modelling and finite time stability analysis of psoriasis pathogenesis a new systems model of psoriasis is presented and analysed from the perspective of control theory cytokines are treated as actuators to the plant model that govern the cell population under the reasonable assumption that cytokine dynamics are faster than the cell population dynamics the analysis of various equilibria is undertaken based on singular perturbation theory finite time stability and stabilisation have been studied in various engineering applications where the principal paradigm uses non lipschitz functions of the states a comprehensive study of the finite time stability properties of the proposed psoriasis dynamics is carried out it is demonstrated that the dynamics are finite time convergent to certain equilibrium points rather than asymptotically or exponentially convergent this feature of finite time convergence motivates the development of a modified version of the michaelis menten function frequently used in biology this framework is used to model cytokines as fast finite time actuators

nonlinear feedback design for fixed time stabilization of linear control systems two types of nonlinear control algorithms are presented for uncertain linear plants controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions the control design procedure uses block control principles and finite time attractivity properties of polynomial feedbacks controllers of the second type are modifications of the second order sliding mode control algorithms they provide global finite time stability of the closed loop system and allow to adjust a guaranteed settling time independently on initial conditions control algorithms are presented for both single input and multi input systems theoretical results are supported by numerical simulations

finite time attractive ellipsoid method implicit lyapunov function approach abstracta finite time version based on implicit lyapunov functions ilfs for the attractive ellipsoid method aem is developed based on this a robust control scheme is presented to ensure finite time convergence of the solutions of a chain of integrators with bounded output perturbations to a minimal ellipsoidal set the control parameters are obtained by solving a minimisation problem of the size of the ellipsoid subject to a set of linear matrix inequalities lmis constraints and by applying the implicit function theorem a numerical example is presented to support the implementability of these theoretical results

hybrid zero dynamics of planar biped walkers planar underactuated biped walkers form an important domain of applications for hybrid dynamical systems this paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree of freedom greater than the number of available actuators the within step control action creates an attracting invariant set a two dimensional zero dynamics submanifold of the full hybrid model whose restriction dynamics admits a scalar linear time invariant return map exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model a convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed loop exponentially stable walking with low energy consumption while meeting natural kinematic and dynamic constraints the general theory developed in the paper is illustrated on a five link walker consisting of a torso and two legs with knees

robust trajectory tracking for a class of hybrid systems an internal model principle approach this paper deals with the asymptotic tracking of periodic trajectories for hybrid systems having linear dynamics in each operating mode and isolated discrete switching events switching systems parametric uncertainties are considered and the dimension of the state vector is allowed to vary among modes to deal with the hybrid nature of the system and the possible discontinuities of its solutions at switching times a properly amended tracking control problem is defined and a feedback control law based on a discontinuous version of the classical internal model principle is proposed the innovative design of the discrete time dynamics of the compensator guarantees the robust existence of a steady state response giving zero tracking error in the controlled output and local convergence to it

input to state stability of periodic orbits of systems with impulse effects via poincare analysis in this paper we investigate the relation between robustness of periodic orbits exhibited by systems with impulse effects and robustness of their corresponding poincare maps in particular we prove that input to state stability iss of a periodic orbit under external excitation in both continuous and discrete time is equivalent to iss of the corresponding zero input fixed point of the associated forced poincare map this result extends the classical poincare analysis for asymptotic stability of periodic solutions to establish orbital iss of such solutions under external excitation in our proof we define the forced poincare map and use it to construct iss estimates for the periodic orbit in terms of iss estimates of this map under mild assumptions on the input signals as a consequence of the availability of these estimates the equivalence between exponential stability es of the fixed point of the zero input unforced poincare map and the es of the corresponding orbit is recovered the results can be applied naturally to study the robustness of periodic orbits of continuous time systems as well although our motivation for extending classical poincare analysis to address iss stems from the need to design robust controllers for limit cycle walking and running robots the results are applicable to a much broader class of systems that exhibit periodic solutions

finite time stability conditions for non autonomous continuous systems finite time stability is defined for continuous non autonomous systems starting with a result from haimo 1986 we then extend this result to n dimensional non autonomous systems through the use of smooth and non smooth lyapunov functions as in perruquetti and drakunov 2000 one obtains two different sufficient conditions and a necessary one for finite time stability of continuous non autonomous systems

