a cosine maximization method for the priority vector derivation in ahp abstract the derivation of a priority vector from a pair wise comparison matrix pcm is an important issue in the analytic hierarchy process ahp the existing methods for the priority vector derivation from pcm include eigenvector method ev weighted least squares method wls additive normalization method an logarithmic least squares method lls etc the derived priority vector should be as similar to each column vector of the pcm as possible if a pair wise comparison matrix pcm is not perfectly consistent therefore a cosine maximization method cm based on similarity measure is proposed which maximizes the sum of the cosine of the angle between the priority vector and each column vector of a pcm an optimization model for the cm is proposed to derive the reliable priority vector using three numerical examples the cm is compared with the other prioritization methods based on two performance evaluation criteria euclidean distance and minimum violation the results show that the cm is flexible and efficient

a small gain theorem for switched interconnected nonlinear systems and its applications a small gain theorem for switched interconnected nonlinear systems is set up which provides a tool for analyzing the behavior of switched systems also a method exploiting an average dwell time and the small gain technique is proposed based on the small gain theorem this technical note investigates the problem of global stabilization of switched nonlinear systems in strict feedback form whose all zero dynamics are input to state stable iss or only some are iss and others are not a sufficient condition for the global stabilization problem under a class of switching signals with average dwell time is derived by constructing state feedback controllers for subsystems the result is also applied to a class of switched nonlinear network control systems

stability of nonlinear asynchronous systems in this work we focus on a class of nonlinear asynchronous systems defined by two different modes of operation one stable and the other one unstable the switching between the two modes of operation is driven by external asynchronous events it is assumed that on any time interval of a given length the maximum time in which the system evolves in the unstable mode is bounded this property is given in the form of a rate constraint under this assumption we study the behavior of this class of systems and provide existential results of conditions on this rate constraint under which various types of stability of the origin of the nonlinear asynchronous system can be assured

a consistency improving method in the analytic hierarchy process in this paper we propose a method to modify a given comparison matrix by which the consistency ratio cr value of the modified matrix is less than that of the original one and give an algorithm to derive a positive reciprocal matrix with acceptable consistency i e cr 0 1 then the convergence theorem for the given algorithm is established and its practicality is shown by some examples

input to state stabilization of switched nonlinear systems this note derives some sufficient conditions to ensure that the whole switched nonlinear system is input to state stabilizable iss when each mode is iss both cases that the switchings of system modes coincide exactly and that they do not coincide with those of the corresponding controllers are considered for the latter a model based identification scheme is used to identify the system modes the proposed scheme can overcome the finite escape time that may happen in this case

algorithms for improving consistency or consensus of reciprocal 0 1 valued preference relations we investigate the consistency and consensus of reciprocal 0 1 valued preference relations also called fuzzy preference relations by many authors based on the multiplicative consistency property which is an important issue in fuzzy set theory an algorithm is first developed to improve the consistency level of a reciprocal 0 1 valued preference relation and the corresponding algorithm for the incomplete reciprocal 0 1 valued preference relation is also developed we further propose the consensus improving algorithms for individual reciprocal 0 1 valued preference relations or incomplete ones the convergence and robustness of the algorithms are proven and some important conclusions are obtained in addition the proposed algorithms can improve the consistency or consensus of reciprocal 0 1 valued preference relations with less interactions with the decision makers which can save a lot of time and obtain the results quickly

robust matrix commutator conditions for stability of switched linear systems under restricted switching this article treats global uniform exponential stability gues of discrete time switched linear systems under restricted switching given admissible minimum and maximum dwell times we provide sufficient conditions on the subsystems under which they admit a set of switching signals that obeys the given restrictions on dwell times and preserves stability of the resulting switched system our analysis relies on combinatorial arguments applied to matrix commutators the proposed set of stabilizing switching signals is characterized in terms of duration of activation of schur stable subsystems and non consecutive activation of distinct unstable subsystems

