lyapunov stability for impulsive control affine systems abstract this article studies several notions of lyapunov stability for impulsive control affine systems in the setting of nonautonomous dynamical systems it presents some relations between the stability of an impulsive control affine system and the stability of its adjacent control system stability of compact sets and their components are specially investigated lyapunov functionals are employed to characterize each type of stability of closed sets

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

spectral tests for observability and detectability of periodic markov jump systems with nonhomogeneous markov chain this paper addresses observability and detectability of discrete time periodic systems with nonhomogeneous markov jump parameter popov belevitch hautus pbh type criteria are proposed for the concerned structural properties it is shown that different from stochastic systems with constant coefficients or homogeneous markov chain the spectral criteria of considered plants do not rely on a single operator but on a finite sequence of linear evolution operators by use of the obtained detectability criterion an extended lyapunov theorem is established which relates asymptotic mean square stability to a periodic lyapunov equation further a difference riccati equation with periodic coefficients is studied and some sufficient conditions are presented for the existence of stabilizing solution

brief paper detectability and observability of discrete time stochastic systems and their applications this paper studies detectability and observability of discrete time stochastic linear systems based on the standard notions of detectability and observability for time varying linear systems corresponding definitions for discrete time stochastic systems are proposed which unify some recently reported detectability and exact observability concepts for stochastic linear systems the notion of observability leads to the stochastic version of the well known rank criterion for observability of deterministic linear systems by using these two concepts the discrete time stochastic lyapunov equation and riccati equations are studied the results not only extend some of the existing results on these two types of equation but also indicate that the notions of detectability and observability studied in this paper take analogous functions as the usual concepts of detectability and observability in deterministic linear systems it is expected that the results presented may play important roles in many design problems in stochastic linear systems

prolongational limit sets of control systems abstract this article introduces the notions of prolongations and prolongational limit sets of control systems it is shown how the prolongational limit sets play in studying recursive and dispersive concepts of control systems

robust h infinity control in the presence of stochastic uncertainty this paper considers a robust h infinity state feedback control problem for linear uncertain systems with stochastic uncertainty the uncertainty class considered in the paper involves uncertain multiplicative white noise perturbations which satisfy a certain variance constraint a state feedback controller is presented which guarantees a prescribed level of disturbance attenuation for all admissible stochastic uncertainties

higher order moment stability region for markov jump systems based on cumulant generating function this paper is concerned with the solution of higher order moment stability region for markov jump systems with respect to cases of both known and unknown transition probabilities by exploring the cumulant generating function the original stochastic system with markov jumping modes is transformed to a deterministic system then based on the estimation of matrix eigenvalues the explicit solution for higher order moment stability region is expressed in terms of transition probabilities operation modes state transition matrix and its dimension and the moment order several examples are presented to illustrate the effectiveness of the proposed method and its associated algorithm

brief paper complete controllability of impulsive stochastic integro differential systems this paper is concerned with the controllability of impulsive stochastic integro differential systems sufficient conditions of complete controllability for impulsive stochastic integro differential systems are obtained by using schaefer s fixed point theorem a numerical example is provided to show the effectiveness of the proposed results

generalized detectability for discrete event systems in our previous work we investigated detectability of discrete event systems which is defined as the ability to determine the current and subsequent states of a system based on observation for different applications we defined four types of detectabilities weak detectability strong detectability weak periodic detectability and strong periodic detectability in this paper we extend our results in three aspects 1 we extend detectability from deterministic systems to nondeterministic systems such a generalization is necessary because there are many systems that need to be modeled as nondeterministic discrete event systems 2 we develop polynomial algorithms to check strong detectability the previous algorithms are based on observer whose construction is of exponential complexity while the new algorithms are based on a new automaton called detector 3 we extend detectability to d detectability while detectability requires determining the exact state of a system d detectability relaxes this requirement by asking only to distinguish certain pairs of states with these extensions the theory on detectability of discrete event systems becomes more applicable in solving many practical problems

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

growth in an impulsive integral inequality abstract in this paper we study a finite sum integral inequality with a sequence of impulses making a sequential monotonization we give recursively defined functions to estimate solutions of the inequality piecewise in order to use the estimate to study boundedness and asymptotics of solutions for differential equations we regard the estimating function as a solution of a nonautonomous difference equation simplify the equation with composition of operators and reduce our discussion to qualitative analysis of the difference equation so that we give results on monotonicity boundedness and weighted boundedness for solutions of the inequality as applications we study boundedness and asymptotics of solutions for two impulsive differential equations

