analysis and control of switched linear systems via dwell time min switching abstract this paper addresses analysis and switching control problems of switched linear systems to this end a mixed time driven and state dependent switching strategy is proposed it guarantees an average dwell time even when all subsystems are unstable the switching rule and its associated switching output feedback controllers are designed to stabilize the switched system and satisfy a weighted l 2 gain performance the proposed analysis and switching control approach could refrain frequent switches commonly observed in min switching based designs the effectiveness of the proposed approach has been illustrated through a spherical inverted pendulum example

on equivalence of two stability criteria for continuous time switched systems with dwell time constraint in this note a study on the equivalence of two stability criteria for continuous time switched linear systems with dwell time constraint is presented it is demonstrated that for any dwell time satisfying the conditions in stability criterion proposed in geromel and colaneri 2006 the conditions in stability criterion of allerhand and shaked 2011 also hold as long as the number of decision variables and related lmis is sufficiently large which implies the two stability criteria are intrinsically equivalent the equivalence is obtained by showing that two criteria can be derived from each other with a sufficiently large number of decision variables and lmis a numerical example is proposed to illustrate the theoretical results and an extension to uncertain case is briefly presented

necessary and sufficient condition for stabilizability of discrete time linear switched systems in this paper the stabilizability of discrete time linear switched systems is considered several sufficient conditions for stabilizability are proposed in the literature but no necessary and sufficient the main contributions are the necessary and sufficient conditions for stabilizability based on the set theory and the characterization of a universal class of lyapunov functions an algorithm for computing the lyapunov functions and a procedure to design the stabilizing switching control law are provided based on such conditions moreover a sufficient condition for non stabilizability for switched system is presented several academic examples are given to illustrate the efficiency of the proposed results in particular a lyapunov function is obtained for a system for which the lyapunov metzler condition for stabilizability does not hold

convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled data systems under dwell time constraints stability analysis and control of linear impulsive systems is addressed in a hybrid framework through the use of continuous time time varying discontinuous lyapunov functions necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas extensions to the stability of aperiodic systems under minimum maximum and ranged dwell times are then derived by exploiting further the particular structure of the stability conditions the results are non conservatively extended to quadratic stability analysis of linear uncertain impulsive systems these stability criteria are in turn losslessly extended to stabilization using a particular yet broad enough class of state feedback controllers providing then a convex solution to the open problem of robust dwell time stabilization of impulsive systems using hybrid stability criteria relying finally on the representability of sampled data systems as impulsive systems the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled data systems are straightforwardly solved using the same ideas several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach

delay independent minimum dwell time for exponential stability of uncertain switched delay systems in this technical note the problem of delay independent minimum dwell time for exponential stability of uncertain switched delay systems is considered piecewise time varying lyapunov functionals functions which are decreasing at switching times by construction are introduced to investigate exponential stability of switched delay systems with constant or time varying delays this type of delicately constructed lyapunov functionals functions can efficiently eliminate the jump phenomena of adjacent lyapunov functionals functions at switching times without imposing any restriction on the sizes of time delays by applying this type of lyapunov functionals functions it is shown that if each subsystem is delay independently exponentially stable then under some conditions there exists a delay independent minimum dwell time in the sense that the switched delay system with such minimum dwell time is exponentially stable irrespective of the sizes of the time delays two numerical examples are provided to demonstrate the efficiency of the proposed approach

a characterization of switched linear control systems with finite l_ 2 gain motivated by an open problem posed by j p hespanha we extend the notion of barabanov norm and extremal trajectory to classes of switching signals that are not closed under concatenation we use these tools to prove that the finiteness of the l 2 gain is equivalent for a large set of switched linear control systems to the condition that the generalized spectral radius associated with any minimal realization of the original switched system is smaller than one

robust stability and stabilization of linear switched systems with dwell time sufficient conditions are given for the stability of linear switched systems with dwell time and with polytopic type parameter uncertainty a lyapunov function in quadratic form which is non increasing at the switching instants is assigned to each subsystem during the dwell time this function varies piecewise linearly in time after switching occurs it becomes time invariant afterwards this function leads to asymptotic stability conditions for the nominal set of subsystems that can be readily extended to the case where these subsystems suffer from polytopic type parameter uncertainties the method proposed is then applied to stabilization via state feedback both for the nominal and the uncertain cases

