system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

absolute stability of third order systems a numerical algorithm the problem of absolute stability is one of the oldest open problems in the theory of control even for the particular case of second order systems a complete solution was presented only very recently for third order systems the most general theoretical results were obtained by barabanov he derived an implicit characterization of the most destabilizing nonlinearity using a variational approach in this paper we show that his approach yields a simple and efficient numerical scheme for solving the problem in the case of third order systems this allows the determination of the critical value where stability is lost in a tractable and accurate fashion this value is important in many practical applications and we believe that it can also be used to develop a deeper theoretical understanding of this interesting problem

nilpotent and high order approximations of vector field systems this paper is concerned with the study of structurally stable properties associated with systems described by one or several real analytic vector fields via approximating systems which retain inf

universal property of the housekeeping entropy production the entropy production of a nonequilibrium system with broken detailed balance is a random variable whose mean value is nonnegative the housekeeping entropy production which is a part of total entropy production is associated with the heat dissipation in maintaining a nonequilibrium steady state we derive a langevin type stochastic differential equation for the housekeeping entropy production the equation allows us to define a housekeeping entropic time ensuremath tau remarkably it turns out that the probability distribution of the housekeeping entropy production at a fixed value of ensuremath tau is given by the gaussian distribution regardless of system details the gaussian distribution is universal for any systems whether in the steady state or in the transient state and whether they are driven by time independent or time dependent driving forces we demonstrate the universal distribution numerically for model systems

lie algebraic stability conditions for nonlinear switched systems and differential inclusions abstract we present a stability criterion for switched nonlinear systems which involves lie brackets of the individual vector fields but does not require that these vector fields commute a special case of the main result says that a switched system generated by a pair of globally asymptotically stable nonlinear vector fields whose third order lie brackets vanish is globally uniformly asymptotically stable under arbitrary switching this generalizes a known fact for switched linear systems and provides a partial solution to the open problem posed in d liberzon lie algebras and stability of switched nonlinear systems in v blondel a megretski eds unsolved problems in mathematical systems and control theory princeton university press nj 2004 pp 203 207 to prove the result we consider an optimal control problem which consists in finding the most unstable trajectory for an associated control system and show that there exists an optimal solution which is bang bang with a bound on the total number of switches this property is obtained as a special case of a reachability result by bang bang controls which is of independent interest by construction our criterion also automatically applies to the corresponding relaxed differential inclusion

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

the effect of coupling conditions on the stability of bimodal systems in r3 abstract this paper investigates the global asymptotic stability of a class of bimodal piecewise linear systems in r 3 the approach taken allows the vector field to be discontinuous on the switching plane in this framework verifiable necessary and sufficient conditions are proposed for global asymptotic stability of bimodal systems being considered it is further shown that the way the subsystems are coupled on the switching plane plays a crucial role on global asymptotic stability along this line it is demonstrated that a constant which is called the coupling constant in the paper can be changed without changing the eigenvalues of subsystems and this change can make bimodal system stable or unstable

simulation of the effects of loudness recruitment and threshold elevation on the intelligibility of speech in quiet and in a background of speech these experiments simulated the threshold elevation and loudness recruitment associated with three different types of cochlear hearing loss moderate flat condition r2 severe flat condition r3 and moderate to severe sloping condition rx this was done to allow an examination of the effects of these factors on the intelligibility of speech in isolation from other factors that are normally associated with cochlear hearing loss such as reduced frequency selectivity the simulation was performed by splitting the input signal into 13 frequency bands and processing the envelope in each band so as to create loudness sensations in a normal ear that would resemble those produced in an impaired ear with recruitment the bands were then recombined all tests were performed using subjects with normal hearing for speech in quiet simulation of hearing loss produced a reduction in the ability to understand low level speech however speech at sufficiently high levels was highly intelligible in all conditions linear amplification according to the national acoustic laboratory nal prescription gave high intelligibility for speech at normal conversational levels for speech presented at a fixed input level of 65 db spl against a background of a single competing talker simulation of hearing loss produced substantial decrements in performance the speech to background ratios in conditions r2 and rx had to be 11 13 db higher than in the control condition unprocessed stimuli to achieve similar levels of performance linear amplification according to the nal prescription improved performance markedly for the conditions simulating flat losses but was less effective for the condition simulating a sloping loss this indicates that threshold elevation combined with recruitment produces a loss of intelligibility for speech in the presence of a single competing talker that is only partly compensated by linear amplification of the type typically used in hearing aids

stability of discrete linear inclusion let m ai be a set of linear operators on rn the discrete linear inclusion dli m is the set of possible trajectories xi i 0 such that xn ainain 1 ai1x0 where x0 rn and aij m we study several notions of stability for dli m including absolute asymptotic stability aas which is that all products ain ai1 0 as n we mainly study the case that m is a finite set we give criteria for the various forms of stability two new approaches are taken one relates the question of aas of dli m to formal language theory and finite automata while the second connects the aas property to the structure of a lie algebra associated to the elements of m more generally the discrete linear inclusion dli m makes sense for m contained in a banach algebra b we prove some results for aas in this case and give counterexamples showing that some results valid for finite sets of operators on rn are not true for finite sets m in a general banach algebras b

