stability and stabilization of switched linear time invariant systems with saddle points and switching delays this paper addresses global asymptotic stability gas and stabilization issues of switched linear time invariant lti systems with saddle points and time varying switching delays firstly two criteria of gas are proposed for such switched systems with all subsystems sharing a common unique saddle point under arbitrary periodic quasi periodic switching paths psp qsp secondly by using our stability results we design global asymptotic stabilizing controls gasc periodic quasi periodic stabilizing switching paths pssp qssp and an algorithm of gasc and pssp qssp for the switched systems finally we present a numerical example of a switching multi agent system to illustrate the effectiveness and practicality of our new results

asynchronous control for 2 d switched systems with mode dependent average dwell time abstract this work is concerned with asynchronous control for a class of two dimensional switched systems with mode dependent average dwell time the systems are formulated by the famous fornasini marchesini local state space model and the switching signal of the switched controller involves time delays which lead to the asynchronism between controllers and subsystems by extending mode dependent average dwell time with the switched quadratic lyapunov functional approach the stabilization condition is established for 2 d asynchronously switched systems based on the stabilization result mode dependent state feedback controllers are designed to guarantee h performance and asymptotic stability of the corresponding closed loop system finally two examples are provided to illustrate the effectiveness of the proposed design scheme

stability and stabilization analysis of positive polynomial fuzzy systems with time delay considering piecewise membership functions this paper is concerned with the stability analysis of positive polynomial fuzzy model based control systems with time delay each of the polynomial fuzzy model and the polynomial fuzzy controller is allowed to have its own set of premise membership functions which can improve the design and realization flexibility conditions showing the positivity of the system are first obtained then to deal with the difficulty resulting from the mismatched premise membership functions to the stability stabilization analysis approximated membership functions representing the original ones are constructed and the information of membership functions is brought into the stability conditions this way the stability conditions can be relaxed since the extra knowledge on the system is considered stability conditions are obtained by using the sum of squares approach based on the lyapunov stability theory a simulation example is provided to verify the effectiveness of this method

fault detection observer design for discrete time 2 d t s fuzzy systems with finite frequency specifications abstract this work designs a fault detection observer for two dimensional 2 d non linear systems having discrete dynamics expressed in takagi sugeno t s form the finite frequency ff domain is considered during designing the observers which makes them different from previously proposed 2 d detection observers faults and disturbances are considered in two different ff domain intervals respectively fault sensitivity and disturbance robustness are measured by two ff performance indices the aim here is to formulate an observer that assures the fault sensitivity and disturbance robustness of the residual error system essential lemmas have been proposed for nonlinear 2 d roesser model which are expected to serve as a bridge between two domains frequency and time conditions have been provided that are sufficient to design a desired fault detection fuzzy observer and effectivity of the proposed method is shown by simulation results

asynchronously switched control of discrete impulsive switched systems with time delays this paper is concerned with the stabilization problem for a class of uncertain discrete impulsive switched delay systems under asynchronous switching the so called asynchronous switching means that the switches between the candidate controllers and system modes are asynchronous by using the average dwell time adt approach sufficient conditions for the existence of an asynchronously switched controller is derived such that the resulting closed loop system is exponentially stable the desired controller gains and the admissible switching signals are obtained in terms of a set of matrix inequalities a numerical example is given to illustrate the effectiveness of the proposed method

model approximation for discrete time state delay systems in the t s fuzzy framework this paper is concerned with the problem of h model approximation for discrete time takagi sugeno t s fuzzy time delay systems for a given stable t s fuzzy system our attention is focused on the construction of a reduced order model which not only approximates the original system well in an h performance but is also translated into a linear lower dimensional system by applying the delay partitioning approach a delay dependent sufficient condition is proposed for the asymptotic stability with an h error performance for the error system then the h model approximation problem is solved by using the projection approach which casts the model approximation into a sequential minimization problem subject to linear matrix inequality lmi constraints by employing the cone complementary linearization algorithm moreover by further extending the results h model approximation with special structures is obtained i e delay free model and zero order model finally two numerical examples are provided to illustrate the effectiveness of the proposed methods

