convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled data systems under dwell time constraints stability analysis and control of linear impulsive systems is addressed in a hybrid framework through the use of continuous time time varying discontinuous lyapunov functions necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas extensions to the stability of aperiodic systems under minimum maximum and ranged dwell times are then derived by exploiting further the particular structure of the stability conditions the results are non conservatively extended to quadratic stability analysis of linear uncertain impulsive systems these stability criteria are in turn losslessly extended to stabilization using a particular yet broad enough class of state feedback controllers providing then a convex solution to the open problem of robust dwell time stabilization of impulsive systems using hybrid stability criteria relying finally on the representability of sampled data systems as impulsive systems the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled data systems are straightforwardly solved using the same ideas several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach

quotients of fully nonlinear control systems in this paper we introduce and study quotients of fully nonlinear control systems our definition is inspired by categorical definitions of quotients as well as recent work on abstractions of affine control systems we show that quotients exist under mild regularity assumptions and characterize the structure of the quotient state input space this allows one to understand how states and inputs of the quotient system are related to states and inputs of the original system we also introduce a notion of projectability which turns out to be equivalent to controlled invariance this allows one to regard previous work on symmetries partial symmetries and controlled invariance as leading to special types of quotients we also show the existence of quotients that are not induced by symmetries or controlled invariance such decompositions have a potential use in a theory of hierarchical control based on quotients

stabilization of hybrid stochastic differential equations by feedback control based on discrete time state observations recently mao 2013 discusses the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations mao 2013 also obtains an upper bound on the duration between two consecutive state observations however it is due to the general technique used there that the bound on is not very sharp in this paper we will consider a couple of important classes of hybrid sdes making full use of their special features we will be able to establish a better bound on our new theory enables us to observe the system state less frequently so costs less but still to be able to design the feedback control based on the discrete time state observations to stabilize the given hybrid sdes in the sense of mean square exponential stability

controlled lagrangians and the stabilization of mechanical systems ii potential shaping for pt i see ibid vol 45 p 2253 70 2000 we extend the method of controlled lagrangians cl to include potential shaping which achieves complete state space asymptotic stabilization of mechanical systems the cl method deals with mechanical systems with symmetry and provides symmetry preserving kinetic shaping and feedback controlled dissipation for state space stabilization in all but the symmetry variables potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables the approach also extends the method of controlled lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline

stability of time delay systems equivalence between lyapunov and scaled small gain conditions it is demonstrated that many previously reported lyapunov based stability conditions for time delay systems are equivalent to the robust stability analysis of an uncertain comparison system free of delays via the use of the scaled small gain lemma with constant scales the novelty of this note stems from the fact that it unifies several existing stability results under the same framework in addition it offers insights on how new less conservative results can be developed

moment stability of nonlinear stochastic systems with time delays based on cal h representation technique in this note moment stability of nonlinear stochastic systems with time delays is investigated based on a kind of kronecker algebra and the h representation technique we obtain the second order moment equations of nonlinear stochastic systems with time delays by the comparison principle and the established moment equations we get the comparative systems of the nonlinear stochastic systems with time delays then we establish moment stability theorems for the systems with the stability properties of the comparative systems finally an example is presented to illustrate the efficiency of our results

optimal control for holonomic and nonholonomic mechanical systems with symmetry and lagrangian reduction in this paper we establish necessary conditions for optimal control using the ideas of lagrangian reduction in the sense of reduction under a symmetry group the techniques developed here are designed for lagrangian mechanical control systems with symmetry the benefit of such an approach is that it makes use of the special structure of the system especially its symmetry structure and thus it leads rather directly to the desired conclusions for such systems lagrangian reduction can do in one step what one can alternatively do by applying the pontryagin maximum principle followed by an application of poisson reduction the idea of using lagrangian reduction in the sense of symmetry reduction was also obtained by bloch and crouch proc 33rd cdc ieee 1994 pp 2584 2590 in a somewhat different context and the general idea is closely related to those in montgomery comm math phys 128 1990 pp 565 592 and vershik and gershkovich dynamical systems vii v arnold and s p novikov eds springer verlag 1994 here we develop this idea further and apply it to some known examples such as optimal control on lie groups and principal bundles such as the ball and plate problem and reorientation examples with zero angular momentum such as the satellite with moveable masses however one of our main goals is to extend the method to the case of nonholonomic systems with a nontrivial momentum equation in the context of the work of bloch krishnaprasad marsden and murray arch rational mech anal 1996 to appear the snakeboard is used to illustrate the method

