stabilization by means of state space depending switching rules abstract in this paper we consider switched systems defined by a pair of linear systems x a 1 x x a 2 x such that there exists a neutrally stable linear combination of the matrices a 1 a 2 under an additional assumption we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense the result is illustrated by some simulations and examples

closed loop stabilization of planar bilinear switched systems in this paper we address the closed loop switched stabilization problem for planar bilinear systems under the assumption that the control is one dimensional and takes only the values 0 and 1 we construct a class of state static memoryless stabilizing feedback laws which preserve the properties of open loop switching signals in order to prove the stability of the implemented system we use lyapunov techniques for differential equations with discontinuous righthand side finally we point out some possible extensions of our result and compare it with related results previously proven by other authors

on switching stabilizability for continuous time switched linear systems this technical note studies switching stabilization problems for continuous time switched linear systems we consider four types of switching stabilizability defined under different assumptions on the switching control input the most general switching stabilizability is defined as the existence of a measurable switching signal under which the resulting time varying system is asymptotically stable discrete switching stabilizability is defined similarly but requires the switching signal to be piecewise constant on intervals of uniform length in addition we define feedback stabilizability in filippov sense respectively sample and hold sense as the existence of a feedback law under which closed loop filippov solution respectively sample and hold solution is asymptotically stable it is proved that the four switching stabilizability notions are equivalent and their sufficient and necessary condition is the existence of a piecewise quadratic control lyapunov function that can be expressed as the pointwise minimum of a finite number of quadratic functions

robustness properties of an algorithm for the stabilisation of switched systems with unbounded perturbations abstractin this paper it is shown that an algorithm for the stabilisation of switched systems introduced by the authors is robust with respect to perturbations which are unbounded in the supremum norm but bounded in a power like sense the obtained stability results comprise among others both the exponential input to state stability and the exponential integral input to state stability properties of the closed loop system and give a better description of the behaviour of the closed loop system

stability results for switched controller systems there are many practical control problems where the control action is determined by switching among a given set of control laws this paper presents necessary and sufficient conditions to test for quadratic stabilizability and for robust stabilizability with a quadratic storage function for switched controller systems algorithms which can be used to construct appropriately stabilizing control laws are also presented

dissimilarity judgments in relation to temporal and spatial factors for the sound field in an existing hall in relation to the temporal and spatial factors of sound fields dissimilarity judgments for different source locations on a stage were performed this study is based on the model of the auditory brain system which consists of the autocorrelation and crosscorrelation mechanisms for sound signals arriving at two ears and the specialization of human cerebral hemispheres there are three temporal factors 1 1 and e extracted from the autocorrelation function and four spatial factors ll iacc iacc and w iacc from the interaural crosscorrelation function of binaural signals in addition to these temporal and spatial factors the orthogonal factors of the subjective preference for sound field t 1 and t sub were taken into account the psychological distance between sound fields of different source locations on the stage were calculated by using these temporal spatial and orthogonal factors of sound fields using these distances and their linear combination dissimilarity can be calculated results of multivariable analysis show that the calculated scale values of dissimilarity agree well with the measured scale values

nonstandard finite difference equations for odes and 1 d pdes based on piecewise linearization a method for the solution of initial and boundary value problems in nonlinear ordinary differential equations and for one dimensional partial differential equations which provides c 1 solutions is presented the method is based on the linearization of the differential equation in intervals which contain only two grid points and provides three point nonstandard finite difference equations for the nodal amplitudes the method is applied to steady reaction diffusion equations two point singularly perturbed boundary value problems and the steady burgers equation and compared with standard finite difference and finite element formulations for one dimensional partial differential equations the temporal derivatives are first discretized and the resulting ordinary differential equation accounts for both the temporal and spatial stiffnesses and is solved by means of piecewise linearization since the linearization includes a jacobian matrix it may be easily employed to refine the mesh where steep gradients occur