ℋ stabilisation of switched linear stochastic systems under dwell time constraints based on the determination of a minimum dwell time this article addresses the problem of characterising a switching strategy for stabilisation of switched linear stochastic systems with adapted external inputs sufficient conditions that assure exponential mean square stability and an performance index are established by analysing the time evolution of the second order moment of the state and a recursive dynamic programming inequality respectively alternative conditions are derived for numerical implementations the proposed method is illustrated by numerical simulations

quadratic stability of a class of switched nonlinear systems quadratic stability of a class of switched nonlinear systems is studied in this note we first transform quadratic stability problem into an equivalent nonlinear programming problem then we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using karush kuhn tucker condition for nonlinear programming problems the necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space which is much easier to check

finite order solutions of linear differential equations in the unit disc abstract necessary and sufficient conditions for the analytic coefficients of the complex linear differential equation f k a k 1 z f k 1 a 1 z f a 0 z f a k z are found such that all solutions satisfy f lim sup r 1 log t r f log 1 r moreover estimates for the number of linearly independent solutions of maximal growth are found in terms of the growth of the coefficients in addition sufficient conditions for the coefficients such that the zero sequence z n of any non trivial solution f of with a k 0 satisfies 1 z n 1 are found several non trivial examples are given in order to show that the established results are in a sense sharp

the possible orders of growth of solutions to certain linear differential equations near a singular point abstract in this paper we give the possible orders of growth of solutions to certain linear differential equations near a finite singular point for that an asymptotic equality of wiman valiron type is proved for the derivatives of functions which are analytic in the closed complex plane except at a finite singular point

lmi characterization of structural and robust stability abstract this paper introduces several stability conditions for a given class of matrices expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable diagonal and simultaneous stability both characterized by polytopes of matrices are addressed using this approach a method particularly attractive to test a given matrix for d stability is proposed lyapunov parameter dependent functions are built in order to reduce conservativeness of the stability conditions the key idea is to relate hurwitz stability with a positive realness condition

suboptimal switching control consistency analysis for switched linear systems this paper introduces the concept of consistency for continuous time switched linear systems having the switching function as a primary control signal to be designed a switching control strategy is strictly consistent whenever it improves performance compared to the ones of all isolated subsystems conditions under which a min type switching strategy is strictly consistent for the classes of h2 and h performance indexes are determined this property makes clear the importance of switching systems control design in both theoretical and practical application frameworks moreover with this property it is not necessary to assume that all the subsystems are not stable in order to make a switching strategy design problem well posed the theory is illustrated by means of several academic examples

brief paper dynamic output feedback h control of switched linear systems this paper is devoted to dynamic output feedback h control design of switched linear systems in both continuous and discrete time domains more specifically the main purpose is to jointly design a switching rule and a full order dynamic output feedback switched controller that render the associated closed loop switched linear system globally asymptotically stable and impose a pre specified upper bound to the l 2 gain an example of practical importance is presented to illustrate the validity and efficiency of the theory

dwell time based stabilisation of switched linear delay systems using clock dependent lyapunov krasovskii functionals dwell time stability conditions of the switched delay systems are derived using multiple clock dependent lyapunov krasovskii functionals the corresponding conditions are approximated by both using

characterising the stabilisability for second order linear switched systems the stabilisability of second order linear switched systems is the topic focused on in a number of papers however some of its fundamental characteristics are still unrevealed in this article regarding a pair of subsystems we are interested in characterising this problem from both the state triggering and time domain viewpoints and in revealing the inherent connection between them to this end we first use polar coordinates to represent the geometric property of switching and the dynamical behaviours caused by it and then put the geometrised switching control into correspondence with the implicit stabilisation mechanism behind it doing this in a strong way relies on classifying switching control into two types intuitively namely chattering switching and spinning switching and then clarifying their distinction and properties rigorously furthermore the uniform convergence of the forced trajectory is shown by presenting estimation on its decay rate and the limit cycles and sliding motions genera