reset adaptive observer for a class of nonlinear systems this technical note proposes a novel kind of state estimator called reset adaptive observer reo a reo is an adaptive observer consisting of an integrator and a reset law that resets the output of the integrator depending on a predefined condition the main contribution of this technical note is that the reset element theory is applied for the first time to the nonlinear adaptive observer framework the introduction of the reset element in the adaptive law can decrease the overshooting and settling time of the estimation process without sacrificing the rising time the stability and convergence lmi based analysis of the proposed reo is addressed and additionally an easily computable method to determine the l2 gain of the reo dealing with noise corrupted systems is presented

on associated polynomials and decay rates for birth death processes abstract we consider sequences of orthogonal polynomials and pursue the question of how partial knowledge of the orthogonalizing measure for the associated polynomials can lead to information about the orthogonalizing measure for the original polynomials in particular we relate the supports of the two measures and their moments as an application we analyse the relation between two decay rates connected with a birth death process

a large family of semi classical polynomials the perturbed chebyshev some results concerning finite perturbations of order s of the chebyshev polynomials are shown their semi classical character follows from the stieltjes transform of their orthogonality measure according to the choice of the perturbation parameters polynomials of arbitrary class can be generated the second order differential equation satisfied by these polynomials is obtained and several examples are worked out some particular cases of this differential equation had already been obtained by shohat and allaway

finite time semistability and consensus for nonlinear dynamical networks this paper focuses on semistability and finite time stability analysis and synthesis of systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we merge the theories of semistability and finite time stability to develop a rigorous framework for finite time semistability in particular finite time semistability for a continuum of equilibria of continuous autonomous systems is established continuity of the settling time function as well as lyapunov and converse lyapunov theorems for semistability are also developed in addition necessary and sufficient conditions for finite time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite time semistable if and only if it is semistable and has a negative degree of homogeneity unlike previous work on homogeneous systems our results involve homogeneity with respect to semistable dynamics and require us to adopt a geometric description of homogeneity finally we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time

finite time observers application to secure communication in this paper control theory is used to formalize finite time chaos synchronization as a nonlinear finite time observer design issue this paper introduces a finite time observer for nonlinear systems that can be put into a linear canonical form up to an output injection the finite time convergence relies on the homogeneity properties of nonlinear systems the observer is then applied to the problem of secure data transmission based on the finite time chaos synchronization and the two channel transmission method

on an output feedback finite time stabilization problem studies the problem of finite time output feedback stabilization for the double integrator system a class of output feedback controllers that can achieve global finite time stability for the double integrator system are constructed based on a finite time separation principle furthermore it is shown that the closed loop system resulting from our control law can maintain its local finite time stability regardless of some nonlinear perturbations thus our control law actually applies to a large class of nonlinear second order systems

continuous finite time stabilization of the translational and rotational double integrators a class of bounded continuous time invariant finite time stabilizing feedback laws is given for the double integrator lyapunov theory is used to prove finite time convergence for the rotational double integrator these controllers are modified to obtain finite time stabilizing feedback that avoid unwinding

invertibility of switched nonlinear systems this article addresses the invertibility problem for switched nonlinear systems affine in controls the problem is concerned with reconstructing the input and switching signal uniquely from given output and initial state we extend the concept of switch singular pairs introduced recently to nonlinear systems and develop a formula for checking if the given state and output form a switch singular pair a necessary and sufficient condition for the invertibility of switched nonlinear systems is given which requires the invertibility of individual subsystems and the nonexistence of switch singular pairs when all the subsystems are invertible we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs detailed examples are included to illustrate these newly developed concepts

switched mode feedback control laws for nonholonomic systems in extended power form abstract a class of nonholonomic control systems in extended power form is studied it is demonstrated that under appropriate assumptions lagrange s equations including classical nonholonomic constraints can be transformed into the extended power form a switched mode feedback controller is used to obtain global convergence of the states of the extended power form to the origin this feedback controller can be interpreted as a hybrid system consisting of a high level discrete event supervisor and a family of low level feedback controllers the closed loop system exhibits finite time responses