delay dependent exponential stabilization of positive 2d switched state delayed systems in the roesser model this paper deals with the controller synthesis for a class of positive two dimensional 2d switched delay systems described by the roesser model this kind of systems has the property that the states take nonnegative values whenever the initial boundaries are nonnegative some delay dependent sufficient conditions for the exponential stability of positive 2d switched systems with state delays are given furthermore the design of positive state feedback controller under which the resulting closed loop system meets the requirements of positivity and exponential stability is presented in terms of linear matrix inequalities lmis an example is included to illustrate the effectiveness of the proposed approach

exponential stability analysis for delayed neural networks with switching parameters average dwell time approach this paper is concerned with the problem of exponential stability analysis of continuous time switched delayed neural networks by using the average dwell time approach together with the piecewise lyapunov function technique and by combining a novel lyapunov krasovskii functional which benefits from the delay partitioning method with the free weighting matrix technique sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with constant and time varying delays respectively moreover the decay estimates are explicitly given the results reported in this paper not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism numerical examples are presented to demonstrate the usefulness of the derived theoretical results

testing hypotheses about sun climate complexity linking we reexamine observational evidence presented in support of the hypothesis of a sun climate complexity linking by n scafetta and b j west phys rev lett 90 248701 2003 which contended that the integrated solar flare index sfi and the global temperature anomaly gta both follow l evy walk statistics with the same waiting time exponent ensuremath mu ensuremath approx 2 1 however their analysis does not account for trends in the signal cannot deal correctly with infinite variance processes l evy flights and suffers from considering only the second moment our analysis shows that properly detrended the integrated sfi is well described as a l evy flight and the integrated gta as a persistent fractional brownian motion these very different stochastic properties of the solar and climate records do not support the hypothesis of a sun climate complexity linking

h control of 2 d continuous markovian jump delayed systems with partially unknown transition probabilities abstract this study focuses on stochastic stability and h control of two dimensional 2 d continuous delayed markovian jump systems mjss with partial information on transition probability at first a sufficient condition for the stochastic stability of 2 d mjss is proposed by choosing an appropriate lyapunov krasovskii functional then the results are developed by designing a state feedback controller that guarantees the stochastic stability of the resultant closed loop system with a prescribed h performance level finally the proposed results are validated with the help of examples

σ finiteness of elliptic measures for quasilinear elliptic pde in space abstract in this paper we study the hausdorff dimension of a elliptic measure f in space associated to a positive weak solution to a certain quasilinear elliptic pde in an open subset and vanishing on a portion of the boundary of that open set we show that this measure is concentrated on a set of finite n 1 dimensional hausdorff measure for p n and the same result holds for p n with an assumption on the boundary we also construct an example of a domain in space for which the corresponding measure has hausdorff dimension n 1 for p n for some which depends on various constants including p the first result generalizes the authors previous work in 3 when the pde is the p laplacian and the second result generalizes the well known theorem of wolff in 24 when p 2 and n 2

on the hausdorff dimension of harmonic measure in higher dimension assume a i n e a domain in f n where e is a compact set denote o a a x the harmonic measure for a of a evaluated at x r d according to 0ksendal s theorem o o e o a x is singular with respect to d dimensional lebesgue measure for d 2 and general domains this result seemed to be so far the only known localization property recently for d 2 it has been shown by p jones and t wolff j w that s o9 has dimension at most 1 this result completes previous work due to n g makarov and l carleson see i m and c2 let g be the green s function of a r with pole at some point of c r o9 in both the carleson and jones wolff arguments the integral g g nn log nn as boundary

the general state space model for a two dimensional linear digital system the general state space model for a 2 d linear digital system is presented a new definition of state transition matrix is given based on the definition it is easy to calculate the state transition matrix for any linear digital system the general response formula for a system follows simply from the definition a new definition of the characteristic function of a system and a theorem parallel to the cayley hamilton theorem are also given the presented results apply to any linear causal system