peridynamic petrov galerkin method a generalization of the peridynamic theory of correspondence materials abstract the peridynamic petrov galerkin ppg method is a meshfree approach based on the peridynamic integro differential form of the momentum equation the spurious oscillations in the common peridynamic correspondence formulation are investigated they occur due to an inadmissible linearized mapping of the family deformation field this leads to a generalized correspondence formulation which contains the common formulation as a special case it is based on the weak form of the peridynamic momentum equation test and trial function requirements are examined which ensure an exact imposition of dirichlet and neumann boundary conditions and weighted least square wls shape functions as well as local maximum entropy lme approximants are utilized to examine the ppg method a consistent linearization is provided which can also be used to speed up common implicit peridynamic correspondence codes it is used in an implicit quasistatic framework to investigate the impact of different shape function combinations test cases show that low energy modes can be prevented by the ppg method and highlight the fast convergence and stability

are inconsistent decisions better an experiment with pairwise comparisons this paper tries to contribute to the well known and lengthy discussion on whether we should allow decision makers to be inconsistent or to put it in another way if intransitive decisions better represent their preferences we will focus specifically on the multiple criteria decision making problem since it is one of the most usual stances where this intransitivity appears results from an experiment carried out with graduate students shows that when intransitivities are removed the preferences of decision makers are not better represented and therefore that the effort to do so may not be justified

finite time stochastic input to state stability of impulsive switched stochastic nonlinear systems this paper mainly tends to investigate the finite time stochastic input to state stability ftsiss problem for a class of impulsive switched stochastic nonlinear systems an efficient lemma is firstly established to construct a generalized class kl function further a set of lyapunov based sufficient conditions are derived to check the finite time stability in probability ftsip and finite time input to state stability ftiss properties of switched stochastic nonlinear systems with or without impulses in particular some useful results in favor of simulations are obtained in terms of average dwell time technique finally a numerical example is provided to illustrate the effectiveness of proposed results

stabilizing switching signals a transition from point wise to asymptotic conditions abstract characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature this article collects a multitude of stabilizing switching signals under an umbrella framework we achieve this in two steps firstly given a family of systems possibly containing unstable dynamics we propose a new and general class of stabilizing switching signals secondly we demonstrate that prior results based on both point wise and asymptotic characterizations follow our result this is the first attempt in the switched systems literature where these switching signals are unified under one banner

input to state stability for impulsive stochastic nonlinear systems with delayed impulses in this paper the problems of the stochastic input to state stability siss properties are investigated for impulsive stochastic nonlinear systems with delayed impulses by employing lyapunov method together with average impulsive interval approach the sufficient conditions are established to ensure properties for impulsive stochastic systems with all stable subsystems moreover the iss properties are also derived for the stochastic systems when the system is with both stable and unstable subsystems then we also study impulsive systems with multiple jumps i e there exist different impulses in a system by now there has been no papers to consider multiple jumps for stochastic cases finally two examples are provided to illustrate the effectiveness of our results

on finite time stability of cyclic switched nonlinear systems this technical note considers the global finite time stability problem for a class of switched nonlinear systems with the cyclic switching sequence dissipative or non dissipative impulsive effects may appear at each switching instant and each mode may or may not be finite time stable individually a new concept named cycle dwell time is proposed based on which two stability conditions are established these conditions fully reveal the trade off among each mode s dynamics impulsive dynamics and initial conditions an example of multi agent systems illustrates the efficiency of the new results

switched observer based adaptive neural control of mimo switched nonlinear systems with unknown control gains in this paper the problem of adaptive neural output feedback control is addressed for a class of multi input multioutput mimo switched uncertain nonlinear systems with unknown control gains neural networks nns are used to approximate unknown nonlinear functions in order to avoid the conservativeness caused by adoption of a common observer for all subsystems an mimo nn switched observer is designed to estimate unmeasurable states a new switched observer based adaptive neural control technique for the problem studied is then provided by exploiting the classical average dwell time adt method and the backstepping method and the nussbaum gain technique it effectively handles the obstacle about the coexistence of multiple nussbaum type function terms and improves the classical adt method since the exponential decline property of lyapunov functions for individual subsystems is no longer satisfied it is shown that the technique proposed is able to guarantee semiglobal uniformly ultimately boundedness of all the signals in the closed loop system under a class of switching signals with adt and the tracking errors converge to a small neighborhood of the origin the effectiveness of the approach proposed is illustrated by its application to a two inverted pendulum system