finite perturbations of orthogonal polynomials in this paper we study orthogonal polynomials pn which arise from a given system of orthogonal polynomials pn by a finite perturbation of the recurrence coefficients i e the recurrence coefficients n n 1 of pn respectively n n 1 of pn are related to each other by n l n m and n 1 l n 1 m for n n where l and m are fixed nonnegative integers closed expressions for the polynomial pn in terms of pn and its associated polynomial pn 1 1 as well as for the orthogonality measure of pn in terms of the orthogonality measure of pn are given in fact the results are presented for the most general case when is an arbitrary not necessarily positive measure

exponential stabilization of an underactuated autonomous surface vessel this paper studies the problem of controlling the planar position and orientation of an autonomous surface vessel using two independent thrusters it is first shown that although the system is not asymptotically stabilizable to a given configuration using a time invariant continuous feedback it is strongly accessible and small time locally controllable at any equilibrium time invariant discontinuous feedback laws are then constructed to asymptotically stabilize the system to the desired configuration with exponential convergence rates a simulation example is included to demonstrate the results

regularization of the indefinite stieltjes moment problem abstract a not regular indefinite stieltjes moment problem is studied in the generalized stieltjes class n k the new class of the sequence s s i i 0 l is defined which is called regular class regularization of the indefinite stieltjes moment problem is obtained the set of solutions of this problem is found in terms of the generalized stieltjes polynomials and s fractions with the shift

on orthogonal polynomials with perturbed recurrence relations abstract orthogonal polynomials may be fully characterized by the following recurrence relation pn x x n 1 pn 1 x n 1pn 2 x with p0 x 1 p1 x x 0 and n 0 here we study how the structure and the spectrum of these polynomials get modified by a local perturbation in the and parameters of a co recursive k k co dilated k k and co modified k k k k nature for an arbitrary but fixed kth element 1 k specifically stieltjes functions differential equations and distributions of zeros as well as representations of the new perturbed polynomials in terms of the old unperturbed ones are given this type of problems is strongly related to the boundary value problems of finite difference equations and to the quantum mechanical study of physical many body systems atoms molecules nuclei and solid state systems

finite time controllers continuous finite time differential equations are introduced as fast accurate controllers for dynamical systems these have qualities superior to controllers which are currently in use in such appl

rational spectral transformations and orthogonal polynomials abstract we show that generic rational transformations of the stieltjes function with polynomial coefficients st can be presented as a finite superposition of four fundamental elementary transforms christoffel transform ct geronimus transform gt and forward and backward associated transformations a t a t it is shown that the laguerre hahn polynomials lhp on arbitrary nonuniform lattice are covariant with respect to st i e st of a lhp yields another lhp whereas the semi classical polynomials are covariant with respect to a subclass of linear st some applications of these results to the theory of the semi classical polynomials are considered

global finite time stabilization via time varying feedback for uncertain nonlinear systems this paper focuses on the global finite time stabilization via time varying state feedback for a class of uncertain time varying nonlinear systems the problem is rather difficult to solve mainly due to the presence of more serious unknowns and time variations and higher nonlinearities in the systems under investigation particularly those in the control coefficients of the systems to solve the problem by skillfully combining time varying methods and finite time control theory in the existing literature a novel time varying nonadaptive design scheme is successfully proposed to finite time stabilizing controllers the remarkable feature of the design scheme is the selection of time varying design functions which can capture the unknowns and time variations in the systems as time increases it is shown that if the design parameters and design functions in the designed controller are suitably chosen then all the signals i e the system states and control input of the closed loop system are globally

continuous uniform finite time stabilization of planar controllable systems continuous homogeneous controllers are utilized in a full state feedback setting for the uniform finite time stabilization of a perturbed double integrator in the presence of uniformly decaying piecewise continuous disturbances semiglobal strong mathcal c 1 lyapunov functions are identified to establish uniform asymptotic stability of the closed loop planar system uniform finite time stability is then proved by extending the homogeneity principle of discontinuous systems to the continuous case with uniformly decaying piecewise continuous nonhomogeneous disturbances a finite upper bound on the settling time is also computed the results extend the existing literature on homogeneity and finite time stability by both presenting uniform finite time stabilization and dealing with a broader class of nonhomogeneous disturbances for planar controllable systems while also proposing a new class of homogeneous continuous controllers