p harmonic measure in simply connected domains revisited let be a bounded simply connected domain in the complex plane c let n be a neighborhood of let p be xed 1 p 1 and let be a positive weak solution to the p laplace equation in n assume that u has zero boundary values on

exponential stability of two dimensional homogeneous monotone systems with bounded directional delays one dimensional 1 d monotone systems have received considerable attention recently due to their wide applicability and interesting mathematical properties one of these special properties is that for lti monotone systems exponential stability is insensitive to time delays some extensions to 1 d nonlinear monotone systems based on conditions of homogeneity have also been reported in this paper we study the problem of exponential stability of discrete time 2 d nonlinear monotone systems described by the roesser model with time varying delays specifically based on the monotone property and homogeneity of the associated vector fields necessary and sufficient delay independent exponential stability conditions are derived the magnitudes of delays are also taken into deriving an explicit estimation of the exponential decay rate which correlates the impact of delays on the system performance two examples are given to demonstrate the effectiveness of the obtained results

investigating the effects of time delays on stochastic stability and designing l1 gain controllers for positive discrete time markov jump linear systems with time delay this paper is concerned with stochastic stability l1 gain performance analysis and positivity preserving l1 gain controller design for a positive discrete time markov jump linear system with time delay first necessary and sufficient conditions for stochastic stability of the system are derived by constructing a linear co positive stochastic lyapunov functional and establishing a system equation whose state variables consist of the mathematical expectation of the markovianized states and whose coefficient matrices depend on time delay and the transition probability it is revealed that stochastic stability of the positive discrete time markov jump linear system with time delay is influenced by the size of time delay and it is demonstrated by an example that the effect of time delay on stochastic stability can be either positive or negative second exact computation on an l1 gain index of a stochastically stable positive discrete time markov jump linear system with time delay is presented and a necessary and sufficient condition for the l1 gain performance is derived in the form of linear programming third an iterative algorithm is proposed to design a positivity preserving l1 gain controller and in single input case an optimal controller is obtained analytically such that the closed loop system achieves the minimal l1 gain performance then a modified pest s structured population dynamic model is developed to illustrate the effectiveness of the designed method

dissipativity based sliding mode control of switched stochastic systems this technical brief is concerned with dissipativity analysis and dissipativity based sliding mode control smc of continuous time switched stochastic systems firstly a sufficient condition is proposed to guarantee the mean square exponential stability and strict dissipativity for the switched stochastic system then an integral type sliding surface function is designed for establishing a sliding mode dynamics which can be formulated by a switched stochastic system with an external disturbance uncertainty dissipativity analysis and synthesis are both investigated for the sliding mode dynamics and consequently sufficient conditions are derived which pave the way for solving the dissipativity analysis and control problems moreover a smc law is synthesized to drive the system trajectories onto the predefined sliding surface in a finite time finally the efficiency of the theoretical findings is demonstrated by an illustrative example

a novel approach to filter design for t s fuzzy discrete time systems with time varying delay in this paper the problem of l2 l filtering for a class of discrete time takagi sugeno t s fuzzy time varying delay systems is studied our attention is focused on the design of full and reduced order filters that guarantee the filtering error system to be asymptotically stable with a prescribed h performance sufficient conditions for the obtained filtering error system are proposed by applying an input output approach and a two term approximation method which is employed to approximate the time varying delay the corresponding full and reduced order filter design is cast into a convex optimization problem which can be efficiently solved by standard numerical algorithms finally simulation examples are provided to illustrate the effectiveness of the proposed approaches

stability and exponential stability of linear discrete systems with constant coefficients and single delay this paper investigates the exponential stability and exponential estimate of the norms of solutions to a linear system of difference equations with single delay x k 1 a x k b x k m k 0 1 where a b are square constant matrices and m n sufficient conditions for exponential stability are derived using the method of lyapunov functions and its efficiency is demonstrated by examples