exponential stabilization of a constrained bilinear system for a bilinear system that is open loop neutrally stable a quadratic state feedback control has been proposed to ensure global asymptotical stability of the closed loop system in this paper a new nonlinear control is proposed so that the closed loop system is not only asymptotically stable but also exponentially stable the new control results in a much faster state convergence rate than the quadratic control furthermore it can be applied to systems with tight saturation limits on the control input

on controllability of switched linear systems in this paper the controllability of a switched linear system which is a collection of linear time invariant systems along with some maps for switching among them is addressed first a controllable state set is defined as a basic tool to discuss the controllability condition next it is proved that the controllability of a multi input system is equivalent to that of a single input system finally a sufficient and necessary condition for controllability of third order systems is presented according to the proof of this criterion we state a conjecture on the controllability condition of n dimensional systems a numeric example is given to illustrate the result

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

switching stabilizability for continuous time uncertain switched linear systems this paper investigates the switching stabilizability problem for a class of continuous time switched linear systems with time variant parametric uncertainties first a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived under the assumption that the closed loop switched system does not generate sliding motions then an additional condition is introduced to exclude the possibility of unstable sliding motions finally a necessary and sufficient for the asymptotic stabilizability of such continuous time uncertain switched linear systems is presented this result improves upon conditions found in the literature which are either sufficient only or necessary only

on stability l2 gain and h control for switched systems this paper addresses the issues of stability l 2 gain analysis and h control for switched systems via multiple lyapunov function methods a concept of general lyapunov like functions is presented a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized lyapunov like functions which enables derivation of improved stability tests an l 2 gain characterization and a design method for stabilizing switching laws a solution to the h control problem for switched systems is also provided

extended invariance principle for nonautonomous switched systems stability analysis is developed for nonlinear nonautonomous switched systems trajectories of which admit generally speaking a nonunique continuation on the right for these systems krasovskii lasalle s invariance principle is extended in such a manner to remain true even in the nonautonomous case in addition to a nonsmooth lyapunov function with negative semidefinite time derivatives along the system trajectories the extended invariance principle involves a coupled indefinite function to guarantee asymptotic stability of the system in question as an illustration of the capabilities of this principle a switched regulator of a fully actuated manipulator with frictional joints is constructed

common quadratic lyapunov like functions with associated switching regions for two unstable second order lti systems in this paper we establish quadratic lyapunov like functions for qualitative analysis of switched systems specifically for a class of switched systems consisting of two unstable second order lti linear time invariant subsystems we explore in detail some necessary and sufficient conditions for the existence of common weakly quadratic lyapunov like functions with associated switching regions in r 2 plane the existence conditions and the construction of such quadratic lyapunov like functions are established by using the conic switching laws

necessary and sufficient conditions for regional stabilisability of second order switched linear systems with a finite number of subsystems in this paper the switching stabilisation problem of second order switched linear systems is studied by extending the best case switching signal bcss criteria for second order switched linear systems with two subsystems to the general case with any finite number of subsystems necessary and sufficient conditions for regional stabilisability of second order switched linear systems with any finite number of subsystems are proposed in this paper the main idea of this paper is to divide all the subsystems in a region into two groups based on their trajectory directions in that region by comparing pairwise the most stable subsystem for each group in a region can be determined and the bcss analysis among all the subsystems in that region is reduced to the bcss analysis between the two most stable subsystems in that region

brief paper robust output feedback stabilizability via controller switching the paper considers the output feedback robust stabilizability problem for uncertain dynamical systems the uncertain system under consideration is a composite of a continuous time plant and a switched controller a necessary and sufficient condition of absolute stabilizability is given in terms of the existense of suitable solutions to a dynamic programming equation and a riccati algebraic equation of the h filtering type a real time implementable method for robust stabilization is also presented