stability analysis of lur e type switched systems this technical note aims to introduce stability analysis of lur e type switched systems in frequency domain a new state input dependent switching function is proposed and it is the key issue to obtain a stability condition that generalizes the celebrated popov criterion to deal with this class of switched nonlinear systems likewise the case of time invariant systems we propose a frequency domain stability test that is expressed through a convex combination of the subsystems state space matrices this task is not trivial due to the time varying nature of the nonlinear systems under consideration the theory is illustrated by a simple example

almost sure stability of markov jump linear systems with deterministic switching the technical note studies a class of linear systems whose piecewise constant dynamic matrix is subject to both stochastic jumps governed by a markov chain and deterministic switches these systems will be dubbed switching dynamics markov jump linear systems sd mjls sufficient conditions for exponential almost sure stability eas stability are established under either hard or average constraints on the dwell time between switching instants the proof relies on easy to check norm contractivity conditions and the ergodic law of large numbers

output reachable set estimation for switched linear systems and its application in safety verification this paper addresses the output reachable set estimation problem for continuous time switched linear systems consisting of hurwtiz stable subsystems based on a common lyapunov function approach the output reachable set is estimated by a union of bounding ellipsoids then multiple lyapunov functions with time scheduled structure are employed to estimate the output reachable set for switched systems under dwell time constraint furthermore the safety verification problem of uncertain switched systems is investigated based on the result of output reachable set estimation first a sufficient condition ensuring the existence of an approximate bisimulation relation between two switched linear systems with a prescribed precision is proposed then the safety verification for an uncertain switched system can be performed through an alternative safety verification for a switched system with exact parameters numerical examples are provided to illustrate our results

dwell time and average dwell time methods based on the cycle ratio of the switching graph abstract a new method to find an upper bound on dwell time and average dwell time for switched linear systems is proposed the method is based on computing the maximum cycle ratio and the maximum cycle mean of the directed graph that governs switchings for planar switched systems an upper bound for dwell time and average dwell time can be estimated by considering only the cycles of length two

a novel lyapunov function for a non weighted l2 gain of asynchronously switched linear systems abstract in this paper a novel lyapunov function is proposed to study switched linear systems with a switching delay between activation of system modes and activation of candidate controller modes the novelty consists in continuity of the lyapunov function at the switching instants and discontinuity when the system modes and controller modes are matched this structure is exploited to construct a time varying lyapunov function that is non increasing at time instants of discontinuity stability criteria based on the novel lyapunov function are developed to guarantee global asymptotic stability in the noiseless case most importantly when exogenous disturbances are considered the proposed lyapunov function can be used to guarantee a finite non weighted l 2 gain for asynchronously switched systems for which lyapunov functions proposed in literature are inconclusive a numerical example illustrates the effectiveness of the proposed method

sliced inverse regression for dimension reduction abstract modern advances in computing power have greatly widened scientists scope in gathering and investigating information from many variables information which might have been ignored in the past yet to effectively scan a large pool of variables is not an easy task although our ability to interact with data has been much enhanced by recent innovations in dynamic graphics in this article we propose a novel data analytic tool sliced inverse regression sir for reducing the dimension of the input variable x without going through any parametric or nonparametric model fitting process this method explores the simplicity of the inverse view of regression that is instead of regressing the univariate output variable y against the multivariate x we regress x against y forward regression and inverse regression are connected by a theorem that motivates this method the theoretical properties of sir are investigated under a model of the form y f 1 x k x e where the k s are the unknown