on the local structure of optimal trajectories in r 3 we analyze the structure of a control function u t corresponding to an optimal trajectory for the system dot q f q u g q in a three dimensional manifold near a point where some nondegeneracy conditions are satisfied the kind of optimality which is studied includes time optimality the control turns out to be the concatenation of some bang and some singular arcs studying the index of the second variation of the switching times the number of such arcs is bounded by four

a condition for the stability of switched nonlinear systems in this paper we present a sufficient condition for the global asymptotic stability of a switched nonlinear system composed of a finite family of subsystems we show that the global asymptotic stability of each subsystem and the pairwise commutation of the vector fields that define the subsystems i e the lie bracket of any pair of them is zero are sufficient for the global asymptotic stability of the switched system we also show that these conditions are sufficient for the existence of a common lyapunov function

brief paper root mean square gain of discrete time switched linear systems under dwell time constraints this paper deals with discrete time switched linear systems and considers the problem of computing an upper bound to the dwell time ensuring a pre specified root mean square rms gain as a natural consequence of treating general systems of this class in terms of the order and the number of subsystems only sufficient conditions are worked out they depend on the complete separation of the stabilizing and anti stabilizing solutions of the algebraic riccati equation associated to each subsystem moreover as positive features it is shown that the dwell time preserving the specification can be calculated through linear matrix inequalities lmis and line search being thus numerically solvable in polynomial time and this allows the treatment of stable switched linear systems which do not admit a common lyapunov function the case of a guaranteed rms gain for arbitrary switching signals is also addressed a simple academic example constituted by three subsystems of third order is included for illustration

the problem of absolute stability a dynamic programming approach we consider the problem of absolute stability of a feedback system composed of a linear plant and a single sector bounded nonlinearity pyatnitskiy and rapoport used a variational approach and the maximum principle to derive an implicit characterization of the most destabilizing nonlinearity in this paper we address the same problem using a dynamic programming approach we show that the corresponding value function is composed of simple building blocks which are the generalized first integrals of appropriate linear systems we demonstrate how the results can be used to design stabilizing switched controllers

noncyclic and nonadiabatic geometric phase for counting statistics we propose a general framework of the geometric phase interpretation for counting statistics counting statistics is a scheme to count the number of specific transitions in a stochastic process the cumulant generating function for the counting statistics can be interpreted as a phase and it is generally divided into two parts the dynamical phase and a remaining one it has already been shown that for cyclic evolution the remaining phase corresponds to a geometric phase such as the berry phase or aharonov anandan phase we here show that the remaining phase has also an interpretation as a geometric phase even in noncyclic and nonadiabatic evolution

stabilization of switched continuous time systems with all modes unstable via dwell time switching stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems in this brief paper a sufficient condition ensuring the asymptotic stability of switched continuous time systems with all modes unstable is proposed the main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes then by using a discretized lyapunov function approach a computable sufficient condition for switched linear systems is proposed in the framework of dwell time it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability based on derived results an algorithm is proposed to compute the stability region of admissible dwell time a numerical example is proposed to illustrate our approach

brief paper a full characterization of stabilizability of bimodal piecewise linear systems with scalar inputs this paper studies open loop stabilization problem for bimodal systems with continuous vector field it is based on the earlier work of the authors on the controllability problem for the same class of systems a full characterization of stabilizability is established by presenting algebraic necessary and sufficient conditions it is also shown that controllability implies stabilizability for these systems in a very similar fashion to the linear case

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

fluctuation theorems and inequalities generalizing the second law of thermodynamics out of equilibrium we present a general framework for systems which are prepared in a nonstationary nonequilibrium state in the absence of any perturbation and which are then further driven through the application of a time dependent perturbation by assumption the evolution of the system must be described by markovian dynamics we distinguish two different situations depending on the way the nonequilibrium state is prepared either it is created by some driving or it results from a relaxation following some initial nonstationary conditions our approach is based on a recent generalization of the hatano sasa relation for nonstationary probability distributions we also investigate whether a form of the second law holds for separate parts of the entropy production and for any nonstationary reference process a question motivated by the work of m esposito et al phys rev lett 104 090601 2010 we find that although the special structure of the theorems derived in this reference is not recovered in the general case detailed fluctuation theorems still hold separately for parts of the entropy production these detailed fluctuation theorems contain interesting generalizations of the second law of thermodynamics for nonequilibrium systems

study of multichannel amplitude compression and linear amplification for persons with sensorineural hearing loss experiments were conducted on five listeners with sensorineural hearing impairments using two 16 channel computer controlled amplitude compression systems and four linear systems one of the compression systems was designed to restore normal equal loudness contours the other employed reduced high frequency emphasis and reduced compression ratios the linear systems differed only in their frequency gain characteristics orthotelephonic plus three characteristics with high frequency emphasis that were expected to produce better results than orthotelephonic in the main experiment all systems were compared for each listener using nonsense cvc monosyllables and sentence materials spoken by male and female talkers and presented in quiet anechoic and noisy reverberant environments at the most comfortable level for each listener the linear systems with high frequency emphasis performed substantially better than the orthotelephonic system performance with compression was generally slightly worse than with linear amplification compression was superior to linear amplification only when speech materials with significant item to item level variation were used in quiet with subjects with more severe losses and when reduced input speech levels were used to the extent that these two conditions represent real life communication conditions these results suggest that compression is preferable to linear amplification in a wearable hearing aid