brief paper input to state stability of switched systems and switching adaptive control in this paper we prove that a switched nonlinear system has several useful input to state stable iss type properties under average dwell time switching signals if each constituent dynamical system is iss this extends available results for switched linear systems we apply our result to stabilization of uncertain nonlinear systems via switching supervisory control and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide iss properties with respect to the estimation errors detailed illustrative examples are included

input output to state stability this work explores lyapunov characterizations of the input output to state stability ioss property for nonlinear systems the notion of ioss is a natural generalization of the standard zero detectability property used in the linear case the main contribution of this work is to establish a complete equivalence between the ioss property and the existence of a certain type of smooth lyapunov function as corollaries one shows the existence of norm estimators and obtains characterizations of nonlinear detectability in terms of relative stability and of finite energy estimates

the theory of ratio scale estimation saaty s analytic hierarchy process the analytic hierarchy process developed by saaty saaty t l 1980 the analytic hierarchy process mcgraw hill new york has proven to be an extremely useful method for decision making and planning however some researchers in these areas have raised concerns over the theoretical basis underlying this process this paper addresses currently debated issues concerning the theoretical foundations of the analytic hierarchy process we also illustrate through proof and through examples the validity or fallaciousness of these criticisms

an integral type multiple lyapunov functions approach for switched nonlinear systems an integral type multiple lyapunov functions mlfs approach for switched nonlinear systems is set up for the first time which gives a more general condition for analyzing the behavior of switched nonlinear systems since the branicky s nonincreasing condition is no longer assumed and the generalized mlfs condition is a special case of the condition provided meanwhile based on the integral type mlfs approach global stabilization for a class of switched nonlinear systems in p normal form is achieved by constructing state feedback controllers of subsystems and a proper switching law where the solvability of the problem under study for individual subsystems is not assumed two examples are also provided to demonstrate the effectiveness of the proposed design method

stability of switched nonlinear systems with delay and disturbance we consider a class of nonlinear time varying switched control systems for which stabilizing feedbacks are available we study the effect of the presence of a delay in the input of switched nonlinear systems with an external disturbance by contrast with most of the contributions available in the literature we do not assume that all the subsystems of the switched system we consider are stable when the delay is present through a lyapunov approach we derive sufficient conditions in terms of size of the delay ensuring the global exponential stability of the switched system moreover under appropriate conditions the input to state stability of the system with respect to an external disturbance is established

input output to state stability and state norm estimators for switched nonlinear systems in this paper the concepts of input output to state stability ioss and state norm estimators are considered for switched nonlinear systems under average dwell time switching signals we show that when the average dwell time is large enough a switched system is ioss if all of its constituent subsystems are ioss moreover under the same conditions a non switched state norm estimator exists for the switched system furthermore if some of the constituent subsystems are not ioss we show that still ioss can be established for the switched system if the activation time of the non ioss subsystems is not too big again under the same conditions a state norm estimator exists for the switched system however in this case the state norm estimator is a switched system itself consisting of two subsystems we show that this state norm estimator can be constructed such that its switching times are independent of the switching times of the switched system it is designed for

convergence domain for time varying switched systems abstract in this paper we investigate the convergence domain for time varying switched systems we construct multiple lyapunov functions and each lyapunov function is decreasing outside a ball whose radius is time varying we give a relatively accurate convergence domain for a general time varying switched system finally a numerical example a mass spring damper system is provided to show the effectiveness of the theoretical results

unified stability criteria for slowly time varying and switched linear systems this paper presents a unified approach to formulating stability conditions for slowly time varying linear systems and switched linear systems the concept of total variation is generalized to the case of matrix valued functions using this generalized concept a result extending existing stability conditions for slowly time varying linear systems is derived as special cases of this result two sets of stability conditions are derived for switched linear systems which match known results in the literature a numerical example is included to further illustrate the application of the main result

interval estimation for continuous time lpv switched systems this paper deals with interval state estimation for continuous time linear parameter varying lpv switched systems with measured polytopic parameter dependence assuming a known switching signal