stability analysis and synthesis for switched takagi sugeno fuzzy positive systems described by the roesser model abstract this article focuses on stability analysis and controller synthesis of a class of roesser type switched takagi sugeno fuzzy systems with delays first sufficient conditions derived by use of the co positive lyapunov function and the average dwell time method are presented to guarantee the proposed system is positive and exponentially stable then via a state feedback fuzzy controller criteria are also given under which not only the resulting closed loop system is positive and exponentially stable but also the desired controller gain matrices can be designed by solving a set of coupled matrix inequalities finally two illustrative examples are provided to show the effectiveness of the approach outlined in this article

a cautionary note on modeling with fractional levy flights abstract temporal scaling and infinite variance are two stylized features often seen together in times series of complex systems we find that because of their infinite moments samples from fractional levy flights produce bi linear scaling functions which may be incorrectly attributed as evidence of multifractality we argue that it is unnecessary to consider truncated fractional levy flights which are inherently problematic

further studies on relaxed stabilization conditions for discrete time two dimension takagi sugeno fuzzy systems this paper investigates the stabilization problem of discrete time two dimension 2 d takagi sugeno t s fuzzy systems based on a novel non parallel distributed compensation non pdc control scheme combined with a new non quadratic lyapunov function less conservative stabilization conditions are developed the proposed non quadratic lyapunov function is homogeneous polynomially parameter dependent on membership functions as the degree of the lyapunov function increases the conservatism of the obtained stabilization conditions is gradually reduced by exploiting the algebraic property of membership functions the stabilization conditions approach to exactness in the sense of convergence compared with the existing methods no slack variables are introduced in control synthesis and hence the same or less conservative results can be obtained with a lower computational cost a numerical example is given to illustrate the effectiveness of the proposed method

stabilization for switched stochastic neutral systems under asynchronous switching in this paper the mean square exponential stability of switched stochastic neutral systems with time varying delay under asynchronous switching is investigated a new lyapunov function dependent on the controllers switching signal is constructed which can counteract the difficulty of controller design to stabilize the system under asynchronous switching moreover the value of the lyapunov function is allowed to increase during mismatched periods based on the average dwell time approach a sufficient condition expressed by a set of linear matrix inequalities lmis is derived to guarantee the mean square exponential stability for the closed loop system and the controllers with asynchronous switching are designed finally a numerical example illustrates the effectiveness of the results

hausdorff dimension and σ finiteness of p harmonic measures in space when p n abstract in this paper we study a measure associated with a positive p harmonic function u defined in an open set o r n and vanishing on a portion of o if p n we show is concentrated on a set of finite h n 1 measure while if p n the same conclusion holds provided is uniformly fat in the sense of n capacity our work nearly answers in the affirmative a conjecture in lewis 2015 and also appears to be the natural extension of jones and wolff 1988 wolff 1993 to higher dimensions

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

l gain performance analysis for two dimensional roesser systems with persistent bounded disturbance and saturation nonlinearity the l gain approach has been an essential tool in one dimensional system theory however limited results have been presented in the literature for the two dimensional 2 d l gain approach this paper investigates the l gain performance for 2 d systems in the roesser model with persistent bounded disturbance input and saturation nonlinearity a linear matrix inequality lmi based condition is established to reduce the effect of persistent bounded disturbance input on 2 d systems within a given disturbance attenuation level based on the discrete jensen inequality lower bounds lemma and diagonally dominant matrices we apply the obtained results to the l gain performance analysis for 2 d digital filters with saturation arithmetic

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory

dynamic output feedback control for positive roesser system under the switched and t s fuzzy rules abstract this paper is concerned with the dynamic output feedback controller design for the positive roesser type nonlinear system which is intrinsically characterized by the switched mechanism and subtly decomposed into the linear form under the takagi sugeno fuzzy rules firstly based on the co positive lyapunov function and the average dwell time method sufficient conditions are presented under which the resulting closed loop system is exponentially stable and has l 1 gain bound then explicit expressions are also given to derive the expected controller gain matrices with desired l 1 gain bound finally effectiveness of the proposed results is illustrated by two numerical examples