stability analysis of switched systems using variational principles an introduction many natural and artificial systems and processes encompass several modes of operation with a different dynamical behavior in each mode switched systems provide a suitable mathematical model for such processes and their stability analysis is important for both theoretical and practical reasons we review a specific approach for stability analysis based on using variational principles to characterize the most unstable solution of the switched system we also discuss a link between the variational approach and the stability analysis of switched systems using lie algebraic considerations both approaches require the use of sophisticated tools from many different fields of applied mathematics the purpose of this paper is to provide an accessible and self contained review of these topics emphasizing the intuitive and geometric underlying ideas

fluctuation theorem for birth death or chemical master equations with time dependent rates for systems described by univariate birth death or chemical master equations driven out of equilibrium by externally controlled time dependent transition rates a nonlinear fluctuation theorem is derived for paradigmatic chemical reactions this theorem acquires a particularly transparent form

stability analysis of second order switched homogeneous systems we study the stability of second order switched homogeneous systems using the concept of generalized first integrals we explicitly characterize the most destabilizing switching law and construct a lyapunov function that yields an easily verifiable necessary and sufficient condition for asymptotic stability using the duality between stability analysis and control synthesis this also leads to a novel algorithm for designing a stabilizing switching controller

nonholonomic motion planning steering using sinusoids methods for steering systems with nonholonomic c onstraints between arbitrary configurations are investigated suboptimal trajectories are derived for systems that are not in canonical form systems in which it takes more than one level of bracketing to achieve controllability are considered the trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level a class of systems that can be steered using sinusoids claimed systems is defined conditions under which a class of two input systems can be converted into this form are given

the explicit form of the rate function for semi markov processes and its contractions we derive the explicit form of the rate function for semi markov processes here the random time change trick plays an essential role also by exploiting the contraction principle of the large deviation theory to the explicit form we show that the fluctuation theorem gallavotti cohen symmetry holds for semi markov cases furthermore we elucidate that our rate function is an extension of the level 2 5 rate function for markov processes to semi markov cases

distribution of work in isothermal nonequilibrium processes diffusive motion in an externally driven potential is considered it is shown that the distribution of work required to drive the system from an initial equilibrium state to another is gaussian for slow but finite driving our result is obtained by projection method techniques exploiting a small parameter defined as the switching rate between the two states of the system the exact solution for a simple model system shows that such an expansion may fail in higher orders since the mean and the variance following from the exact distribution show nonanalytic behavior

a unifying framework for the siso circle criterion and other quadratic stability criteria we present a result on the existence of a common quadratic lyapunov function for a pair of stable linear time invariant systems we show that this result characterizes generalizes and provides new perspectives on several well known stability results

the campbell baker hausdorff dynkin formula and solutions of differential equations the campbell baker hausdorff dynkin formula is a special case of a simpler and more general formula for the solution of nonautonomous systems of first order ordinary differential equations in terms of autonomous systems specifically suppose u t takes values in a c manifold and satisfies the initial value problem u t a t u t u 0 a where a t is a vector field on the manifold depending continuously on t then u t exp z t a here exp z a means the solution at s 1 to v s z v s v 0 a for z t r 1 pr e r2r 1e tr t x a s 1 a s 2 a s r ds as t 0 where tr t s rr 0 s1 s2 sr t pr is the set of permutations on 1 r e is the number of errors in ordering consecutive terms in 1 r and is the usual commutator of vector fields under appropriate analyticity assumptions the series for z t is convergent for small t this formula gives an explicit formulation of results of k t chen published in 1957 applications are given to problems in sub riemannian geometry and to improving convergence estimates for the campbell baker hausdorff dynkin formula in the context of banach algebras our formula can be thought of as a noncommutative generalization of the familiar formula u t a exp 0t a s ds in the scalar linear case in the same way that the campbell baker hausdorff dynkin formula is a noncommutative generalization of the familiar formula exey ex y

a generalization of zubov s method to perturbed systems a generalization of zubov s theorem on representing the domain of attraction via the solution of a suitable partial differential equation is presented for the case of perturbed systems with a singular fixed point for the construction it is necessary to consider solutions in the viscosity sense as a consequence maximal robust lyapunov functions can be characterized as viscosity solutions

on the marginal instability of linear switched systems abstract stability properties for continuous time linear switched systems are at first determined by the largest lyapunov exponent associated with the system which is the analogue of the joint spectral radius for the discrete time case the purpose of this paper is to provide a characterization of marginally unstable systems i e systems for which the lyapunov exponent is equal to zero and there exists an unbounded trajectory and to analyze the asymptotic behavior of their trajectories our main contribution consists in pointing out a resonance phenomenon associated with marginal instability in the course of our study we derive an upper bound of the state at time t which is polynomial in t and whose degree is computed from the resonance structure of the system we also derive analogous results for discrete time linear switched systems