on co polynomials on the real line abstract in this paper we study new algebraic and analytic aspects of orthogonal polynomials on the real line when finite modifications of the recurrence coefficients the so called co polynomials on the real line are considered we investigate the behavior of their zeros mainly interlacing and monotonicity properties furthermore using a transfer matrix approach we obtain new structural relations combining theoretical and computational advantages finally a connection with the theory of orthogonal polynomials on the unit circle is pointed out

a simply stabilized running model the spring loaded inverted pendulum slip or monopedal hopper is an archetypal model for running in numerous animal species although locomotion is generally considered a complex task requiring sophisticated control strategies to account for coordination and stability we show that stable gaits can be found in the slip with both linear and air springs controlled by a simple fixed leg reset policy we first derive touchdown to touchdown poincare maps under the common assumption of negligible gravitational effects during the stance phase we subsequently include and assess these effects and briefly consider coupling to pitching motions we investigate the domains of attraction of symmetric periodic gaits and bifurcations from the branches of stable gaits in terms of nondimensional parameters

trajectory tracking for a particle in elliptical billiards an infinitely rigid unitary mass particle is considered moving on a planar region delimited by a rigid elliptical barrier elliptical billiards under the action of proper control forces a class of periodic trajectories involving an infinite sequence of non smooth impacts between the mass and the barrier at fixed times is found by using an lmis based procedure the jumps in the velocities at the impact times render difficult if not impossible to obtain the classical stability and attractivity properties for the dynamic system describing the tracking error behaviour hence the tracking control problem is properly stated using notions similar to the quasi stability concept in v lakshmikantham d d bainov and p s simeonov theory of impulsive differential equations 6 world scientific 1989 a controller whose state is subject to discontinuities based on the internal model principle is shown to solve the proposed tracking problem giving rise to control forces that are piecewise continuous fun

fourth order differential equations satisfied by the generalized co recursive of all classical orthogonal polynomials a study of their distribution of zeros the unique fourth order differential equation satisfied by the generalized co recursive of all classical orthogonal polynomials is given for any but fixed level of recursivity up to now these differential equations were known only for each classical family separately and also for a specific recursivity level moreover we use this unique fourth order differential equation in order to study the distribution of zeros of these polynomials via their newton sum rules i e the sums of powers of their zeros which are closely related with the moments of such distribution both results are obtained with the help of two programs built in mathematica symbolic language

a monotone method for constructing extremal solutions to fourth order periodic boundary value problems in this paper we describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problemu 4 t f t u t u t email protected 0 email protected u 0 u email protected u 0 u email protected u 0 u email protected u 0 u email protected in the presence of an upper solution b and a lower solution a with b a

orthogonal polynomials with a constant recursion formula and an application to harmonic analysis on calcule la mesure pour laquelle une suite de polynomes avec une formule de recurrence constante est orthogonale

fourth order differential equations for numerator polynomials the author gives explicitly the fourth order differential equation satisfied by the numerator polynomials associated polynomials of the classical orthogonal polynomials the coefficients of the differential equation are at most a quadratic combination of the polynomials sigma and tau and their derivatives defined via the relation sigma rho te this differential equation is therefore valid for the jacobi laguerre hermite and bessel associated polynomials

existence of multiple positive periodic solutions for delay differential equation whose order is a multiple of 4 abstract this article shows the existence of positive periodic solutions for retarded advanced neutral and ordinary differential equations whose order is a multiple of 4 first we find a positive green s function explicitly then assuming that the coefficient of the unknown in the linear part of the equation is bounded above and below by positive constants we find one and then three solutions by applying the krasnoselskii and legget william fixed point theorems

global finite time stabilisation by output feedback for a class of uncertain nonlinear systems this article considers the problem of global finite time stabilisation by output feedback for a class of nonlinear systems comprised of a chain of power integrators perturbed by an uncertain vector field to solve the problem we first construct a homogeneous observer and controller in a recursive way for the nominal system without the perturbing nonlinearities then using the homogeneous domination approach we scale the homogeneous observer and controller with an appropriate choice of gain to render the uncertain nonlinear system globally finite time stable due to the use of a reduced order observer the proposed output feedback controller is applicable to those systems with unknown gains associated with the power integrators