on the h0 h stabilization of switched nonlinear systems via state dependent switching rule abstract this paper considers switching stabilization of some general nonlinear systems assuming certain properties of a convex linear combination of the nonlinear vector fields two ways of generating stabilizing switching signals are proposed i e the minimal rule and the generalized rule both based on a partition of the time state space the main theorems show that the resulting switched system is globally uniformly asymptotically stable and globally uniformly exponentially stable respectively it is shown that the stabilizing switching signals do not exhibit chattering i e two consecutive switching times are separated by a positive amount of time in addition under the generalized rule the switching signal does not exhibit zeno behavior accumulation of switching times in a finite time stability analysis is performed in terms of two measures so that the results can unify many different stability criteria such as lyapunov stability partial stability orbital stability and stability of an invariant set applications of the main results are shown by several examples and numerical simulations are performed to both illustrate and verify the stability analysis

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

global stabilisation of switched nonlinear systems in p normal form with mixed odd and even powers this article investigates the problem of global stabilisation for a class of switched nonlinear systems in p normal form whose subsystems are not assumed to be asymptotically stabilisable unlike the existing results on systems in p normal form where the power order is only positive odd integer we allow positive even integer of the power order using the convex combination method and the adding a power integrator technique we construct a switching law and design state feedback controllers of individual subsystems explicitly by a recursive design algorithm to guarantee asymptotic stability of the closed loop system the designed method is also extended to the global stabilisation problem of switched nonlinear systems in p normal form with zero dynamics as an application of the proposed design method a continuously stirred tank reactor is studied

extraction of the envelope from impulse responses using pre processed energy detection for early decay estimation the schroeder s backward integration method and its applications have been widely studied in the literature some papers analyze the performance of the method some others suggest various enhancement techniques in spite of these findings there exist several cases where the energy decay curve extracted using the classical backward integration method and the parameters computed from it seem not always representative of the phenomenon under study among them the cases where the early decay is dependent on strong distinct reflections occurring just after the direct wave as in most italian opera houses other cases are measured impulse responses with a very low signal to noise ratio or missing the direct wave in the literature alternatives to the schroeder s method have been proposed ranging from hilbert transform to non linear processing techniques in this work a method for the extraction of the envelope based on pre processed energy detection for early decay estimation is proposed it is shown that it returns an envelope well matching the first part of the decay even in non linear cases returning detailed information on the first part of the decay the performance of the proposed method is presented and discussed for some exemplary impulse responses measured in historical opera houses a preliminary study on the perceptive relevance of the method is finally presented

a constructive approach to reachability realization of discrete time switched linear systems this paper studies the reachability of discrete time switched linear systems a new constructive approach to designing switching sequences is developed so that not only the reachable subspace is realized but also the required number of switchings is reduced significantly detailed comparison between the obtained result and that reported in the open literature is also made which verifies the advantage of the proposed approach

existence of carathe spl acute odory solutions in nonlinear systems with discontinuous switching feedback controllers in this note we consider the existence of a carathe spl acute odory solution in a single input single output nonlinear system with a discontinuous switching feedback controller the main contribution is to show that if the nonlinear system can be transformed into a global normal form then we can specify the value of the discontinuous switching feedback controller on the switching hypersurface so that the closed loop system has a carathe spl acute odory solution

necessary and sufficient conditions for regional stabilisability of generic switched linear systems with a pair of planar subsystems in this article the regional stabilisability issues of a pair of planar lti systems are investigated through the geometrical approach and easily verifiable necessary and sufficient conditions are derived the main idea of the article is to characterise the best case switching signals based upon the variations of the constants of the integration of the subsystems the conditions are generic as all possible combinations of the subsystem dynamics are considered

quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays abstract this paper deals with the quadratic stability and linear state feedback and output feedback stabilization of switched delayed linear dynamic systems with in general a finite number of non commensurate constant internal point delays the results are obtained based on lyapunov s stability analysis via appropriate krasovsky lyapunov s functionals and the related stability study is performed to obtain both delay independent and delay dependent results it is proved that the stabilizing switching rule is arbitrary if all the switched subsystems are quadratically stable and that it exists a in general non unique stabilizing switching law when the system is polytopic stable at some interior point of the polytope but with non necessarily stable parameterizations at the vertices defining the subsystems it is also proved that two subsystems individually parametrized in different polytopic type sets which are not quadratically stable might be stabilized by a in general non unique switching law provided that a convexity type condition is fulfilled at each existing pair of vertices one corresponding to each subsystem some extensions are provided for a typical class of neutral time delay systems

asymptotic stabilization of the bilinear time invariant system via piecewise constant feedback abstract sufficient conditions for the asymptotic stabilization in a preassigned domain of the nonhomogeneous bilinear system bls via piecewise constant feedback are given based on those for an auxillary bls with additional control in the drift term application to the swing equation is also discussed

stabilization of uncertain systems with norm bounded uncertainty a control a robust stabilization problem in a state space setting is treated it is assumed that the states are available for feedback using a fixed lyapunov function approach quadratic stability it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state feedback controller as a consequence it is shown that the existence of a quadratically stabilizing nonlinear time varying dynamic state feedback controller implies the existence of a quadratically stabilizing memoryless linear time invariant state feedback compensator

graph lyapunov function for switching stabilization and distributed computation abstract this paper studies stabilization of discrete time switched linear systems slss using the notion of graph control lyapunov functions gclfs a gclf is a set of lyapunov functions defined on a weighted digraph where each lyapunov function is represented by a node in the digraph and there is a lyapunov inequality associated with each subgraph consisting of a node and its out neighbors the weight of a directed edge indicates the decay or growth rate of the lyapunov functions it is proved that an sls is switching stabilizable if and only if there exists a gclf the main benefits of gclfs are reduced computational cost and conservatism for stabilizability tests besides we show that the proposed gclf framework unifies several control lyapunov functions and the related stabilization theorems moreover we propose a distributed algorithm to evaluate the stabilizability with reduced computational costs by taking benefits of the graph structure of gclfs several examples are given to demonstrate the efficiency of the algorithm

exponential stabilization of discrete time switched linear systems this article studies the exponential stabilization problem for discrete time switched linear systems based on a control lyapunov function approach it is proved that a switched linear system is exponentially stabilizable if and only if there exists a piecewise quadratic control lyapunov function such a converse control lyapunov function theorem justifies many of the earlier synthesis methods that have adopted piecewise quadratic lyapunov functions for convenience or heuristic reasons in addition it is also proved that if a switched linear system is exponentially stabilizable then it must be stabilizable by a stationary suboptimal policy of a related switched linear quadratic regulator lqr problem motivated by some recent results of the switched lqr problem an efficient algorithm is proposed which is guaranteed to yield a control lyapunov function and a stabilizing policy whenever the system is exponentially stabilizable

stability of planar switched systems the linear single input case we study the stability of the origin for the dynamical system dot x t u t ax t 1 u t bx t where a and b are two 2 2 real matrices with eigenvalues having strictly negative real part x in mbox bf r 2 and u 0 infty to 0 1 is a completely random measurable function more precisely we find a coordinates invariant necessary and sufficient condition on a and b for the origin to be asymptotically stable for each function u the result is obtained without looking for a common lyapunov function but studying the locus in which the two vector fields ax and bx are collinear there are only three relevant parameters the first depends only on the eigenvalues of a the second depends only on the eigenvalues of b and the third contains the interrelation among the two systems and it is the cross ratio of the four eigenvectors of a and b in the projective line cp1 in the space of these parameters the shape and the convexity of the region in which there is stability are studied this bidimensional problem assumes particular interest since linear systems of higher dimensions can be reduced to our situation

h control of switched delayed systems with average dwell time this paper considers the problems of stability analysis and h controller design of time delay switched systems with average dwell time in order to obtain less conservative results than what is seen in the literature a tighter bound for the state delay term is estimated based on the scaled small gain theorem and the model transformation method an improved exponential stability criterion for time delay switched systems with average dwell time is formulated in the form of convex matrix inequalities the aim of the proposed approach is to reduce the minimal average dwell time of the systems which is made possible by a new lyapunov krasovskii functional combined with the scaled small gain theorem it is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature moreover the exponential h controller can be constructed by solving a set of conditions which is developed on the basis of th