geometric and asymptotic properties associated with linear switched systems abstract consider a continuous time linear switched system on r n associated with a compact convex set of matrices when it is irreducible and its largest lyapunov exponent is zero there always exists a barabanov norm associated with the system this paper deals with two types of issues a properties of barabanov norms such as uniqueness up to homogeneity and strict convexity b asymptotic behavior of the extremal solutions of the linear switched system regarding issue a we provide partial answers and propose four related open problems as for issue b we establish when n 3 a poincare bendixson theorem under a regularity assumption on the set of matrices we then revisit a noteworthy result of n e barabanov describing the asymptotic behavior of linear switched system on r 3 associated with a pair of hurwitz matrices a a b c t after pointing out a gap in barabanov s proof we partially recover his result by alternative arguments

a note on the stability of bimodal systems in with discontinuous vector fields this paper presents the necessary and sufficient conditions for global asymptotic stability of a class of bimodal piecewise linear systems in r3 the approach being used allows the vector field to be discontinuous on the switching plane it is shown that the discontinuity of the vector field plays a crucial role in global asymptotic stability this point is illustrated by examples where the change in the discontinuity of the vector field without changing the eigenvalues of subsystems can cause the system to be globally asymptotically stable or unstable

universal interpretation of efficacy parameter in perturbed nonequilibrium systems abstract the fluctuation theorems have remained one of the cornerstones in the study of systems that are driven far out of equilibrium and they provide strong constraints on the fraction of trajectories that behave atypically in light of the second law they have mainly been derived for a predetermined external drive applied to the system however to improve the efficiency of a process one needs to incorporate protocols that are modified by receiving feedbacks about the recent state of the system during its evolution in such a case the forms of the conventional fluctuation theorems get modified the correction term involving terms that depend on the way the reverse conjugate process is defined namely the rules of using feedback in order to generate the exact time reversed conjugate protocols we show in this paper that this can be done in a large number of ways and in each case we would get a different expression for the correction terms this would in turn lead to several lower bounds on the mean work that must be performed on the system or on the entropy changes here we analyze a form of the extended fluctuation theorems that involves the efficacy parameter and find that this form retains a consistent physical meaning regardless of the design of feedback along the conjugate process as opposed to the case of the previously mentioned form of the modified fluctuation theorems

temperature measurement from perturbations the notion of configuration temperature is extended to discontinuous systems by identifying the temperature as the nontrivial root of several integral equations regarding the distribution of the energy change upon configuration perturbations the relations are generalized to pressure and a distribution mean force

loudness growth in 1 2 octave bands lgob a procedure for the assessment of loudness in this paper a method that has been developed for the assessment and quantification of loudness perception in normal hearing and hearing impaired persons is described the method has been named lgob which stands for loudness growth in 1 2 octave bands the method uses 1 2 octave bands of noise centered at 0 25 0 5 1 0 2 0 and 4 0 khz with subjective levels between a subject s threshold of hearing and the too loud level the noise bands are presented to the subject randomized over frequency and level and the subject is asked to respond with a loudness rating one of very soft soft ok loud very loud too loud subject responses normal and hearing impaired are then compared to the average responses of a group of normal hearing subjects this procedure allows one to estimate the subject s loudness growth relative to normals as a function of frequency and level the results may be displayed either as isoloudness contours or as recruitment curves in its present form the measurements take less than 30 min the signal presentation and analysis is done using a pc and a pc plug in board having a digital to analog converter

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

effects of amplitude nonlinearity on phoneme recognition by cochlear implant users and normal hearing listeners it is widely assumed that the proper transformation of acoustic amplitude to electric amplitude is a critical factor affecting speech recognition in cochlear implant users and normal hearing listeners a four channel noise band speech processor was implemented reducing spectral information to four bands a power law transformation was applied to the amplitude mapping stage in the speech processor design and the exponent of the power function varied from a strongly compressive p 0 05 to a weakly compressive p 0 75 for implant listeners and from 0 3 to 3 0 for acoustic listeners results for implants showed that the best performance was achieved with an exponent of about 0 2 and performance gradually deteriorated when either more compressive or less compressive exponents were applied the loudness growth functions of the four activated electrodes in each subject were measured and those data were well fit by a power function with a mean exponent of 2 72 the results indicated that the best performance was achieved when the normal loudness growth was restored for acoustic listeners results were similar to those observed with cochlear implant listeners except that best performance was achieved with no amplitude nonlinearity p 1 0 the similarity of results in both acoustic and electric stimulation indicated that the performance deterioration observed for extreme nonlinearity was due to similar perceptual effects the function relating amplitude mapping exponent and performance was relatively flat indicating that phoneme recognition was only mildly affected by amplitude nonlinearity