positive quadrature formulas iii asymptotics of weights first we discuss briefly our former characterization theorem for positive interpolation quadrature formulas abbreviated qf provide an equivalent characterization in terms of jacobi matrices and give links and applications to other qf in particular to gauss kronrod quadratures and recent rediscoveries then for any polynomial t n which generates a positive qf a weight function depending on n is given with respect to which t n is orthogonal to p n 1 with the help of this result an asymptotic representation of the quadrature weights is derived in general the asymptotic behaviour is different from that of the gaussian weights only under additional conditions do the quadrature weights satisfy the so called circle law corresponding results are obtained for positive qf of radau and lobatto type

rapidly exponentially stabilizing control lyapunov functions and hybrid zero dynamics this paper addresses the problem of exponentially stabilizing periodic orbits in a special class of hybrid models systems with impulse effects through control lyapunov functions the periodic orbit is assumed to lie in a c1 submanifold z that is contained in the zero set of an output function and is invariant under both the continuous and discrete dynamics the associated restriction dynamics are termed the hybrid zero dynamics the orbit is furthermore assumed to be exponentially stable within the hybrid zero dynamics prior results on the stabilization of such periodic orbits with respect to the full order dynamics of the system with impulse effects have relied on input output linearization of the dynamics transverse to the zero dynamics manifold the principal result of this paper demonstrates that a variant of control lyapunov functions that enforce rapid exponential convergence to the zero dynamics surface z can be used to achieve exponential stability of the periodic orbit in the full order dynamics thereby significantly extending the class of stabilizing controllers the main result is illustrated on a hybrid model of a bipedal walking robot through simulations and is utilized to experimentally achieve bipedal locomotion via control lyapunov functions

nonlinear control of mechanical systems with an unactuated cyclic variable numerous robotic tasks associated with underactuation have been studied in the literature for a large number of these in the plane the mechanical models have a cyclic variable the cyclic variable is unactuated and all shape variables are independently actuated this paper formulates and solves two control problems for this class of models if the generalized momentum conjugate to the cyclic variable is not conserved conditions are found for the existence of a set of outputs that yields a system with a one dimensional exponentially stable zero dynamics i e an exponentially minimum phase system along with a dynamic extension that renders the system locally input output decouplable if the generalized momentum conjugate to the cyclic variable is conserved a reduced system is constructed and conditions are found for the existence of a set of outputs that yields an empty zero dynamics along with a dynamic extension that renders the system feedback linearizable a common element in these two feedback problems is the construction of a scalar function of the configuration variables that has relative degree three with respect to one of the input components the function arises by partially integrating the conjugate momentum the results are illustrated on two balancing tasks and on a ballistic flip motion

global set stabilisation of the spacecraft attitude using finite time control technique in this article we revisit the classical problem of attitude stabilisation for a rigid spacecraft with external disturbances a global set stabilisation method using finite time control technique is proposed in the absence of disturbances the states of the closed loop system will be stabilised in finite time to a set consisting of two equilibria in the presence of disturbances the states will be stabilised to a neighbourhood of this set by constructing a particular lyapunov function it is proved that the closed loop system satisfies global set stability the control method in this article is based on set control idea and thus is more natural and energy efficient numerical simulation results show the effectiveness of the method

finite time output feedback stabilization of high order uncertain nonlinear systems this paper studies the problem of finite time output feedback stabilization for a class of high order nonlinear systems with the unknown output function and control coefficients under the

on the associated orthogonal polynomials abstract by using the second order recurrence relation this paper gives some new results on associated orthogonal polynomials without referring to the continued fractions tool some results are very useful for obtaining the second order differential equation satisfied by the semi classical orthogonal polynomials hendriksen and van rossum 1985 maroni 1987 cf section 3 also the main formula derives from proposition 2 6 by which the fourth order differential equation satisfied by some laguerre hahn polynomials magnus 1984 is obtained cf belmehdi and ronveaux 1989 dini 1989 ronveaux 1990

periodic motion planning for virtually constrained euler lagrange systems the paper suggests an explicit form of a general integral of motion for some classes of dynamical systems including n degrees of freedom euler lagrange systems subject to n 1 virtual holonomic