meromorphic solutions of difference equations integrability and the discrete painleve equations the painlev e property is closely connected to differential equations that are integrable via related iso monodromy problems many apparently integrable discrete analogues of the painlev e equations have appeared in the literature the existence of sufficiently many finite order meromorphic solutions appears to be a good analogue of the painlev e property for discrete equations in which the independent variable is taken to be complex a general introduction to nevanlinna theory is presented together with an overview of recent applications to meromorphic solutions of difference equations and the difference and q difference operators new results are presented concerning equations of the form w z 1 w z 1 r z w where r is rational in w with meromorphic coefficients

robust control of linear systems via switching the standard approach to the problem of controlling linear systems with large parameter uncertainty is to seek a controller that stabilizes the system and achieves a required performance over the whole polytope of uncertainty in the case where the latter polytope is large the design may become very conservative we present an alternative approach where the uncertainty polytope is divided into overlapping smaller regions and where each of these regions is assigned to a separate subsystem assuming that there is online information on which of the regions the parameters of the system move to a recently developed method for h design of switched system with dwell time is applied a lyapunov function lf in a quadratic form which is non increasing at the switching instants is assigned to each subsystem this function is used to determine the stability and to find a bound on the l2 gain of the switched system the obtained results are used to solve the corresponding robust h state feedback and static output feedback control problems

on lyapunov metzler inequalities and s procedure characterizations for the stabilization of switched linear systems in this note we present connections between two celebrated tools for the design of stabilising switching laws for continuous time and discrete time switched linear systems namely lyapunov metzler inequalities and s procedure

optimal control of switched systems based on parameterization of the switching instants this paper presents a new approach for solving optimal control problems for switched systems we focus on problems in which a prespecified sequence of active subsystems is given for such problems we need to seek both the optimal switching instants and the optimal continuous inputs in order to search for the optimal switching instants the derivatives of the optimal cost with respect to the switching instants need to be known the most important contribution of the paper is a method which first transcribes an optimal control problem into an equivalent problem parameterized by the switching instants and then obtains the values of the derivatives based on the solution of a two point boundary value differential algebraic equation formed by the state costate stationarity equations the boundary and continuity conditions along with their differentiations this method is applied to general switched linear quadratic problems and an efficient method based on the solution of an initial value ordinary differential equation is developed an extension of the method is also applied to problems with internally forced switching examples are shown to illustrate the results in the paper

finite time annular domain stability of impulsive switched systems mode dependent parameter approach this paper investigates the finite time stability of impulsive switched systems by applying mode dependent parameter approach and average impulsive switched interval technique the conditions that

stabilization of switched positive system with impulse and marginally stable subsystems a mode dependent dwell time method abstract in this article the problem of stabilization for the switched positive linear system spls with impulse and marginally stable subsystems is studied in which both the continuous time case and the discrete time case are taken into account by the usage of a piecewise weak linear copositive lyapunov function lclf and the mode dependent dwell time mdt time dependent switching control laws are designed to guarantee the asymptotic stability of the system furthermore based on the comparison principal for positive systems the main results are generalized to the time variant spls two examples are worked out to indicate that our results have advantages over some known results in the literature

technical communique switched state feedback control for continuous time uncertain systems this paper is concerned to design a switched state feedback robust control for continuous time systems subject to norm bounded uncertainty as important features of the proposed design method we mention that it can handle a general lft structure for the uncertainty and it is based on stability conditions that can be numerically solved by means of lmis and a line search moreover the switching rule as well as the state feedback gains are determined from the minimization of a guaranteed cost function derived from a multi objective criterion the theoretical results are illustrated with an academic example

brief paper markov jump linear systems with switching transition rates mean square stability with dwell time the stability of a class of markov jump linear systems characterized by piecewise constant transition rates and system dynamics is investigated for these switching markov jump linear systems mean square stability is analyzed through the time evolution of the second order moment of the state the main result is a sufficient condition that guarantees mean square stability under constraints on the dwell time between switching instants an alternative condition based on kronecker calculus is worked out it is shown that both the stability criteria admit an lmi implementation

the possible orders of solutions of linear differential equations with polynomial coefficients we find specific inforrnation about the possible orders of transeendental solutions of equations of the form f n pn l z f n l po z f0 where po z pl z apnl z are polynomials with po z g 0 several examples are given