integral fluctuation theorem for the housekeeping heat the housekeeping heat qhk is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states by analysing the evolution of its probability distribution we prove an integral fluctuation theorem exp qhk 1 valid for arbitrary driven transitions between steady states we discuss gaussian limiting cases and the difference between the new theorem and both the hatano sasa and the jarzynski relation

stability of switched systems a lie algebraic condition we present a sucient condition for asymptotic stability of a switched linear system in terms of the lie algebra generated by the individual matrices namely if this lie algebra is solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of linear systems satisfying this condition possesses a quadratic common lyapunov function we also discuss the implications of this result for switched nonlinear systems c 1999 elsevier science b v all rights reserved

a numerical technique for the stability analysis of linear switched systems in this paper the ray gridding approach a new numerical technique for the stability analysis of linear switched systems is presented it is based on uniform partitions of the state space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance in this framework the existence of a polyhedral lyapunov function that is common to a family of asymptotically stable subsystems can be checked efficiently via simple iterative algorithms the technique can be used to prove the stability of switched linear systems classes of linear time varying systems and linear differential lnclusions we also present preliminary results on another related problem namely the construction of multiple polyhedral lyapunov functions for the specification of stabilizing switching sequences for a switched system constructed from a family of stable linear subsystems

mode identifying time estimation and switching delay tolerant control for switched systems in this paper an elementary time unit etu method is proposed to study the problem of estimating the admissible delay in the identification of the active mode in the analysis and design of switched systems the activation interval of a subsystem is considered to consist of a finite time number of segments called etus by which a novel class of time scheduled lyapunov function is used to estimate the admissible delay in mode identification for switched systems further the etu method is applied for switching delay tolerant control problem and a class of time scheduled state feedback controllers are designed to achieve the exponentially stability several numerical examples are presented to validate the theoretic findings

cal h _ infty and dwell time specifications of continuous time switched linear systems this technical note deals with continuous time switched linear systems and addresses the problem of characterizing open loop switching strategies based on dwell time specifications assuring a pre specified root mean square gain rms as a natural consequence of treating general systems of this particular class in terms of order and number of subsystems only sufficient conditions are worked out however as positive features they are expressed through linear matrix inequalities lmi being thus numerically solvable in polynomial time and allow the treatment of stable switched linear systems which do not admit a common lyapunov function the conservativeness of the proposed design method is evaluated by comparison with other results available in the literature by means of two simple illustrative examples

nice reachability for planar bilinear control systems with applications to planar linear switched systems corrected we consider planar bilinear control systems with measurable controls we show that any point in the reachable set can be reached by a ldquonicerdquo control specifically a control that is a concatenation of a bang arc with either 1 a bang bang control that is periodic after the third switch or 2 a piecewise constant control with no more than two discontinuities under the additional assumption that the bilinear system is positive or invariant for any proper cone we show that the reachable set is spanned by a concatenation of a bang arc with either 1 a bang bang control with no more than two discontinuities or 2 a piecewise constant control with no more than two discontinuities in particular any point in the reachable set can be reached using a piecewise constant control with no more than three discontinuities several known results on the stability of planar linear switched systems under arbitrary switching follow as corollaries of our result we demonstrate this with an example

periodicity and chaos from switched flow systems contrasting examples of discretely controlled continuous systems two examples of the discrete control of a continuous variable system are analyzed these examples exhibit what may be regarded as the two extremes of complexity of the closed loop behavior one is eventually periodic the other is chaotic the examples are derived from sampled deterministic flow models these are of interest in their own right but have also been used as models for certain aspects of manufacturing systems in each case the authors give a precise characterization of the closed loop behavior

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

the generalized spectral radius and extremal norms the generalized spectral radius also known under the name of joint spectral radius or after taking logarithms maximal lyapunov exponent of a discrete inclusion is examined we present a new proof for a result of barabanov which states that for irreducible sets of matrices an extremal norm always exists this approach lends itself easily to the analysis of further properties of the generalized spectral radius we prove that the generalized spectral radius is locally lipschitz continuous on the space of compact irreducible sets of matrices and show a strict monotonicity property of the generalized spectral radius sufficient conditions for the existence of extremal norms are obtained

stability and stabilizability criteria for discrete time positive switched systems in this paper we consider the class of discrete time switched systems switching between p autonomous positive subsystems first sufficient conditions for testing stability based on the existence of special classes of common lyapunov functions are investigated and these conditions are mutually related thus proving that if a linear copositive common lyapunov function can be found then a quadratic positive definite common function can be found too and this latter in turn ensures the existence of a quadratic copositive common function secondly stabilizability is introduced and characterized it is shown that if these systems are stabilizable they can be stabilized by means of a periodic switching sequence which asymptotically drives to zero every positive initial state conditions for the existence of state dependent stabilizing switching laws based on the values of a copositive linear quadratic lyapunov function are investigated and mutually related too finally some properties of the patterns of the stabilizing switching sequences are investigated and the relationship between a sufficient condition for stabilizability the existence of a schur convex combination of the subsystem matrices and an equivalent condition for stabilizability the existence of a schur matrix product of the subsystem matrices is explored