properties of the polynomials associated with the jacobi polynomials abstract power forms and jacobi polynomial forms are found for the polynomials w associated with jacobi polynomials also some differential difference equations and evalua tions of certain integrals involving wii 1 are given 1 introduction let w be a nonnegative function defined on an interval a b forwhich all momentsm j x w x dx n 0 1 exist and are finite m0 0 let be the monic polynomials orthogonal on a b with respect to w the polynomials 1 1 q x n pax rztt wu at pn t jt n 0 1 j a x are called the polynomials associated with the pn as is well known pn x a x are linearly independent solutions of the recurrence formula i 2 yn i x a y bny x q 0 1 where l3 an xpn p p pn n 0 o o b pn pn pn x pn x n l and f g f f x g x w x dx ja the initial conditions arep i x 0 pa x 1

limit cycle generation for a class of non linear systems with jumps using a low dimensional predictive control in this paper it is shown that using a low dimensional non linear predictive control scheme provably stable limit cycles can be obtained for open loop non linear systems with unstable equilibrium point a particular case where the limit cycle may be reduced to a single point in the state space can be obtained which corresponds to asymptotic stabilization the system may present hybrid nature in the sense that discontinuities jump phenomena on the state evolution may be handled the proposed feedback scheme holds for classical jump free systems as a particular case the proposed strategy is illustrated through two examples a jump free system the ball and beam and a non linear hybrid dynamical system including state jumps the modified impulsive lorenz chaotic system

observer based finite time robust control of nonlinear time delay systems via hamiltonian function method this paper investigates the observer based finite time robust control problem of a general class of nonlinear time delay systems via hamiltonian function method and proposes some new finite time r

the weight functions generating functions and miscellaneous properties of the sequences of orthogonal polynomials of the second kind associated with the jacobi and the gegenbauer polynomials abstract in the introduction the main object of the paper namely the calculation and study of the weight functions and orthogonality relations corresponding to the sequences of polynomials of the second kind associated with the jacoby and the gegenbauer polynomials is briefly discussed section 2 contains the underlying theory restricted to the citation of a few general formulas regarding the orthogonality property of associated polynomials of the second kind section 3 which deals with the application to the case of the jacobi polynomials p n z n n starts with the construction of the orthogonality relation and the weight function 1 of the associated polynomials for arbitrary gt 1 the denominator of the fraction representing 1 comprises the principal value of an integral which is studied in detail in order to bring it in an explicit form most suited for practical use attention is also paid to the associated functions of the second kind and some of their properties next in a subsection 1 is expressed solely in terms of elementary functions in a number of special cases involving subsets of pairs when 1 1 n gt 1 1 1 gt0 and 1 0 gt 1 in another subsection the generating function for the associated polynomials is calculated and the analysis of the result comprises some related formulas in the final subsection the moments of the weight function 1 with respect to 0 1 and 1 are expressed in terms of the corresponding moments of the weight function of the jacobi polynomials both in finite determinantal form and by means of a recurrence relation in section 4 which concerns the application to the case of the gegenbauer polynomials c v n z n n the advantages of a new definition of the associated polynomials of the second kind are at first expounded then follow the orthogonality relation and the weight function 1 for arbitrary v gt 1 2 next 1 is calculated in terms of elementary functions for all integer and half odd integer values of v exceeding 1 2 in the former case a remarkable simplification occurs in the denominator of the fraction representing 1 after that follow three subsections devoted respectively to the functions of the second kind associated with the gegenbauer polynomials two different generating functions for the associated polynomials and related formulas and the moments of the weight function 1 the paper ends with two appendices in which certain types of sums are reduced to a one term expression

finite time consensus in networks of integrator like dynamic agents with directional link failure this technical note proposes a general class of nonlinear protocols in the form of continuous state feedbacks for finite time consensus in networks of integrator like dynamic agents with directional link failure these protocols with adjustable terms are applicable in a wide range of situations such as with input saturation restrictions and with convergence rate constraints based on the assumption of a common positive dwell time for all active information links it is shown that if the union of the interaction topology over some fixed length of time always contains a spanning tree then the system will solve an asymptotical consensus problem in addition if the length sum of time intervals over which the interaction topology contains a spanning tree is larger than a threshold determined by the state differences between agents then the system will solve a finite time consensus problem the validity of the protocols is proven in the case with external reference inputs finally simulations are presented to demonstrate the effectiveness of the theoretical results