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

on the stabilizability of discrete time switched linear systems novel conditions and comparisons in this paper we deal with the stabilizability property for discrete time switched linear systems a recent necessary and sufficient characterization of stabilizability based on set theory is considered as the reference for comparing the computation oriented sufficient conditions the classical bmi conditions based on lyapunov metzler inequalities are considered and extended novel lmi conditions for stabilizability derived from the geometric ones are presented that permit to combine generality with computational affordability for the different conditions the geometrical interpretations are provided and the induced stabilizing switching laws are given the relations and the implications between the stabilizability conditions are analyzed to infer and compare their conservatism and their complexity

technical communique stabilizing controllers design for switched nonlinear systems in strict feedback form this paper considers the stabilization problem for a class of switched nonlinear systems under arbitrary switching based on the backstepping method and the control lyapunov function approach it is shown that under a simultaneous domination assumption a switched nonlinear system in strict feedback form can be globally uniformly asymptotically stabilized by a continuous state feedback controller a universal formula for constructing stabilizing feedback laws is presented one example is included for verifying the obtained results

feedback stabilization for multiinput switched nonlinear systems two subsystems case in this note based on the control lyapunov function approach a new method for solving the feedback stabilization problem of switched systems that are switching arbitrarily between two multiinput nonlinear subsystems is introduced necessary and sufficient conditions for the existence of globally uniformly asymptotically stabilizing state feedback controllers are derived additionally a universal formula for constructing implementable stabilizing controllers is given when the presented conditions hold one numerical example is given to illustrate the results

stabilisability of nonlinear systems by means of time dependent switching rules given a family of linear systems which admit an asymptotically stable convex combination the existence of stabilising time dependent switching rules can be proved by using the baker campbell hausd

robust h control of discrete switched system with time delay this paper deals with the stabilization and robust h infinity control of discrete switched system with time delay the switching is time driven and the design is based on the average dwell time method the controller parameters and the permissible switching sequence subject to the given average dwell time can be obtained by solving a set of linear matrix inequalities lmis two examples are given to demonstrate the proposed methods

stabilization of second order lti switched systems this paper studies and solves the problem of asymptotic stabilization of switched systems consisting of unstable secondorder linear time invariant lti subsystems necessary and sufficient conditi

flow stability of patchy vector fields and robust feedback stabilization the paper is concerned with patchy vector fields a class of discontinuous piecewise smooth vector fields that were introduced by the authors to study feedback stabilization problems we prove the stability of the corresponding solution set w r t a wide class of impulsive perturbations these results yield the robustness of patchy feedback controls in the presence of measurement errors and external disturbances

exponential stability with l_ 2 gain condition of nonlinear impulsive switched systems in this technical note we consider exponential stability and stabilization problems of a general class of nonlinear impulsive switched systems with time varying disturbances by using the switched lyapunov function method sufficient conditions expressed as algebraic inequality constraints and linear matrix inequalities are obtained they ensure that the nonlinear impulsive switched systems are not only exponentially stable but also satisfy the l2 gain condition based on the stability results obtained an effective computational method is devised for the construction of switched linear stabilizing feedback controllers a numerical example is presented to illustrate the effectiveness of the results obtained