equivalence of two bochkov kuzovlev equalities in quantum two level systems we present two kinds of bochkov kuzovlev work equalities in a two level system that is described by a quantum markovian master equation one is based on multiple time correlation functions and the other is based on the quantum trajectory viewpoint we show that these two equalities are indeed equivalent importantly this equivalence provides us a way to calculate the probability density function of the quantum work by solving the evolution equation for its characteristic function we use a numerical model to verify these results

towards a stability theory of general hybrid dynamical systems in recent work we proposed a general model for hybrid dynamical systems whose states are defined on arbitrary metric space and evolve along some notion of generalized abstract time for such systems we introduced the usual concepts of lyapunov and lagrange stability we showed that it is always possible to transform this class of hybrid dynamical systems into another class of dynamical systems with equivalent qualitative properties but defined on real time r 0 the motions of this class of systems are in general discontinuous this class of systems may be finite or infinite dimensional for the above discontinuous dynamical systems and hence for the above hybrid dynamical systems we established the principal lyapunov stability theorems as well as lagrange stability theorems for some of these we also established converse theorems we demonstrated the applicability of these results by means of specific classes of hybrid dynamical systems in the present paper we continue the work described above in doing so we first develop a general comparison theory for the class of hybrid dynamical systems resp discontinuous dynamical systems considered herein making use of stability preserving mappings we then show how these results can be applied to establish some of the principal lyaponov stability theorems for the latter we also state and prove a converse theorem not considered previously finally to demonstrate the applicability of our results we consider specific examples throughout the paper

extended forms of the second law for general time dependent stochastic processes the second law of thermodynamics represents a universal principle applicable to all natural processes physical systems and engineering devices hatano and sasa have recently put forward an extended form of the second law for transitions between nonequilibrium stationary states phys rev lett 86 3463 2001 in this paper we further extend this form to an instantaneous interpretation which is satisfied by quite general time dependent stochastic processes including master equation models and langevin dynamics without the requirements of the stationarity for the initial and final states the theory is applied to several thermodynamic processes and its consistence with the classical thermodynamics is shown

technical communique analysis and design of aimd congestion control algorithms in communication networks we present a model of a network of synchronised sources operating additive increase multiplicative decrease aimd congestion control algorithms we show i that networks of such devices in the presence of a drop tail bottleneck buffer may be modelled as a positive linear system ii that such networks possess a unique stationary point and iii that this stationary point is globally exponentially stable we use these results to establish conditions for the fair co existence of traffic in networks employing heterogeneous aimd algorithms and to design a new protocol for operation over high speed and long distance links

the negative effect of amplitude compression in multichannel hearing aids in the light of the modulation transfer function the article deals with the question of why multichannel amplitude compression appears to have a negative rather than a positive effect on speech intelligibility by hearing impaired listeners it is argued that the small time constants of amplitude compression diminish the temporal as well as the spectral contrasts in the speech signal according to the modulation transfer function concept this results in reduced intelligibility scores experimental evidence is reviewed indicating that the following two arguments in favor of amplitude compression in case of sensorineural hearing loss are not valid 1 to compensate for the effects of loudness recruitment and 2 to get weak consonants above threshold the author concludes that in multichannel hearing aids automatic gain control with time constants of 0 25 0 5 s should be given preference to amplitude compression

criteria of asymptotic stability of differential and difference inclusions encountered in control theory abstract for a class of differential inclusions to which many of the practically important control systems can be reduced necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of lyapunov functions similar results are obtained for the corresponding class of difference inclusions

a counterexample to a conjecture of gurvits on switched systems we consider products of matrix exponentials under the assumption that the matrices span a nilpotent lie algebra in 1995 gurvits conjectured that nilpotency implies that these products are in some sense simple more precisely there exists a uniform bound l such that any product can be represented as a product of no more than i matrix exponentials this conjecture has important applications in the analysis of linear switched systems as it is closely related to the problem of reachability using a uniformly bounded number of switches it is also closely related to the concept of nice reachability for bilinear control systems the conjecture is trivially true for the case of first order nilpotency gurvits proved the conjecture for the case of second order nilpotency using the baker campbell hausdorff formula we show that the conjecture is false for the third order nilpotent case using an explicit counterexample yet the underlying philosophy behind gurvits conjecture is valid in the case of third order nilpotency namely such systems do satisfy the following nice reachability property any point in the reachable set can be reached using a piecewise constant control with no more than four switches we show that even this form of finite reachability is no longer true for the case of fifth order nilpotency

fluctuation theorem for hidden entropy production elimination of seemingly unnecessary variables in markovian models may cause a difference in the value of irreversible entropy production between the original and reduced dynamics we show that such difference which we call the hidden entropy production obeys an integral fluctuation theorem if all variables are time reversal invariant or if the density function is symmetric with respect to the change of sign of the time reversal antisymmetric variables the theorem has wide applicability since the proposed condition is mostly satisfied in the case where the hidden fast variables are equilibrated the main consequence of this theorem is that the entropy production decreases by the coarse graining procedure by contrast in the case where a stochastic process is obtained by coarse graining a deterministic and reversible dynamics the entropy production may increase implying that the integral fluctuation theorem should not hold for such reductions we reveal with an explicit example that the nonequilibrated time reversal antisymmetric variables play a crucial role in distinguishing these two cases thus guaranteeing the consistency of the presented theorem