decision making with the ahp why is the principal eigenvector necessary in this paper it is shown that the principal eigenvector is a necessary representation of the priorities derived from a positive reciprocal pairwise comparison judgment matrix a aij when a is a small perturbation of a consistent matrix when providing numerical judgments an individual attempts to estimate sequentially an underlying ratio scale and its equivalent consistent matrix of ratios near consistent matrices are essential because when dealing with intangibles human judgment is of necessity inconsistent and if with new information one is able to improve inconsistency to near consistency then that could improve the validity of the priorities of a decision in addition judgment is much more sensitive and responsive to large rather than to small perturbations and hence once near consistency is attained it becomes uncertain which coefficients should be perturbed by small amounts to transform a near consistent matrix to a consistent one if such perturbations were forced they could be arbitrary and thus distort the validity of the derived priority vector in representing the underlying decision

stabilizing switching signals for switched systems this article deals with stability of continuous time switched systems under constrained switching given a family of systems possibly containing unstable dynamics we characterize a new class of switching signals under which the switched system generated by it and the family of systems is globally asymptotically stable our characterization of such stabilizing switching signals involves the asymptotic frequency of switching the asymptotic fraction of activation of the constituent systems and the asymptotic densities of admissible transitions among them our techniques employ multiple lyapunov like functions and extend preceding results both in scope and applicability

adaptive fuzzy output feedback dynamic surface control of mimo switched nonlinear systems with unknown gain signs this paper investigates the problem of adaptive fuzzy tracking control for a class of multi input multi output mimo switched uncertain nonlinear systems with unknown gain signs and unmeasurable states fuzzy logic systems are used to approximate the unknown nonlinear functions a fuzzy mimo switched observer is designed to estimate the unmeasurable states the nussbaum type functions are utilized to handle the unknown gain signs of the system under study a switched dynamic surface based adaptive fuzzy control approach is then established by exploiting the average dwell time method and backstepping and the dynamic surface control technique which constructs multiple switched first order filters to overcome the multiple explosion of complexity problem when applying the backstepping recursive design scheme also the proposed approach extends the classical dynamic surface control technique from its original non switched nonlinear version to a switched nonlinear version it is proved that all the signals in the closed loop system are semiglobal uniformly ultimately boundedness under a class of switching signals with average dwell time and the tracking errors converge to a small neighborhood of the origin a mass spring damper system with controller switching as a practical example is provided to demonstrate the effectiveness of the proposed design method

a revised framework for deriving preference values from pairwise comparison matrices in a recent study choo and wedley proposed a framework to categorize and conduct simulations to compare methods for deriving preference values from pairwise comparison matrices this study demonstrates that some pairs in the examined methods are identical and some methods can be solved in better ways additionally the simulations of choo and wedley are somewhat idealized thus this study provides additional simulations the simulation results lead to different method ranking and conclusions from those of choo and wedley

relaxed conditions for the input to state stability of switched nonlinear time varying systems this technical note considers the problem of input to state stability iss for switched nonlinear time varying systems first a sufficient condition is proposed to verify the iss of nonlinear time varying systems by using an improved lyapunov function then the results obtained are extended to study the iss of switched nonlinear time varying systems three relaxed conditions are given by using the methods of multiple lyapunov functions minimum dwell time and infinite switchings respectively comparing with the existing results the conditions obtained have two relaxations i e the derivative of lyapunov functions of subsystems are allowed to be indefinite and all subsystems are allowed to be unstable in the case of infinite switchings all results obtained also be used to study the uniformly asymptotic stability uas of systems finally a numerical example is given to illustrate the theoretical results

vector lyapunov function based input to state stability of stochastic impulsive switched time delay systems in this paper the input to state stability is studied for stochastic impulsive switched time delay systems using the vector lyapunov function average dwell time and the properties of m matrix different types of sufficient conditions are established both the case that the continuous dynamics is stable and the case that the discrete dynamics is stable are addressed and the stability conditions are obtained in the obtained stability conditions different components of the vector lyapunov function are allowed to be coupled the information in consecutive impulsive switching intervals is also allowed to be coupled therefore the magnification on the corresponding coupling items is avoided and the obtained results are more general and less conservative than the existing results furthermore we investigate the relationships among the vector lyapunov function approach the approach based on the comparison principle and the scalar lyapunov function approach according to the vector lyapunov function the comparison system is constructed and the scalar lyapunov function based stability conditions are established finally the applicability of our results is illustrated through two examples from neural systems and the synchronization problem of chaos based secure communication systems