from nonlinear to hamiltonian via feedback mechanical control systems are an especially interesting and important class of nonlinear control systems they possess a rich mathematical structure and yet physical considerations are extremely important for the solution of a large class of control problems we broaden the applicability of design methodologies developed for mechanical control systems by rendering nonlinear control systems mechanical by a proper choice of feedback in particular we characterize which control systems can be transformed to hamiltonian control systems by a feedback transformation

brief paper delay dependent stability of reset systems this work presents results on the stability of time delay systems under reset control the case of delay dependent stability is addressed by developing a generalization of previous stability results for reset systems without delay and also a generalization of the delay independent case the stability results are derived by using appropriate lyapunov krasovskii functionals obtaining lmi linear matrix inequality conditions and showing connections with passivity and positive realness the stability conditions guarantee that the reset action does not destabilize the base lti linear time invariant system several interpretations are given for these conditions in terms of impulsive control which provide insights into the potentials of reset control

tracking for fully actuated mechanical systems a geometric framework we present a general framework for the control of lagrangian systems with as many inputs as degrees of freedom relying on the geometry of mechanical systems on manifolds we propose a design algorithm for the tracking problem the notions of error function and transport map lead to a proper definition of configuration and velocity error these are the crucial ingredients in designing a proportional derivative feedback and feedforward controller the proposed approach includes as special cases a variety of results on control of manipulators pointing devices and autonomous vehicles our design provides particular insight into both aerospace and underwater applications where the configuration manifold is a lie group

consistent abstractions of affine control systems in this paper we consider the problem of constructing abstractions of affine control systems that preserve reachability properties and in particular local accessibility in this framework showing local accessibility of the higher level abstracted model is equivalent to showing local accessibility of the more detailed lower level model given an affine control system and a smooth surjective map we present a canonical construction for extracting an affine control system describing the trajectories of the abstracted variables we then obtain conditions on the abstraction maps that render the original and abstracted system equivalent from a local accessibility point of view such consistent hierarchies of accessibility preserving abstractions of nonlinear control systems are then considered for various classes of affine control systems including linear bilinear drift free and strict feedback systems

delay independent stability of reset systems reset control systems have potential advantages to overcome fundamental limitations of lti compensation however since a reset compensator may destabilize a stable base lti system stability needs to be guaranteed in advance for a proper practical application of reset control this works extends previous stability results of reset control systems to consider the case of lti plants with time delays stability independent of the delay criteria are developed both by means of lmis and in the frequency domain by using the kyp lemma

cal h representation and applications to generalized lyapunov equations and linear stochastic systems this paper introduces an h representation method to express an n2 1 vector x as x h x tilde based on the introduced h representation approach several topics are extensively discussed including the generalized lyapunov equations gles arising from stochastic control stochastic observability generalized d stability and d stabilization weak stability and stabilization a necessary and sufficient condition for the existence and uniqueness of the symmetric and skew symmetric solutions of gles is presented respectively moreover the solution structure of gles is also clarified through the h representation method several necessary and sufficient conditions are also obtained for stochastic observability generalized d stability and d stabilization weak stability and stabilization

some new criteria on p th moment stability of stochastic functional differential equations with markovian switching this note gives some new razumikhin type theorems on th moment stability of stochastic functional differential equations with markovian switching sfdewms by using auxiliary ordinary differential equation the main results of this note allow the diffusion operator associated with the underlying sfdewms of the lyapunov function along a solution of the system to be not always negative an example is provided to illustrate the effectiveness of the proposed results

stability of nontrivial solution of delay differential equations with state dependent impulses this paper considers the stability problem of nontrivial solutions of delay differential equations with state dependent impulses by using the concepts of reduced system and quasi stability the stability problem of a nontrivial solution of the impulsive delay differential equation with state dependent impulses is converted to that of the trivial solution of the impulsive delay differential equation with fixed impulses several stability criteria are then established utilizing the known results for systems with fixed impulses