stability tests and stabilization for piecewise linear systems based on poles and zeros of subsystems this paper provides several stability tests for piecewise linear systems and proposes a method of stabilization for bimodal systems in particular we derive an explicit and exact stability test for planar systems which is given in terms of coefficients of transfer functions of subsystems restricting attention to the bimodal and planar case we show simple stability tests in addition we drive a necessary stability condition and a sufficient stability condition for higher order and bimodal systems they are given in terms of the eigenvalue loci and the observability of subsystems all the stability tests provided in this paper are computationally tractable and our results are applied to the stabilizability problem we confirm the exactness and effectiveness of our approach by illustrative examples

lie algebraic stability criteria for switched systems it was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable lie algebra possesses a quadratic common lyapunov function which implies that the corresponding switched linear system is exponentially stable for arbitrary switching in this paper we prove that the same properties hold under the weaker condition that the lie algebra generated by given matrices can be decomposed into a sum of a solvable ideal and a subalgebra with a compact lie group the corresponding local stability result for nonlinear switched systems is also established moreover we demonstrate that if a lie algebra fails to satisfy the above condition then it can be generated by a family of stable matrices such that the corresponding switched linear system is not stable relevant facts from the theory of lie algebras are collected at the end of the paper for easy reference

a note on stability conditions for planar switched systems this article is concerned with the stability problem for the planar linear switched system where the real matrices a 1 a 2 2 2 are hurwitz and u 0 0 1 is a measurable function we give coordinate invariant necessary and sufficient conditions on a 1 and a 2 under which the system is asymptotically stable for arbitrary switching functions u the new conditions unify those given in previous papers and are simpler to be verified since we reduced to study 4 cases instead of 20 most of the cases are analysed in terms of the function

thermodynamic formula for the cumulant generating function of time averaged current the cumulant generating function of time averaged current is studied from an operational viewpoint specifically for interacting brownian particles under nonequilibrium conditions we show that the first derivative of the cumulant generating function is equal to the expectation value of the current in a modified system with an extra force added where the modified system is characterized by a variational principle the formula reminds us of einstein s fluctuation theory in equilibrium statistical mechanics furthermore since the formula leads to the fluctuation dissipation relation when the linear response regime is focused on it is regarded as an extension of the linear response theory to that valid beyond the linear response regime the formula is also related to previously known theories such as the donsker varadhan theory the additivity principle and the least dissipation principle but it is not derived from them examples of its application are presented for a driven brownian particle on a ring subject to a periodic potential

brief on absolute stability analysis by polyhedral lyapunov functions this paper addresses the problem of computing a polyhedral lyapunov function plf for a linear differential inclusion ldi a numerically efficient algorithm is presented to compute a plf for an ldi it is also pointed out that for the case of a polyhedron defined by vertices rather than by faces one can state algebraic stability conditions analogous to those given by molchanov and pyatnitskiy 1986

numerical methods of lyapunov function construction and their application to the absolute stability problem the minimax approach is used to study numerical selection of a lyapunov function from a multiparameter class of functions a numerical method is suggested for plotting an absolute stability region in the space of system gains for a control system with several nonstationary nonlinearities

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

generating functions of switched linear systems analysis computation and stability applications in this paper a unified framework is proposed to study the exponential stability of discrete time switched linear systems and more generally the exponential growth rates of their trajectories under three types of switching rules arbitrary switching optimal switching and random switching it is shown that the maximum exponential growth rates of system trajectories over all initial states under these three switching rules are completely characterized by the radii of convergence of three suitably defined families of functions called the strong the weak and the mean generating functions respectively in particular necessary and sufficient conditions for the exponential stability of the switched linear systems are derived based on these radii of convergence various properties of the generating functions are established and their relations are discussed algorithms for computing the generating functions and their radii of convergence are also developed and illustrated through examples

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

temporal envelope and fine structure cues for speech intelligibility this paper describes a number of listening experiments to investigate the relative contribution of temporal envelope modulations and fine structure to speech intelligibility the amplitude envelopes of 24 1 4 oct bands covering 100 6400 hz were processed in several ways e g fast compression in order to assess the importance of the modulation peaks and troughs results for 60 normal hearing subjects show that reduction of modulations by the addition of noise is more detrimental to sentence intelligibility than the same degree of reduction achieved by direct manipulation of the envelope in some cases the benefit in speech reception threshold srt is almost 7 db two crossover levels can be defined in dividing the temporal envelope into two equally important parts the first crossover level divides the envelope into two perceptually equal parts removing modulations either x db below or above that level yields the same intelligibility score the second crossover level divides the envelope into two acoustically equal peak and trough parts the perceptual level is 9 12 db higher than the acoustic level indicating that envelope peaks are perceptually more important than troughs further results showed that 24 intact temporal speech envelopes with noise fine structure retain perfect intelligibility in general for the present type of signal manipulations no one to one relation between the modulation transfer function and the intelligibility scores could be established

