hille yosida operators in banach spaces abstract we consider a semilinear functional differential inclusion with infinite delay and impulse characteristics in a banach space assuming that its linear part is a non densely defined hille yosida operator we assume that the multivalued nonlinearity of upper caratheodory or almost lower semicontinuous type satisfies a regularity condition expressed in terms of the measures of noncompactness we apply the theory of integrated semigroups and the theory of condensing multivalued maps to obtain local and global existence results the application to an optimization problem for an impulsive feedback control system is given

integral action in output feedback for multi input multi output nonlinear systems we address a particular problem of output regulation for multi input multi output nonlinear systems specifically we are interested in making the stability of an equilibrium point and the regulation to zero of an output robust to small unmodelled discrepancies between design model and actual system in particular those introducing an offset we propose a novel procedure which is intended to be relevant to realistic scenarios as illustrated by a non academic example

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

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

constrained stabilization problems for linear plants linear systems with magnitude and rate constraints on both the state and control variables are considered for such systems semi global and global constrained stabilization problems are formulated when state feedback controllers are used necessary and sufficient conditions for the solvability of the formulated problems are developed moreover design methodologies for such constrained stabilization problems are presented an important aspect of our development here is a taxonomy of constraints to show clearly for what type of constraints what can or cannot be achieved

a remark on the stability of interconnected nonlinear systems we use a notion of generalized l sub 2 gain for nonlinear systems where the gain is considered as a function of the state instead of a global constant for characterizing stability properties of interconnected systems the obtained results generalize the well known small gain theorem

on the tate and mumford tate conjectures in codimension 1 for varieties with h2 0 1 we prove the tate conjecture for divisor classes and the mumford tate conjecture for the cohomology in degree 2 for varieties with h 1 over a finitely generated field of characteristic 0 under a mild assumption on their moduli as an application of this general result we prove the tate and mumford tate conjectures for several classes of algebraic surfaces with pg 1 ams 2010 mathematics subject classification 14c 14d 14j20

existence and controllability results for impulsive partial functional differential inclusions abstract in this paper we prove the existence and the controllability of mild and extremal mild solutions for first order semilinear densely defined impulsive functional differential inclusions in separable banach spaces with local and nonlocal conditions

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

global stabilization of the multiple integrators system by delayed and bounded controls this note is concerned with global stabilization of multiple integrators by delayed and bounded controllers three types of new nonlinear control laws are proposed based on some special canonical forms and explicit conditions are proposed to guarantee the global stability of the closed loop systems differently from the existing canonical forms the new special canonical forms used in this note contain not only time delay in the input but also time delays in its state which are essential in the recursive design since they lead to natural cancellation moreover some free parameters are introduced into these controllers these advantages can help to improve the transient performance of the closed loop system significantly numerical simulations for the fourth order integrators illustrate that the proposed new controllers can indeed outperform the existing one

brief paper decentralized control design of interconnected chains of integrators a case study we develop a constructive decentralized control design procedure for a class of systems that may be loosely described as chained integrators which are dynamically coupled the design method is inspired by nested saturation control ideas and formulated by applying the singular perturbation theory we demonstrate that the proposed design provides a lyapunov function for an associated closed loop system from which semi global stability may be deduced using the proposed idea we design a semi globally stabilizing control law for a four degree of freedom spherical inverted pendulum

on the shafarevich and tate conjectures for hyperkahler varieties 1 problems and results 2 polarized hyperk ihler varieties and cubic fourfoids 3 the period mapping 4 the kuga satake construction 5 the kuga satake construction in the relative setting 6 proof of theorem 1 5 1 7 proof of theorem 1 6 1 8 descent 9 proof of theorem 1 3 1 appendix 1 spinorial shimura varieties appendix 2 a short proof of the hodge conjecture for cubic fourfolds 205 210 212 216 220 224 229 233 240 244 245

controllability of neutral functional differential systems in abstract space in this paper by using fractional power of operators and sadovskii fixed point theorem we study the controllability and the local controllability of abstract neutral functional differential systems with unbounded delay as application an example is provided to illustrate the obtained results

a universal formula for stabilization with bounded controls abstract we provide a formula for stabilizing feedback law using a bounded control under the assumption that an appropriate control lyapunov function is known such a feedback smooth away from the origin and continuous everywhere is known to exist via artstein s theorem as in the unbounded control case treated in a previous note we provide an explicit and universal formula given by an algebraic function of lie derivatives in particular we extended to the bounded case the result that the feedback can be chosen analytic if the lyapunov function and the vector fields defining the system are analytic

existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions abstract in this paper we shall establish sufficient conditions for the existence of integral solutions and extremal integral solutions for some nondensely defined impulsive semilinear functional differential inclusions in separable banach spaces we shall rely on a fixed point theorem for the sum of completely continuous and contraction operators the question of controllability of these equations and the topological structure of the solutions set are considered too

stabilization of feedforward systems approximated by a non linear chain of integrators we prove that for any odd integer p and any strictly positive integer n feedforward systems which are approximated at the origin by a chain of integrators of degree p and length n can be globally asymptotically stabilized by bounded smooth time invariant state feedbacks our proof is based on the construction of a lyapunov function and the feedback laws we obtain are given by explicit formulas

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

fixed point theorems for discontinuous multivalued operators on ordered spaces with applications in this paper some fixed point theorems for discontinuous multivalued operators on ordered spaces are proved these theorems improve the earlier known fixed point theorems of 1 2 the main fixed point theorems are applied to first order discontinuous differential inclusions for proving the existence of extremal solutions under certain monotonicity conditions

controllability of fractional evolution nonlocal impulsive quasilinear delay integro differential systems in this work the controllability result of a class of fractional evolution nonlocal impulsive quasilinear delay integro differential systems in a banach space has been established by using the theory of fractional calculus fixed point technique and also we introduced a new concept called a u resolvent family as an application that illustrates the abstract results an example is given

global stabilization of linear systems via bounded controls abstract this paper is concerned with global stabilization of linear systems by bounded controls two types of nonlinear control laws with one made of cascade connections of saturation functions and the other one consisting of nested connections of saturation functions are firstly proposed for multiple integrators system the possible ranges for the controllers parameters are extended with respect to existing results simultaneously the so called state dependent saturation functions are introduced into these two types of control laws to replace the standard saturation functions which can improve the transient performance of the closed loop system significantly the results are then extended to a class of linear systems that can be globally stabilized by bounded controls an illustrative example is presented to show the effectiveness and advantages of the proposed approaches

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

global stabilization of a chain of integrators with input saturation and disturbances a new approach in this article we solve the problem of global stabilization for a chain of integrators in the presence of input saturation and disturbances a novel and elegant approach to solve this problem in the absence of disturbances was proposed by teel 1992 using saturation functions and coordinate transformation with teel s work as a foundation many results have been proposed to improve the performance of controllers for a chain of integrators naturally all such approaches also inherited the limitations of teel s approach most importantly in the presence of uncertainties and disturbances the transformation introduced in teel 1992 would considerably shrink the region where the controller is unsaturated and severely limit the level of uncertainties and disturbances which can be tolerated in order to overcome these difficulties a conceptually different approach which does not rely on the coordinate transformation is presented in this work specifically modified saturation functions are directly applied to the tracking error of actual states as opposed to transformed fictitious states to develop a globally stable controller the proposed controller is less conservative in terms of the level of uncertainties and disturbances which can be handled in addition arbitrarily good disturbance rejection in the unsaturated region can be achieved theoretically comparative simulation studies performed on a third order integrator chain verified the effectiveness of the proposed scheme

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

saturated rise feedback control for a class of second order nonlinear systems a saturated controller is developed for a class of uncertain second order nonlinear systems which includes time varying and nonlinearly parameterized functions with bounded disturbances using a continuous control law with smooth saturation functions based on the robust integral of the sign of the error rise control methodology the developed controller is able to utilize the benefits of high gain control strategies while guaranteeing saturation limits are not surpassed the bounds on the control are known a priori and can be adjusted by changing the feedback gains the saturated controller yields asymptotic tracking despite model uncertainty and added disturbances in the dynamics experimental results using a two link robot manipulator demonstrate the performance of the developed controller

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

period relations and the tate conjecture for hilbert modular surfaces introduction 319 a sketch of the proof 320 0 notation and preliminaries 322 1 statement of the main results 328 2 twisting correspondences 331 3 period relations 334 4 hodge cycles 339 5 tare cycles 340 6 poles of l functions 341 7 abelian varieties 342 8 concluding remarks and open questions 343 acknowledgements 344 bibliography 344

a geometric characterization of feedforward forms this note addresses the problem of local coordinates and feedback equivalence of single input affine nonlinear systems to feedforward forms in particular using the notions of invariant and controlled invariant distributions we provide necessary and sufficient conditions for a general affine in control nonlinear system to be locally coordinates or feedback equivalent to a system in strict feedforward form for illustration the general theory is applied to a simple four dimensional system describing the dynamics of a food chain