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

waring like decompositions of polynomials 1 abstract let f be a homogeneous form of degree d in n variables a waring decomposition of f is a way to express f as a sum of d th powers of linear forms in this paper we consider the decompositions of a form as a sum of expressions each of which is a fixed monomial evaluated at linear forms

on stabilizability and exact observability of stochastic systems with their applications this paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications with the aid of the operator spectrum a necessary and sufficient condition is given for the stabilizability of stochastic systems some new concepts such as unremovable spectrum and strong solution are introduced an unremovable spectral theorem and a stochastic popov belevith hautus criterion for exact observability are presented as applications a comparison theorem for stochastic algebraic riccati equations and a result on lyapunov type equations are obtained

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

observability and detectability of discrete time stochastic systems with markovian jump abstract this paper studies detectability and observability of markov jump discrete time linear stochastic systems with multiplicative noise mjdls for short the relations between some concepts of detectability and observability are established these relations together with equivalent expressions of observability gramian allow us to obtain some other sufficient and necessary conditions of detectability and observability as applications discrete time stochastic lyapunov equations and stochastic discrete algebraic riccati equations sdare are discussed

generalized lyapunov equation approach to state dependent stochastic stabilization detectability criterion in this paper the generalized lyapunov equation approach is used to study stochastic stabilization detectability with state multiplicative noise some practical test criteria for stochastic stabilization and detectability such as stochastic popov belevitch hautus criterion for exact detectability are obtained moreover useful properties of the generalized lyapunov equation are derived based on critical stability and exact detectability introduced in this paper as applications first the stochastic linear quadratic regulator as well as the related generalized algebraic riccati equation are discussed extensively second the infinite horizon stochastic h 2 h infin control with state and control dependent noise is also investigated which extends and improves the recently published results

attractors for impulsive non autonomous dynamical systems and their relations in this work we deal with several different notions of attractors that may appear in the impulsive non autonomous framework and we explore their relationships to obtain properties regarding the different scenarios of asymptotic dynamics such as the cocycle attractor the uniform attractor and the global attractor for the impulsive skew product semiflow lastly we illustrate our theory by exhibiting an example of a non classical non autonomous parabolic equation with subcritical nonlinearity and impulses

stabilisation of hybrid stochastic differential equations by delay feedback control this paper is concerned with the exponential mean square stabilisation of hybrid stochastic differential equations also known as stochastic differential equations with markovian switching by delay feedback controls although the stabilisation by non delay feedback controls for such equations has been discussed by several authors there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap to make our theory more understandable as well as to avoid complicated notations we will restrict our underlying hybrid stochastic differential equations to a relatively simple form however our theory can certainly be developed to cope with much more general equations without any difficulty

minimum entropy static output feedback control with an h sub spl infin norm performance bound the problem of designing static output feedback controllers is considered the controller is required to minimize the closed loop entropy at s spl infin and to satisfy a prescribed h sub spl infin norm bound the design equations consist of a modified riccati equation and a lyapunov equation that are coupled via a projection these equations are solved using a homotopy algorithm the design procedure is illustrated by two examples the first one is a classical example that was solved in the literature using convex optimization techniques the second example is one of designing a gain scheduled normal acceleration loop for an air launched unmanned air vehicle

stochastic stabilization of a class of nonhomogeneous markovian jump linear systems this paper deals with the problem of stochastic stability analysis and control synthesis of a class of markovian jump linear systems mjls with time varying transition probabilities tps in the discrete time domain the time varying character is considered to be in a polytopic sense the approach followed in this note is based on the use of a parameter dependent stochastic lyapunov function we give a stability condition in terms of a linear matrix inequality lmi feasibility problem the obtained results are illustrated in a numerical example

on the secant varieties to the tangent developable of a veronese variety abstract let v n d p n for n n d n 1 be the order d veronese embedding of p n x n d t v n d p n the tangent developable of v n d and s s 1 x n d p n the s secant variety of x n d i e the closure in p n of the union of all s 1 linear spaces spanned by s points of x n d s s 1 x n d has expected dimension min n 2 n 1 s 1 catalisano geramita and gimigliano conjectured that s s 1 x n d has always the expected dimension except when d 2 n 2 s or d 3 and n 2 3 4 in this paper we prove their conjecture when n 2 and n 3

detectability observability and lyapunov type theorems of linear discrete time varying stochastic systems with multiplicative noise abstractthe objective of this paper is to study detectability observability and related lyapunov type theorems of linear discrete time time varying stochastic systems with multiplicative noise some new concepts such as uniform detectability k exact detectability resp kwft exact detectability kft exact detectability kn exact detectability and k exact observability resp kwft exact detectability kft exact detectability kn exact detectability are introduced respectively and nice properties associated with uniform detectability exact detectability and exact observability are also obtained moreover some lyapunov type theorems associated with generalised lyapunov equations and exponential stability in mean square sense are presented under uniform detectability kn exact observability and kn exact detectability respectively

quantitative measure of observability for linear stochastic systems abstract in this study we define a new observability measure for stochastic systems the mutual information between the state sequence and the corresponding measurement sequence for a given time horizon although the definition is given for a general system representation the paper focuses on the linear time invariant gaussian case some basic analytical results are derived for this special case the measure is extended to the observability of a subspace of the state space specifically an individual state and or the modes of the system a single measurement system represented in the observable canonical form is examined in detail a recursive form of the observability measure for a finite time horizon is derived the possibility of using this form for designing a sensor selection algorithm is demonstrated by two examples

a nondegenerate maximum principle for the impulse control problem with state constraints in this article a free time impulsive control problem with state constraints and equality and inequality constraints on the trajectory endpoints is considered a weakened maximum principle is obtained for problems with data measurable in the time variable being the time transversality conditions deduced with the help of some extra convexity assumption on the state constraints in the case of smooth problems a nondegenerate maximum principle is derived by using a penalty function method