hybrid state feedback stabilization with l 2 performance for discrete time switched linear systems in this paper the co design of continuous variable controllers and discrete event switching logics both in state feedback form is investigated for a class of discrete time switched linear control systems it is assumed that none of the subsystems is stabilized through a continuous state feedback alone however it is possible to stabilize the whole switched system via carefully designing both the continuous controllers and the switching logics sufficient synthesis conditions for this co design problem are proposed here in the form of bilinear matrix inequalities which is based on the argument of multiple lyapunov functions the closed loop switched system forms a special class of linear hybrid system and is shown to be asymptotically stable with a finite l 2 induced gain

asymptotic controllability by means of eventually periodic switching rules in this paper we introduce the notion of eventually periodic switching signal we prove that if a family of linear vector fields satisfies a mild finite time controllability condition and for each initial state there exists a time dependent switching signal which asymptotically drives the system to the origin possibly allowing different signals for different initial states then the same goal can be achieved by means of an eventually periodic switching signal this enables us to considerably reduce the dependence of the control law on the initial state in this sense the problem addressed in this paper can be reviewed as a switched system theory version of the classical problem of investigating whether or to what extent a nonlinear asymptotically controllable system admits stabilizing feedback laws

the running autocorrelation function of different music signals relating to preferred temporal parameters of sound fields this paper defines the minimum value of the effective duration of the running autocorrelation function of a music signal used in subjective preference testing a short duration signal which may relate to psychological present is more suitable for calculating the most preferred time delay of the single reflection than is the long time autocorrelation function this fact is found particularly when passages of japanese music are being played which include a wide range noise component at the very beginning of the signal and the so called ma ma is a stationary sound passage without any rapid movement this paper also shows that for subsequent reverberation time a flat frequency response may be in the range of preferred conditions such preferred conditions may be calculated by the minimum effective duration of the running autocorrelation function of source signals after passing through the a weighting network

on stabilizability of switched positive linear systems under state dependent switching this paper addresses the stabilization of switched positive linear systems by state dependent switching we show that if there is a hurwitz convex or linear combination of the coefficient matrices then the switched positive linear system can be exponentially stabilized by means of a single linear co positive lyapunov function if there is not a stable combination of system matrices it is shown that the exponential stabilizability is equivalent to a completeness condition on the coefficient matrices when the switched positive systems can not be stabilized by the single lyapunov function we provide a unified criterion for piecewise exponential stabilizability in terms of multiple linear co positive lyapunov functions

on reachability and controllability of switched boolean control networks this paper investigates the reachability and controllability of switched boolean control networks bcns by using the semi tensor product method first a kind of switching input state transfer graph is defined based on which and the algebraic expression of switched bcns we thus propose a new kind of switching input state incidence matrix that contains the complete information of the switching input state transfer graph second by the switching input state incidence matrix several necessary and sufficient conditions are obtained for the reachability and controllability of switched bcns finally an algorithm is established to find a switching sequence and a control scheme to realize the reachability of switched bcns in the shortest time the study of an illustrative example shows that the new results obtained in this paper are very effective in investigating the reachability and controllability of switched bcns

stabilisation of second order lti switched positive systems the stabilisation problem of second order switched positive systems consisting of two unstable subsystems is considered in this article by considering the vector fields and geometric characteristics a necessary and sufficient condition for the stabilisability of second order switched positive systems with two unstable subsystems is provided furthermore it is shown via this condition that neither second order switched positive systems consisting of two subsystems with unstable nodes nor second order switched positive systems consisting of one subsystem with unstable nodes and the other with a saddle point can be stabilised via any switching law

sufficient and necessary conditions for the stability of second order switched linear systems under arbitrary switching many practical systems can be modelled as switched systems whose stability problem is challenging even for linear subsystems in this article the stability problem of second order switched linear systems with a finite number of subsystems under arbitrary switching is investigated sufficient and necessary stability conditions are derived based on the worst case analysis approach in polar coordinates the key idea of this article is to partition the whole state space into several regions and reduce the stability analysis of all the subsystems to analysing one or two worst subsystems in each region this article is an extension of the work for stability analysis of second order switched linear systems with two subsystems under arbitrary switching