brief paper an improved treatment of saturation nonlinearity with its application to control of systems subject to nested saturation this paper is concerned with the treatment of saturation nonlinearity existing commonly in practical control systems an improved treatment of such nonlinearity is proposed which includes the well known linear differential inclusion method for handling saturation nonlinearity as a special case to show the effectiveness of this new treatment the problem of analysis and design of linear systems subject to nested saturation function is revisited the proposed results not only complement the existing work on this problem but also are less conservative than the existing methods four numerical examples are worked out to illustrate the applicability of the established approaches

controllability of evolution inclusions with nonlocal conditions in this paper we examine controllability problems of evolution inclusions with nonlocal conditions using kakutani s fixed point theorem and schauder s fixed point theorem we establish sufficient conditions for the controllability under convex and nonconvex orientor fields respectively

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

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

finite time state feedback stabilisation of stochastic high order nonlinear feedforward systems abstractthis paper studies the finite time state feedback stabilisation of stochastic high order nonlinear feedforward systems based on the stochastic lyapunov theorem on finite time stability by using the homogeneous domination method the adding one power integrator and sign function method constructing a c2 lyapunov function and verifying the existence and uniqueness of solution a continuous state feedback controller is designed to guarantee the closed loop system finite time stable in probability

stabilization of positive linear systems we consider stabilization of equilibrium points of positive linear systems which are in the interior of the first orthant the existence of an interior equilibrium point implies that the system matrix does not possess eigenvalues in the open right half plane this allows to transform the problem to the stabilization problem of compartmental systems which is known and for which a solution has been proposed already we provide necessary and sufficient conditions to solve the stabilization problem by means of affine state feedback a class of stabilizing feedbacks is given explicitly

stabilization of multiple input multiple output linear systems with saturated outputs we consider linear time invariant multiple input multiple output systems that are controllable and observable where each output component is saturated we demonstrate by constructive design that such systems can be globally asymptotically stabilized by output feedback without further restrictions this result is an extension of a previous result by kreisselmeier for single input single output systems the control strategy consists of driving the components of the output vector out of saturation one by one to identify the state of the system deadbeat control is then applied to drive the state to the origin

nonlinear impulse evolution systems and applications to population models abstract we apply results on the existence uniqueness and stability of solutions obtained previously for the abstract impulse evolution system to the study of the mathematical model of population subject to abrupt changes of important biological parameters caused by harvesting diseases immigration etc

asymptotically almost periodic solutions of abstract differential equations abstract in this paper we are concerned with the problem of existence and uniqueness of asymptotically almost periodic mild solutions of nonhomogeneous first order abstract differential equations essentially we obtain existence of asymptotically almost periodic solutions when the semigroup is asymptotically almost periodic or when the forcing term is an asymptotically stepanov almost periodic function

local existence and stability for some partial functional differential equations with infinite delay we study the existence regularity and stability of solutions for some partial functional dierential equations with infinite delay we assume that the linear part is not necessarily densely defined and satisfies the hille yosida condition on a banach space x the nonlinear term takes its values in space larger than x namely the extrapolated favard class of the extrapolated semigroup corresponding to the linear part our approach is based on the theory of the extrapolation spaces

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

on improving transient performance in global control of multiple integrators system by bounded feedback abstract the global stabilization problem for multiple integrators systems by bounded control is considered two classes of nonlinear feedback laws are proposed the first one consisting of nested saturation functions is a modification and generalization of that in a r teel global stabilization and restricted tracking for multiple integrators with bounded controls systems control letters 18 3 1992 165 171 and the other one consists of parallel connections of saturation functions both these two types of nonlinear feedback laws need only n n n 2 if n is even and n n 1 2 if n is odd where n is the length of the multiple integrators saturation elements furthermore the poles of the closed loop system can be placed on any location of the left real axis when none of the saturation elements in the control laws is saturated both of them exhibit simpler structure can significantly improve the transient performance of the closed loop system and are very superior to the other existing methods simulation of a fourth order system is used to illustrate the effectiveness of the proposed methods

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

decentralized robust stabilization for large scale feedforward non linear systems in this paper we consider the decentralized robust stabilization problem for large scale feedforward non linear systems which possess an upper triangular structure while in the decentralized control area the commonly studied large scale feedback non linear systems possess a lower triangular structure our decentralized robust stabilizer for each subsystem takes a nested saturation feedback with the saturation levels satisfying a set of equations and inequalities global asymptotic stability of the closed loop large scale system has been proved and a simulation example is given