a power based description of standard mechanical systems this paper is concerned with the construction of a power based modeling framework for mechanical systems mathematically this is formalized by proving that every standard mechanical system with or without dissipation can be written as a gradient vector field with respect to an indefinite metric the form and existence of the corresponding potential function is shown to be the mechanical analog of brayton and moser s mixed potential function as originally derived for nonlinear electrical networks in the early sixties in this way several recently proposed analysis and control methods that use the mixed potential function as a starting point can also be applied to mechanical systems

abstractions of hamiltonian control systems given a control system and a desired property an abstracted system is a reduced system that preserves the property of interest while ignoring modeling detail in previous work abstractions of linear and nonlinear control systems were considered while preserving reachability properties in this paper we consider the abstraction problem for hamiltonian control systems where in addition to the property of interest we also preserve the hamiltonian structure of the control system we show how the hamiltonian structure of control systems can be exploited to simplify the abstraction process we then focus on local accessibility preserving abstractions and provide conditions under which local accessibility properties of the abstracted hamiltonian system are equivalent to the local accessibility properties of the original hamiltonian control system

a converse lyapunov theorem for linear parameter varying and linear switching systems we study families of linear time varying systems where time variations have to satisfy restrictions on the dwell time that is on the minimum distance between discontinuities as well as on the derivative in between discontinuities such classes of systems may be formulated as linear flows on vector bundles the main objective of this paper is to construct parameter dependent lyapunov functions which characterize the exponential growth rate this is possible in the generic irreducible case as an application the gelfand formula is generalized to the class of systems studied here in other words the maximal exponential growth rate may be approximated by only considering the periodic systems in the family of time varying systems a perspective on the question of continuous dependence of the exponential growth rate on the data is given

controllability and motion algorithms for underactuated lagrangian systems on lie groups we provide controllability tests and motion control algorithms for underactuated mechanical control systems on lie groups with lagrangian equal to kinetic energy examples include satellite and underwater vehicle control systems with the number of control inputs less than the dimension of the configuration space local controllability properties of these systems are characterized and two algebraic tests are derived in terms of the symmetric product and the lie bracket of the input vector fields perturbation theory is applied to compute approximate solutions for the system under small amplitude forcing in phase signals play a crucial role in achieving motion along symmetric product directions motion control algorithms are then designed to solve problems of point to point reconfiguration static interpolation and exponential stabilization we illustrate the theoretical results and the algorithms with applications to models of planar rigid bodies satellites and underwater vehicles

uniform asymptotic stability of impulsive delay differential equations abstract in this paper criteria on uniform asymptotic stability are established for impulsive delay differential equations using lyapunov functions and razumikhin techniques it is shown that impulses do contribute to yield stability properties even when the underlying system does not enjoy any stability behavior some examples are also discussed to illustrate the theorems

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network

hierarchically consistent control systems large scale control systems typically possess a hierarchical architecture in order to manage complexity higher levels of the hierarchy utilize coarser models of the system resulting from aggregating the detailed lower level models in this layered control paradigm the notion of hierarchical consistency is important as it ensures the implementation of high level objectives by the lower level system in this paper we define a notion of modeling hierarchy for continuous control systems and obtain characterizations for hierarchically consistent linear systems with respect to controllability objectives as an interesting byproduct we obtain a hierarchical controllability criterion for linear systems from which we recover the best of the known controllability algorithms from numerical linear algebra

necessary and sufficient conditions for 2p th moment stability of several classes of linear stochastic systems this technical note presents necessary and sufficient conditions for 2p th moment stability of several widely used linear stochastic systems by the matrix derivative operator and vectorial ito s formula we first derive two extended systems one is described by stochastic differential equation sde and the other by ordinary differential equation ode it is shown that the stochastic system is 2p th moment exponentially stable if and only if the sde is mean square exponentially stable or the ode is exponentially stable subsequently combining the quasi periodic homogeneous polynomial lyapunov function methods with the proposed techniques a series of nonconservative stability criteria are established for linear impulsive sampled data and switched stochastic systems under dwell time constraints a numerical example illustrates the proposed theoretical results