finite valued feedback laws and piecewise classical solutions abstract often in engineering literature we find control systems in which the open loop inputs are piecewise constant and take values in a finite set such open loop inputs cause the system to have fairly regular solutions on the other hand when acting in closed loop feedback laws taking values in a finite set may not be reinterpreted as open loop inputs of the considered type in fact pathological behaviours such as the accumulation of discontinuities may appear zeno phenomenon we give some conditions which can be used as tools for building finite valued feedback laws not causing such pathological behaviours

hybrid dynamical systems robust control synthesis problems the paper presents a new approach to robust control synthesis problems for hybrid dynamical systems the hybrid system under consideration is a composite of a continuous plant and a discrete event controller state and output feedback problems are considered the main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a riccati differential equation of the h filtering type these results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control

piecewise linearized and linearized θ methods for ordinary and partial differential equations lnitial and boundary value problems appear frequently in many branches of physics in this paper several numerical methods based on linearization techniques for solving these prob lems are reviewed first piecewise linearized methods and linearized 0 methods are considered for the solution of initial value problems in ordinary differential equations second piecewise linearized techniques for two point boundary value problems in ordinary differential equations are developed and used in conjunction with a shooting method in order to overcome the lack of convergence asso ciated with shooting piecewise linearized methods which provide piecewise analytical solutions and yield nonstandard finite difference schemes axe presented third methods of lines in either space or time for the solution of one dimensional convection reaction diffusion problems that transform the original problem into an initial or boundary value one are reviewed methods of lines in time that result in boundary value problems at each time step can be solved by means of the techniques described here whereas methods of lines in space that yield initial value problems and employ ei ther piecewise linearized techniques or linearized 0 methods in time are also developed finally for multidimensional problems approximate factorization methods are first used to transform the multi dimensional problem into a sequence of one dimensional ones which are then solved by means of the linearized and piecewise linearized methods presented here 2003 elsevier science ltd all rights reserved

asymptotic stability and smooth lyapunov functions abstract we establish that differential inclusions corresponding to upper semicontinuous multifunctions are strongly asymptotically stable if and only if there exists a smooth lyapunov function since well known concepts of generalized solutions of differential equations with discontinuous right hand side can be described in terms of solutions of certain related differential inclusions involving upper semicontinuous multifunctions this result gives a lyapunov characterization of asymptotic stability of either filippov or krasovskii solutions for differential equations with discontinuous right hand side in the study of weak as opposed to strong asymptotic stability the existence of a smooth lyapunov function is rather exceptional however the methods employed in treating the strong case of asymptotic stability are applied to yield a necessary condition for the existence of a smooth lyapunov function for weakly asymptotically stable differential inclusions this is an extension to the context of lyapunov functons of brockett s celebrated covering condition from continuous feedback stabilization theory

subjective preference for sound sources located on the stage and in the orchestra pit of an opera house abstract the present study investigates whether the subjective preference theory can be applied to the sound field in an opera house paired comparison tests were conducted to obtain scale values of subjective preference as the source locations of the music on the stage and in the orchestra pit were moved listeners were asked to give their acoustical preference the acoustical factors at each listening position were obtained from the interaural cross correlation function and binaural impulse responses measured at each listening position the relationship between the scale values of subjective preference and orthogonal acoustical factors ll iacc iacc t1 for the pit source t1 for the stage tsub for the pit source and tsub for the stage source was determined by using factor analysis which shows that the preference theory is applicable total scores obtained from factor analysis and measured scale values are in good agreement

a converse lyapunov theorem for a class of dynamical systems which undergo switching the authors investigate the stability of a system in which the dynamics at any instant in time will follow one of a fixed set of vector fields they allow switching between members of the family of vector fields to be completely random the focus of this paper is to prove a converse lyapunov theorem for this class of systems