switching and pi control of walking motions of planar biped walkers a companion paper has addressed the problem of designing controllers that induce exponentially stable periodic walking motions at a fixed walking rate for a planar biped robot with one degree of underactuation this note provides two additional control features 1 the ability to compose such controllers to obtain walking at several discrete walking rates with guaranteed stability during the transitions and 2 the ability to regulate the average walking rate to a continuum of values

szegő transformations and nth order associated polynomials on the unit circle in this paper we analyze the stieltjes functions defined by the szego inverse transformation of a nontrivial probability measure supported on the unit circle such that the corresponding sequence of orthogonal polynomials is defined by either backward or forward shifts in their verblunsky parameters such polynomials are called anti associated respectively associated orthogonal polynomials thus rational spectral transformations appear in a natural way

technical communique finite time stability theorem of stochastic nonlinear systems a new concept of finite time stability called stochastically finite time attractiveness is defined for a class of stochastic nonlinear systems described by the ito differential equation the settling time function is a stochastic variable and its expectation is finite a theorem and a corollary are given to verify the finite time attractiveness of stochastic systems based on lyapunov functions two simulation examples are provided to illustrate the applications of the theorem and the corollary established in this paper

periodic boundary value problems for nonlinear higher order ordinary differential equations we study a class of boundary value problems for linear and nonlinear ordinary differential equations of higher order we study the solution set and present a maximum principle as a consequence we show the validity of the monotone method and obtain the extremal solutions between the upper and lower solutions

finite time stability and stabilization of a class of continuous systems abstract finite time stability is investigated for continuous system x f x which satisfies uniqueness of solutions in forward time a necessary and sufficient condition for finite time stability is given for this class of systems using lyapunov functions then a necessary and sufficient condition is developed for finite time stabilization of class cl k affine systems x f x g x u involving a class cl 0 settling time function for the closed loop system finally an explicit feedback control is addressed by using a control lyapunov function verifying a certain inequality

robust finite time output feedback stabilisation of the double integrator the problem of finite time output stabilization of the double integrator is addressed applying the homogeneity approach a homogeneous controller and a homogeneous observer are designed for different degrees of homogeneity ensuring the finite time stabilization their combination under mild conditions is shown to stay homogeneous and finite time stable as well robustness and effects of discretization on the obtained closed loop system are analyzed the efficiency of the obtained solution is demonstrated in computer simulations

spectral transformations self similar reductions and orthogonal polynomials we study spectral transformations in the theory of orthogonal polynomials which are similar to darboux transformations for the schr dinger equation linear transformations of the stieltjes function with coefficients that are rational in the argument are constructed as iterations of the christoffel and geronimus transformations we describe a characteristic property of semi classical orthogonal polynomials scop on the uniform and the exponential lattice namely that all these polynomials can be obtained through simple quasi periodic and q periodic self similar closures of the chain of linear spectral transformations in the self similar setting a characterization of the laguerre hahn polynomials on linear and q linear lattices is obtained by considering rational transformations of the stieltjes function generated by transitions to the associated polynomials

stability of time delay feedback switched linear systems we address stability of state feedback switched linear systems in which delays are present in both the feedback state and the switching signal of the switched controller for switched systems with average dwell time switching signals we provide a condition in terms of upper bounds on the delays and in terms of a lower bound on the average dwell time to guarantee asymptotic stability of the closed loop the condition also implies that in general feedback switched linear systems are robust with respect to both small state delays and small switching delays our approach combines existing multiple lyapunov function techniques with the merging switching signal technique which gives relationships between the average dwell times of two mismatched switching signals and their mismatched times a methodology for numerical solution based on linear matrix inequality is also included

virtual holonomic constraints for euler lagrange systems this technical brief investigates virtual holonomic constraints for euler lagrange systems with n degrees of freedom and n 1 controls in our framework a virtual holonomic constraint is a relation specifying n 1 configuration variables in terms of a single angular configuration variable the enforcement by feedback of such a constraint induces a desired repetitive behavior in the system we give conditions under which a virtual holonomic constraint is feasible i e it can be made invariant by feedback and it is stabilizable we provide sufficient conditions under which the dynamics on the constraint manifold correspond to an euler lagrange system these ideas are applied to the problem of swinging up an underactuated pendulum while guaranteeing that the second link does not fall over