robust h_ infty filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts in this paper the robust h filtering problem is studied for a class of uncertain nonlinear networked systems with both multiple stochastic time varying communication delays and multiple packet dropouts a sequence of random variables all of which are mutually independent but obey bernoulli distribution are introduced to account for the randomly occurred communication delays the packet dropout phenomenon occurs in a random way and the occurrence probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval the discrete time system under consideration is also subject to parameter uncertainties state dependent stochastic disturbances and sector bounded nonlinearities we aim to design a linear full order filter such that the estimation error converges to zero exponentially in the mean square while the disturbance rejection attenuation is constrained to a give level by means of the h performance index intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the exponential stability as well as prescribed h performance for the overall filtering error dynamics in the presence of random delays random dropouts nonlinearities and the parameter uncertainties these conditions are characterized in terms of the feasibility of a set of linear matrix inequalities lmis and then the explicit expression is given for the desired filter parameters simulation results are employed to demonstrate the effectiveness of the proposed filter design technique in this paper

brief paper stability properties of reset systems stability properties for a class of reset systems such as systems containing a clegg integrator are investigated we present lyapunov based results for verifying l 2 and exponential stability of reset systems our results generalize the available results in the literature and can be easily modified to cover l p stability for arbitrary email protected 1 several examples illustrate that introducing resets in a linear system may reduce the l 2 gain if the reset controller parameters are carefully tuned

brief energy based control for hybrid port controlled hamiltonian systems in this paper we develop an energy based hybrid control framework for hybrid port controlled hamiltonian systems in particular we obtain constructive sufficient conditions for hybrid feedback stabilization that provide a shaped energy function for the closed loop system while preserving a hybrid hamiltonian structure at the closed loop level furthermore an inverse optimal hybrid feedback control framework is developed that characterizes a class of globally stabilizing energy based controllers that guarantee hybrid sector and gain margins to multiplicative input uncertainty of hybrid hamiltonian systems

p th moment exponential input to state stability of delayed recurrent neural networks with markovian switching via vector lyapunov function in this paper the p th moment input to state exponential stability for delayed recurrent neural networks drnns with markovian switching is studied by using stochastic analysis techniques and classical razumikhin techniques a generalized vector mathcal l operator differential inequality including cross item is obtained without additional restrictive conditions on the time varying delay the sufficient criteria on the p th moment input to state exponential stability for drnns with markovian switching are derived by means of the vector mathcal l operator differential inequality when the input is zero an improved criterion on exponential stability is obtained two numerical examples are provided to examine the correctness of the derived results

controlled lagrangians and the stabilization of mechanical systems i the first matching theorem we develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled lagrangians the procedure involves making structured modifications to the lagrangian for the uncontrolled system thereby constructing the controlled lagrangian the euler lagrange equations derived from the controlled lagrangian describe the closed loop system where new terms in these equations are identified with control forces since the controlled system is lagrangian by construction energy methods can be used to find control gains that yield closed loop stability we use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group the procedure is demonstrated for several underactuated balance problems including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane

robust stability and boundedness of nonlinear hybrid stochastic differential delay equations one of the important issues in the study of hybrid stochastic differential delay equations sddes is the automatic control with consequent emphasis being placed on the asymptotic analysis of stability and boundedness in the study of asymptotic properties the robust stability has received a great deal of attention the theory of robust stability shows how much perturbation a given stable hybrid sdde can tolerate so that its perturbed system remains stable almost all results so far on the robust stability require that the underlying sddes be either linear or nonlinear with linear growth condition however little is known on the robust stability of nonlinear hybrid sddes without the linear growth condition which is one of the key topics in this paper the other key topic is the robust boundedness the aim here is to answer the question how much perturbation can a given asymptotically bounded hybrid sdde tolerate so that its perturbed system remains asymptotically bounded

stabilization of hybrid systems by feedback control based on discrete time state observations recently mao automatica j ifac 49 2013 pp 3677 3681 initiated the study the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations in the same paper mao also obtains an upper bound on the duration tau between two consecutive state observations however it is due to the general technique used there that the bound on tau is not very sharp in this paper we will be able to establish a better bound on tau making use of lyapunov functionals we will discuss the stabilization not only in the sense of exponential stability as mao does in automatica j ifac 49 2013 pp 3677 3681 but also in other sense that of h infty stability or asymptotic stability we will consider not only the mean square stability but also the almost sure stability