output to state stability and detectability of nonlinear systems the notion of input to state stability iss has proved to be useful in nonlinear systems analysis this paper discusses a dual notion output to state stability oss a characterization is provided in terms of a dissipation inequality involving storage lyapunov functions combining iss and oss there results the notion of input output to state stability ioss which is also studied and related to the notion of detectability the existence of observers and output injection

on the representation of switched systems with inputs by perturbed control systems this paper provides representations of switched systems described by controlled differential inclusions in terms of perturbed control systems the control systems have dynamics given by differential equations and their inputs consist of the original controls together with disturbances that evolve in compact sets their sets of maximal trajectories contain as a dense subset the set of maximal trajectories of the original system several applications to control theory dealing with properties of stability with respect to inputs and of detectability are derived as a consequence of the representation theorem 2004 elsevier ltd all rights reserved

multiple lyapunov functions based small gain theorems for switched interconnected nonlinear systems multiple lyapunov functions mlfs based small gain theorems are presented for switched interconnected nonlinear systems with unstable subsystems which extend the small gain technique from its original non switched nonlinear version to a switched nonlinear version each low dimensional subsystem does not necessarily have the input to state stability iss property in the whole state space and it only has individual iss property in some subregions of the state space the novelty of this paper is that integral type mlfs and small gain techniques are utilized to establish some mlfs based small gain theorems for switched interconnected nonlinear systems which derive various stability results under some novel switching laws designed and construct integral type mlfs the small gain theorems proposed cover several recent results as special cases which also permit removal of a common restriction in which all low dimensional subsystems in switched interconnected systems are iss or only some are iss and others are not finally two illustrative examples are presented to demonstrate the effectiveness of the results provided

a simple method to improve the consistency ratio of the pair wise comparison matrix in anp tests of consistency for the pair wise comparison matrices have been studied extensively since ahp was introduced by saaty in 1970s however existing methods are either too complicated to be applied in the revising process of the inconsistent comparison matrix or are difficult to preserve most of the original comparison information due to the use of a new pair wise comparison matrix those methods might work for ahp but not for anp as the comparison matrix of anp needs to be strictly consistent to improve the consistency ratio this paper proposes a simple method which combines the theorem of matrix multiplication vectors dot product and the definition of consistent pair wise comparison matrix to identify the inconsistent elements the correctness of the proposed method is proved mathematically the experimental studies have also shown that the proposed method is accurate and efficient in decision maker s revising process to satisfy the consistency requirements of ahp anp

axiomatic foundation of the analytic hierarchy process this paper contains an axiomatic treatment of the analytic hierarchy process ahp the set of axioms corresponding to hierarchic structures are a special case of axioms for priority setting in systems with feedback which allow for a wide class of dependencies the axioms highlight 1 the reciprocal property that is basic in making paired comparisons 2 homogeneity that is characteristic of people s ability for making comparisons among things that are not too dissimilar with respect to a common property and hence the need for arranging them within an order preserving hierarchy 3 dependence of a lower level on the adjacent higher level 4 the idea that an outcome can only reflect expectations when the latter are well represented in the hierarchy the ahp neither assumes transitivity or the stronger condition of consistency nor does it include strong assumptions of the usual notions of rationality a number of facts are derived from these axioms providing an operational basis for the ahp

generalized switching signals for input to state stability of switched systems this article deals with input to state stability iss of continuous time switched nonlinear systems given a family of systems with exogenous inputs such that not all systems in the family are iss we characterize a new and general class of switching signals under which the resulting switched system is iss our stabilizing switching signals allow the number of switches to grow faster than an affine function of the length of a time interval unlike in the case of average dwell time switching we also recast a subclass of average dwell time switching signals in our setting and establish analogs of two representative prior results