global adaptive finite time stabilization of uncertain time varying p normal nonlinear systems without homogeneous growth nonlinearity restriction the problem of global finite time stabilization for p normal nonlinear systems subject to uncertain time varying control coefficients and vanishing nonlinear uncertainties without homogeneous growth restriction is investigated in this paper by virtue of the technique of homogeneous domination a new dual layer adaptive approach is presented to address the uncertainties and nonlinearities of the system for one layer of the adaptive mechanism a nonlinear adaptive parameter estimator is proposed to reconstruct the upper bounds of the unknown uncertainties for the other an explicit construction approach of a new adaptive dynamic gain mechanism is presented for the first time to cope with the uncertain time varying control coefficients of the p normal nonlinear systems it is shown that the global boundedness of the systems under consideration is guaranteed by the presented approach and in addition the time taken to converge to the equilibrium is rendered to be finite time

hybrid invariant manifolds in systems with impulse effects with application to periodic locomotion in bipedal robots motivated by the problem of controlling walking in a biped with series compliant actuation this paper develops two main theorems relating to the stabilization of periodic orbits in systems with impulse effects the first main result shows that when a periodic orbit of a system with impulse effects lies within a hybrid invariant manifold there exist local coordinate transforms under which the jacobian linearization of the poincare return map has a block upper triangular structure one diagonal block is the linearization of the system as restricted to the hybrid invariant manifold also called the hybrid zero dynamics the other is the product of two sensitivity matrices related to the transverse dynamics one pertaining to the impact map and the other pertaining to the closed loop vector field when either of these sensitivity matrices is sufficiently close to zero the stability of the return map is determined solely by the stability of the hybrid zero dynamics the second main result of the paper details the construction of a hybrid invariant manifold such as that required by the first main theorem forward invariance follows from the methods of byrnes and isidori and impact invariance is achieved by a novel construction of impact updated control parameters in addition to providing impact invariance the construction allows entries of the impact sensitivity matrix of the transverse dynamics to be made arbitrarily small a simulation example is provided where stable walking is achieved in a 5 link biped with series compliant actuation

implicit lyapunov krasovski functionals for stability analysis and control design of time delay systems the method of implicit lyapunov krasovski functional ilkf for stability analysis of time delay systems is introduced theorems on lyapunov asymptotic hyper exponential finite time and fixed time stability analysis using ilkf are presented the hyper exponential stabilization algorithm for a time delay system is presented the theoretical result is supported by numerical simulation

finite time stabilization of fractional order uncertain chain of integrator an integral sliding mode approach in this technical note a novel methodology for robust finite time stabilization of a chain of uncertain fractional order integrator is proposed this is achieved by first designing a nominal controller which stabilizes the system in finite time an integral sliding mode like surface and a switching controller is proposed such that when the system is on the surface the equivalent value of the integral sliding mode control is the negative of the disturbance and hence the disturbance is cancelled an improved strategy with more general kind of uncertainty is also proposed numerical examples are presented to illustrate the proposed methods

on co recursive orthogonal polynomials and their application to potential scattering abstract let pn x n 0 be a system of polynomials orthogonal with respect to a positive definite moment functional and satisfying the recurrence relation pn x x cn pn 1 x npn 2 x n 1 2 where p0 x 1 and p 1 x 0 the corresponding co recursive orthogonal polynomials p n x n 0 satisfy the same recurrence relations except for n 1 where now p 1 x x c 1 0 and p 0 x 1 the p n are orthogonal with respect to a moment functional which is positive definite for 0 and quasi definite for p n x separation theorems true interval of orthogonality etc can be determined from those of the pn x these polynomials occur in the l2 solution of the radial schrodinger equation for a separable potential where pn x is the tchebichef polynomial of the second kind in the case of s waves

a general method for deriving some semi classical properties of perturbed second degree forms we present a new general method and the corresponding symbolic algorithm psdf for deriving some semi classical properties of perturbed second degree forms namely the stieltjes function the stieltjes equation the functional equation the class a structure relation and the second order linear differential equation we give new explicit results for some perturbed of order 3 of the second kind chebyshev polynomials

the method of lower and upper solutions for second third fourth and higher order boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u n t t u t u i a u i b i r i 0 n 1 where is a caratheodory function we obtain necessary and sufficient conditions in to guarantee the existence of solutions between a lower solution and an upper solution for n 2 if n 3 either or and n 4 if furthermore we obtain sufficient conditions in for n 2 k 6 when