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

symmetries and conservation laws for hamiltonian systems with inputs and outputs a generalization of noether s theorem the definition of symmetries and conservation laws for autonomous i e without external cases hamiltonian systems are generalized to hamiltonian systems with inputs and outputs it is shown that a symmetry implies the existence of a conservation law and vice versa thereby generalizing noether s theorem for autonomous hamiltonian systems

stability and performance of siso control systems with first order reset elements we consider set point regulation and l2 robust stability properties of a class of reset control systems consisting of a minimum phase relative degree one linear siso plant controlled by a novel first order reset element fore these results rely on necessary and sufficient conditions for exponential and l2 finite gain stability of a class of planar reset systems consisting of a scalar linear plant controlled by the novel fore we show that the l2 gain of the planar reset system decreases to zero as the pole and or the gain of the fore are increased to infinity a number of stability results including lyapunov conditions for lp and exponential stability for a larger class of reset and hybrid systems are presented and used to prove our main results

nonholonomic mechanical systems with symmetry this work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of lagrangian mechanics and with a view to control theoretical applications the basic methodology is that of geometric mechanics applied to the formulation of lagrange d alembert generalizing the use of connections and momentum maps associated with a given symmetry group to this case we begin by formulating the mechanics of nonholonomic systems using an ehresmann connection to model the constraints and show how the curvature of this connection enters into lagrange s equations unlike the situation with standard configuration space constraints the presence of symmetries in the nonholonomic case may or may not lead to conservation laws however the momentum map determined by the symmetry group still satisfies a useful differential equation that decouples from the group variables this momentum equation which plays an important role in control problems involves parallel transport operators and is computed explicitly in coordinates an alternative description using a body reference frame relates part of the momentum equation to the components of the euler poincar e equations along those symmetry directions consistent with the constraints one of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not an example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard a modified version of the skateboard which uses momentum coupling for locomotion generation we construct a synthesis of the mechanical connection and the ehresmann connection defining the constraints obtaining an important new object we call the nonholonomic connection when the nonholonomic connection is a principal connection for the given symmetry group we show how to perform lagrangian reduction in the presence of nonholonomic constraints generalizing previous results which only held in special cases several detailed examples are given to illustrate the theory september 1994 revised march 1995 revised june 1995

a nonconservative lmi condition for stability of switched systems with guaranteed dwell time ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems several methods have been proposed in the literature to address this problem but unfortunately they provide sufficient conditions only this technical note proposes the use of homogeneous polynomial lyapunov functions in the non restrictive case where all the subsystems are hurwitz showing that a sufficient condition can be provided in terms of an lmi feasibility test by exploiting a key representation of polynomials several properties are proved for this condition in particular that it is also necessary for a sufficiently large degree of these functions as a result the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well some examples illustrate the proposed approach

input output stability of sampled data systems the authors study the l sub p input output stability of a continuous time controller using the usual arrangement of periodic sampling and zero order hold it is noted that even if the hybrid system is exponentially stable this arrangement does not yield l sub p 1

on moment non explosions for wishart based stochastic volatility models abstract this paper provides a result on moment non explosions for a stock following a wishart multidimensional stochastic volatility dynamics or a wishart affine stochastic correlation dynamics when the parameter values satisfy certain constraints by reformulating the stock dynamics in terms of the volatility path along with standard results on matrix lyapunov and riccati equations a non explosion result of the moment of order greater than one can be obtained it extends to these frameworks a property well known for the heston model

fundamental properties of reset control systems reset controllers are linear controllers that reset some of their states to zero when their input is zero we are interested in their feedback connection with linear plants and in this paper we establish fundamental closed loop properties including stability and asymptotic tracking this paper considers more general reset structures than previously considered allowing for higher order controllers and partial state resetting it gives a testable necessary and sufficient condition for quadratic stability and links it to both uniform bounded input bounded state stability and steady state performance unlike previous related research which includes the study of impulsive differential equations our stability results require no assumptions on the evolution of reset times

hierarchical trajectory refinement for a class of nonlinear systems trajectory generation for nonlinear control systems is an important and difficult problem in this paper we provide a constructive method for hierarchical trajectory refinement the approach is based on the recent notion of f related control systems given a control affine system satisfying certain assumptions we construct a f related control system of smaller dimension trajectories designed for the smaller abstracted system are guaranteed by construction to be feasible for the original system constructive procedures are provided for refining trajectories from the coarser to the more detailed system