brief paper design of switching sequences for controllability realization of switched linear systems in this paper we study the problem of designing switching sequences for controllability of switched linear systems each controllable state set of designed switching sequences coincides with the controllable subspace both aperiodic and periodic switching sequences are considered for the aperiodic case a new approach is proposed to construct switching sequences and the number of switchings involved in each designed switching sequence is shown to be upper bounded by d d d 1 1 here d is the dimension of the controllable subspace d email protected i 1 m where a i b i are subsystems for the periodic case we show that the controllable subspace can be realized within d switching periods

some results on the stabilization of switched systems this paper deals with the stabilization of switched systems with respect to w r t compact sets we show that the switched system is stabilizable w r t a compact set by means of a family of switched signals if and only if a certain control affine system whose admissible controls take values in a polytope is asymptotically controllable to that set in addition we present a control algorithm that based on a family of open loop controls which stabilizes the aforementioned control system a model of the system and the states of the switched system generates switching signals which stabilize the switched system in a practical sense we also give results about the convergence and the robustness of the algorithm

semiconcave control lyapunov functions and stabilizing feedbacks we study the general problem of stabilization of globally asymptotically controllable systems we construct discontinuous feedback laws and particularly we make it possible to choose these continuous outside a small set closed with measure zero of discontinuity in the case of control systems which are affine in the control moreover this set of singularities is shown to be repulsive for the caratheodory solutions of the closed loop system under an additional assumption

characterization of well posedness of piecewise linear systems one of the basic issues in the study of hybrid systems is the well posedness existence and uniqueness of solutions problem of discontinuous dynamical systems the paper addresses this problem for a class of piecewise linear discontinuous systems under the definition of solutions of caratheodory the concepts of jump solutions or of sliding modes are not considered here in this sense the problem to be discussed is one of the most basic problems in the study of well posedness for discontinuous dynamical systems first we derive necessary and sufficient conditions for bimodal systems to be well posed in terms of an analysis based on lexicographic inequalities and the smooth continuation property of solutions next its extensions to the multimodal case are discussed as an application to switching control in the case that two state feedback gains are switched according to a criterion depending on the state we give a characterization of all admissible state feedback gains for which the closed loop system remains well posed

an invariance principle for nonlinear switched systems abstract in this paper we address the problem of extending lasalle invariance principle to switched system we prove an extension of the invariance principle relative to dwell time switched solutions and a second one relative to constrained switched systems

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

state feedback control of switched linear systems an lmi approach this paper addresses the problem of state feedback control of continuous time switched linear systems with arbitrary switching rules a quadratic lyapunov function with a common matrix is used to derive a stabilizing switching control strategy that guarantees i the assignment of all the eigenvalues of each linear subsystem inside a chosen circle in the left hand half of the complex plane ii a minimum disturbance attenuation level for the closed loop switched system the proposed design conditions are given in terms of linear matrix inequalities that encompass previous results based on quadratic stability conditions with fixed control gains although the quadratic stability based on a fixed lyapunov matrix has been widely used in robust control design the use of this condition to provide a convex design method for switching feedback gains has not been fully investigated numerical examples show that the switching control strategy can cope with more stringent design specifications than the fixed gain strategy being useful to improve the performance of this class of systems

relationship between subjective preference and the alpha brain wave in relation to the initial time delay gap with vocal music abstract previously it was reported that the most preferred initial time delay gap t1 pand subsequent reverberation time are described by the minimum value of the effective duration e minof the running autocorrelation function acf of music signals 2 t 2 0 s y ando et al 1989 journal of acoustical society of america86 644 649 this paper shows whether this result is supported or not by use of the electro physiological method experiments were performed for sound fields changing the initial time delay gap t1 of a single reflection with vocal music as a source signal which has large changes in running e the results at the time interval when e minof the music is observed reveal that the scale value of subjective preference is closely related to the value of eof the alpha wave obtained from the left heimsphere