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

most secant varieties of tangential varieties to veronese varieties are nondefective we prove a conjecture stated by catalisano geramita and gimigliano in 2002 which claims that the secant varieties of tangential varieties to the dth veronese embedding of the projective n space pn have the expected dimension modulo a few wellknown exceptions it is arguably the first complete result on the dimensions of secant varieties of a classically studied variety since the work of alexander and hirschowitz in 1995 as bernardi catalisano gimigliano and ida demonstrated that the proof of this conjecture may be reduced to the case of cubics i e d 3 the main contribution of this work is the resolution of this base case the proposed proof proceeds by induction on the dimension n of the projective space via a specialization argument this reduces the proof to a large number of initial cases for the induction which were settled using a computer assisted proof the individual base cases were computationally challenging problems indeed the largest base case required us to deal with the tangential variety to the third veronese embedding of p79 in p88559

on the observability and detectability of continuous time markov jump linear systems the paper introduces a new detectability concept for continuous time markov jump linear systems with finite markov space that generalizes previous concepts found in the literature the detectability in the weak sense is characterized as mean square detectability of a certain related stochastic system making both detectability senses directly comparable the concept can also ensure that the solution of the coupled algebraic riccati equation associated to the quadratic control problem is unique and stabilizing making other concepts redundant the paper also obtains a set of matrices that plays the role of the observability matrix for deterministic linear systems and it allows geometric and qualitative properties tests for weak observability and detectability of a system are provided the first consisting of a simple rank test similar to the usual observability test for deterministic linear systems

brief paper on detectability of stochastic systems we discuss notions of detectability for stochastic linear control systems of ito type a natural concept of detectability requires a non zero output if the state process is unstable we show that this property can equivalently be characterized by a generalized version of the hautus test the proof is based on spectral theory for positive operators

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

secant varieties to osculating varieties of veronese embeddings of p n a well known theorem by alexander hirschowitz states that all the higher secant varieties of v n d the d uple embedding of pp n have the expected dimension with few known exceptions we study here the same problem for t n d the tangential variety to v n d and prove a conjecture which is the analogous of alexander hirschowitz theorem for n leq 9 moreover we prove that it holds for any n d if it holds for d 3 then we generalize to the case of o k n d the k osculating variety to v n d proving for n 2 a conjecture that relates the defectivity of sigma s o k n d to the hilbert function of certain sets of fat points in pp n

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

on the detectability and observability of discrete time markov jump linear systems abstract this paper presents a new detectability concept for discrete time markov jump linear systems with finite markov state which generalizes the ms detectability concept found in the literature the new sense of detectability can similarly assure that the solution of the coupled algebraic riccati equation associated to the quadratic control problem is a stabilizing solution in addition the paper introduces a related observability concept that also generalizes previous concepts a test for detectability based on a coupled matrix equation is derived from the definition and a test for observability is presented which can be performed in a finite number of steps the results are illustrated by examples including one that shows that a system may be detectable in the new sense but not in the ms sense

on the detectability and observability of continuous stochastic markov jump linear systems abstract this paper is concerned with the detectability and observability of continuous linear stochastic systems subject to markov jump by introducing some operators we investigate the relationship between some different concepts of detectability and observability and obtain their sufficient and necessary conditions continuous time stochastic lyapunov equations and stochastic continuous algebraic riccati equations are also discussed to serve as analysis tools

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

global attractors for semigroup actions abstract in this paper the notions of global attractor and global uniform attractor are extended to the setting of general semigroup actions we study the necessary and sufficient conditions for the existence of the global attractor for semigroups acting on noncompact metric spaces we present conditions for the equivalence between the global attractor and global uniform attractor

necessary conditions of optimality for vector valued impulsive control problems abstract a vector valued impulsive control problem is considered whose dynamics defined by a differential inclusion are such that the vector fields associated with the singular term do not satisfy the so called frobenius condition a concept of robust solution based on a new reparametrization procedure is adopted in order to derive necessary conditions of optimality these conditions are obtained by taking a limit of those for an appropriate sequence of auxiliary standard optimal control problems approximating the original one an example to illustrate the nature of the new optimality conditions is provided