detectability and observer design for switched differential algebraic equations this paper studies detectability for switched linear differential algebraic equations daes and its application to the synthesis of observers which generate asymptotically converging state estimates equating detectability to asymptotic stability of zero output constrained state trajectories and building on our work on interval wise observability we propose the notion of interval wise detectability if the output of the system is constrained to be identically zero over an interval then the norm of the corresponding state trajectories scales down by a certain factor at the end of that interval conditions are provided under which the interval wise detectability leads to asymptotic stability of zero output constrained state trajectories an application is demonstrated in designing state estimators decomposing the state into observable and unobservable components we show that if the observable component of the system is reset appropriately and persistently then the estimation error converges to zero asymptotically under the interval wise detectability assumption

input to state stability of impulsive stochastic delayed systems under linear assumptions in this paper the input to state stability iss integral iss iiss and stochastic iss siss are investigated for impulsive stochastic delayed systems by means of the lyapunov krasovskii function and the average impulsive interval approach the conditions for iss type properties are derived under linear assumptions respectively for destabilizing and stabilizing impulses it is shown that if the continuous stochastic delayed system is iss and the impulsive effects are destabilizing then the hybrid system is iss with respect to a lower bound of the average impulsive interval moreover it is unveiled that if the continuous stochastic delayed system is not iss the impulsive effects can successfully stabilize the system for a given upper bound of the average impulsive interval an improved comparison principle is developed for impulsive stochastic delayed systems which facilitates the derivations of our results for iss iiss siss an example of networked control systems is provided to illustrate the effectiveness of the proposed results

the analytic hierarchy process an exposition this exposition on the analytic hierarchy process ahp has the following objectives 1 to discuss why ahp is a general methodology for a wide variety of decision and other applications 2 to present brief descriptions of successful applications of the ahp and 3 to elaborate on academic discourses relevant to the efficacy and applicability of the ahp vis a vis competing methodologies we discuss the three primary functions of the ahp structuring complexity measurement on a ratio scale and synthesis as well as the principles and axioms underlying these functions two detailed applications are presented in a linked document athttp mdm gwu edu formangass pdf

noise to state stability of random switched systems and its applications noise to state stability of random switched systems is investigated in this technical note by the aid of fubini s formula the criteria on noise to state stability in the moment of random switched systems are established under a reasonable assumption of second order processes as applications the control problems of spring pendulum in random environment are researched in addition nonlinear filtering is considered to ensure noise to state stability of filter error switched systems

stability analysis of impulsive switched time delay systems with state dependent impulses this paper studies the stability for impulsive switched time delay systems with state dependent impulses since the impulses and the switches are not necessarily synchronous we start from a stability analysis of impulsive switched time delay systems with time dependent impulses sufficient conditions are derived to guarantee the stability property which extends the previous results for the synchronous switch and impulse case for the state dependent impulse case using the b equivalent method impulsive switched time delay systems with state dependent impulses are transformed into impulsive switched time delay systems with time dependent impulses the equivalence between the original system and the transformed system is established and stability conditions are obtained for impulsive switched time delay systems with state dependent impulses finally a numerical example is given to demonstrate the obtained results

a lyapunov based small gain theorem for interconnected switched systems abstract stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems there may exist some subsystems that are not input to state stable non iss we show that providing the switching signals neither switch too frequently nor activate non iss subsystems for too long a small gain theorem can be used to conclude global asymptotic stability gas of the interconnected system for each switched system with the constraints on the switching signal being modeled by an auxiliary timer a correspondent hybrid system is defined to enable the construction of a hybrid iss lyapunov function apart from justifying the iss property of their corresponding switched systems these hybrid iss lyapunov functions are then combined to establish a lyapunov type small gain condition which guarantees that the interconnected system is globally asymptotically stable

forward completeness unboundedness observability and their lyapunov characterizations a finite dimensional continuous time system is forward complete if solutions exist globally for positive time this paper shows that forward completeness can be characterized in a necessary and sufficient manner by means of smooth scalar growth inequalities moreover a version of this fact is also proved for systems with inputs and a generalization is also provided for systems with outputs and a notion unboundedness observability of relative completeness we apply these results to obtain a bound on reachable states in terms of energy like estimates of inputs