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

anti windup strategies for discrete time switched systems subject to input saturation this paper deals with the design of anti windup compensator for discrete time switched systems subject to input saturation the cases of static and dynamic anti windup controllers are addressed aiming at maximising the estimate of the basin of attraction of the origin for the closed loop system two aspects of the switching law are taken into account during the design either it is arbitrary or it is a part of the complete control law theoretical conditions allowing to synthesise the anti windup compensator are mainly described through linear matrix inequalities computational oriented conditions are then provided to solve convex optimisation problems that are able to give a constructive solution

switching controller design with dwell times and sampling we consider the problem of obtaining state dependent switching strategies for switching linear time invariant systems which satisfy prespecified dwell time constraints continuous time strategies which yield exponential stability and a guaranteed level of performance are presented we also consider discrete time strategies in which the sampling time is independent of the dwell times a numerical example is included to validate the developed theory

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

first order analytic difference equations and integrable quantum systems we present a new solution method for a class of first order analytic difference equations the method yields explicit minimal solutions that are essentially unique special difference equations give rise to minimal solutions that may be viewed as generalized gamma functions of hyperbolic trigonometric and elliptic type euler s gamma function being of rational type we study these generalized gamma functions in considerable detail the scattering and weight functions u and w functions associated to various integrable quantum systems can be expressed in terms of our generalized gamma functions we obtain detailed information on these u and w functions exploiting the difference equations they satisfy

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

linear differential equations with solutions in the qk spaces abstract for the complex differential equation f n a n 1 z f n 1 a 1 z f a 0 z f 0 with analytic coefficients a j in the unit disk our contribution is to build up a relationship between the coefficients and solutions of the equation we provide conditions for coefficients a j such that all solutions of the equation belong to the q k spaces

a converse lyapunov theorem for linear parameter varying and linear switching systems we study families of linear time varying systems where time variations have to satisfy restrictions on the dwell time that is on the minimum distance between discontinuities as well as on the derivative in between discontinuities such classes of systems may be formulated as linear flows on vector bundles the main objective of this paper is to construct parameter dependent lyapunov functions which characterize the exponential growth rate this is possible in the generic irreducible case as an application the gelfand formula is generalized to the class of systems studied here in other words the maximal exponential growth rate may be approximated by only considering the periodic systems in the family of time varying systems a perspective on the question of continuous dependence of the exponential growth rate on the data is given

dwell time based stabilisation of switched delay systems using free weighting matrices abstractin this paper we present a quasi convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems piecewise lyapunov krasovskii functionals are introduced and the upper bound for the derivative of lyapunov functionals is estimated by free weighting matrices method to investigate non switching stability of each candidate subsystems then a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system once these conditions are represented by a set of linear matrix inequalities dwell time optimisation problem can be formulated as a standard quasi convex optimisation problem numerical examples are given to illustrate the improvements over previously obtained dwell time bounds using the results obtained in the stability case we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers the algorithm solves the problem with successive linearisation of nonlin

stability and stabilization of continuous time switched linear systems this paper addresses two strategies for the stabilization of continuous time switched linear systems the first one is of open loop nature trajectory independent and is based on the determination of a minimum dwell time by means of a family of quadratic lyapunov functions the relevant point on dwell time calculation is that the proposed stability condition does not require the lyapunov function to be uniformly decreasing at every switching time the second one is of closed loop nature trajectory dependent and is designed from the solution of what we call lyapunov metzler inequalities from which the stability condition including chattering is expressed being nonconvex a more conservative but simpler to solve version of the lyapunov metzler inequalities is provided the theoretical results are illustrated by means of examples