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

asymptotic behavior of extremal solutions and structure of extremal norms of linear differential inclusions of order three asymptotic properties of extremal solutions of linear inclusions of order three with zero lyapunov exponent are investigated under certain conditions it is shown that all extremal solutions of such inclusions tend to the same up to a multiplicative factor solution which is central symmetric the structure of the convex set of extremal norm is studied a number of extremal points of this set are described

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

on the computation of switching surfaces in optimal control a grobner basis approach a number of problems in control can be reduced to finding suitable real solutions of algebraic equations in particular such a problem arises in the context of switching surfaces in optimal control a powerful new methodology for doing symbolic manipulations with polynomial data has been developed and tested namely the use of grobner bases we apply the grobner basis technique to find effective solutions to the classical problem of time optimal control

splitting of the rate matrix as a definition of time reversal in master equation systems motivated by recent progress in nonequilibrium fluctuation relations we present a generalized time reversal for stochastic master equation systems with discrete states which is defined as a splitting of the rate matrix into irreversible and reversible parts an immediate advantage of this definition is that a variety of fluctuation relations can be attributed to different matrix splittings additionally we find that the accustomed total entropy production formula and conditions of the detailed balance must be modified appropriately to account for the reversible rate part which was previously ignored

stability and controllability of planar conewise linear systems abstract this paper presents a fairly complete treatment of stability and controllability of piecewise linear systems defined on a conic partition of r 2 this includes necessary and sufficient conditions for stability and controllability as well as establishing that controllability implies stabilizability by piecewise linear state feedback a key tool in the approach is the study of the poincare map

weakly birkhoff recurrent switching signals almost sure and partial stability of linear switched dynamical systems let a1 ak cd d be arbitrary k matrices where k and d both 2 for any 0 we denote by l pc r k the set of all switching sequences u t n 1 k r satisfying tj tj 1 and 0 t0 t1 tj 1 tj with tj differently from the classical weak topology and l1 norm we equip l pc r k with the topology so that the one sided markov type shift l pc r k l pc r k defined by u j tj j 1 u j 1 tj 1 t1 j 1 is continuous which is different from and simpler than the classical continuous time translation we study the stability of the linear switched dynamics a x t au t x t x 0 cd and t 0 where u t j if tj 1 0 then for any ergodic probability p on l pc r k either limj 1jlog u tj 0for p a s u j tj j 1 or j u tj k tj 1 k j 0for p a s u j tj j 1 some applications are presented including i equivalence of various stabilities ii almost sure exponential stability of periodically switched stable systems iii partial stability and iv how to approach arbitrarily the stable manifold by that of periodically switched signals and how to select a stable switching signal for any initial data

stochastic thermodynamics with odd controlling parameters stochastic thermodynamics extends the notions and relations of classical thermodynamics to small systems that experience strong fluctuations the definitions of work and heat and the microscopically reversible condition are two key concepts in the current framework of stochastic thermodynamics herein we apply stochastic thermodynamics to small systems with odd controlling parameters and find that the definition of heat and the microscopically reversible condition are incompatible such a contradiction also leads to a revision to the fluctuation theorems and nonequilibrium work relations by introducing adjoint dynamics we find that the total entropy production can be separated into three parts with two of them satisfying the integral fluctuation theorem revising the definitions of work and heat and the microscopically reversible condition allows us to derive two sets of modified nonequilibrium work relations including the jarzynski equality the detailed crooks work relation and the integral crooks work relation we consider the strategy of shortcuts to isothermality as an example and give a more sophisticated explanation for the jarzynski like equality derived from shortcuts to isothermality

control systems which generate decomposable lie algebras let x y be real analytic vector fields on an n manifold m ad x y x y denote the lie product inductively ad k 1 x y x ad k x y and 1 ad v x y v 0 the attainable set at time t denoted download full size image t for the control system 1 x x x u t y x x 0 p u t 1 is contained in the integral manifold through p of the lie algebra l 1 generated by 1 l 1 is said to be decomposable at p if essentially when dim l 1 p n the solution of 1 can be written as exp tx exp f 1 t u v 1 exp f n t u v n p with v 1 v n l 1 this is true for example at any p if l 1 is nilpotent the f i t u are shown to satisfy a system on n of the form 2 x i u t g i t x 1 x i 1 x i 0 0 i 1 n where if l 1 is nilpotent each g i is a polynomial in x 1 x i 1 in this case reachability properties of 2 for controls being countably additive measures impluses reduce to the study of algebraic equations homogeneity allows these to be considered on projective space n giving local results by bezout s theorem similar results hold for controls in the unit ball of krener s results on approximating systems of the form 1 by systems which generate nilpotent lie algebras can then be used to remove the condition that l 1 be nilpotent the method applies to show that if m denotes the set of all products of k elements of 1 with k m and dim span m 1 p dim span m for all odd m then exp tx p int download full size image t for all t 0