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

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

dynamic output feedback control of switched linear systems this paper is devoted to stability analysis and control design of switched linear systems in both continuous and discrete time domains a particular class of matrix inequalities the so called lyapunov metzler inequalities provides conditions for open loop stability analysis and closed loop switching control using state and output feedback switched linear systems are analyzed in a general framework by introducing a quadratic in the state cost determined from a series of impulse perturbations lower bounds on the cost associated with the optimal switching control strategy are derived from the determination of a feasible solution to the hamilton jacobi bellman inequality an upper bound on the optimal cost associated with a closed loop stabilizing switching strategy is provided as well the solution of the output feedback problem is based on the construction of a full order linear switched filter whose state variable is used by the mechanism for the determination of the switching rule throughout the theoretical results are illustrated by means of academic examples a realistic practical application related to the optimal control of semiactive suspensions in road vehicles is reported

stability and robustness analysis for switched systems with time varying delays a new technique is presented for the stability and robustness analysis of nonlinear switched time varying systems with uncertainties and time varying delays the delays are allowed to be discontinuous but are required to be piecewise continuous and arbitrarily long with known upper bounds the technique uses an adaptation of halanay s inequality and a trajectory based technique and is used for designing switched controllers to stabilize linear time varying systems with time varying delays

robust state dependent switching of linear systems with dwell time a state dependent switching law that obeys a dwell time constraint and guarantees the stability of a switched linear system is designed sufficient conditions are obtained for the stability of the switched systems when the switching law is applied in presence of polytopic type parameter uncertainty a lyapunov function in quadratic form is assigned to each subsystem such that it is non increasing at the switching instants during the dwell time this function varies piecewise linearly in time after the dwell the system switches if the switching results in a decrease in the value of the lf the method proposed is also applicable to robust stabilization via state feedback it is further extended to guarantee a bound on the l2 gain of the switching system it is also used in deriving state feedback control law that robustly achieves a prescribed l2 gain bound

linear differential equations with entire coefficients of p q order in the complex plane in this paper we firstly investigate the complex high order linear differential equations in which the coefficients are entire functions of p q order and obtain some results which improve and generalize some previous results in cao 2009 3 chen and yang 2000 4 heittokangas et al 2006 12 kinnunen 1998 17 tu and yi 2008 20

sufficient reductions in regressions with exponential family inverse predictors abstractwe develop methodology for identifying and estimating sufficient reductions in regressions with predictors that given the response follow a multivariate exponential family distribution this setup includes regressions where predictors are all continuous all categorical or mixtures of categorical and continuous we derive the minimal sufficient reduction of the predictors and its maximum likelihood estimator by modeling the conditional distribution of the predictors given the response whereas nearly all extant estimators of sufficient reductions are linear and only partly capture the sufficient reduction our method is not limited to linear reductions it also provides the exact form of the sufficient reduction which is exhaustive its maximum likelihood ml estimates via an iterated reweighted least square irls estimation algorithm and asymptotic tests for the dimension of the regression supplementary materials for this article are available online

stabilization and robust h control for sector bounded switched nonlinear systems this paper presents stability analysis and robust h control for a particular class of switched systems characterized by nonlinear functions that belong to sector sets with arbitrary boundaries the sector boundaries can have positive and or negative slopes and therefore we cover the most general case in our approach using the special structure of the system but without making additional assumptions e g on the derivative of the nonlinear functions and by proposing new multiple lyapunov function candidates we formulate stability conditions and a control design procedure in the form of matrix inequalities the proposed lyapunov functions are more general than the quadratic functions previously proposed in the literature as they incorporate the nonlinearities of the system and hence lead to less conservative stability conditions the stabilizing switching controllers are designed through a bi level optimization problem that can be efficiently solved using a combination of a convex optimization algorithm and a line search method the proposed optimization problem is achieved using a special loop transformation to normalize the arbitrary sector bounds and by other linear matrix inequalities lmi techniques

a new class of universal lyapunov functions for the control of uncertain linear systems the authors analyze the problem of synthesizing a state feedback control for the class of uncertain continuous time linear systems affected by time varying memoryless parametric uncertainties they consider as candidate lyapunov functions the elements of the class spl sigma sub p sup z which is formed by special homogeneous positive definite functions they show that this class is universal in the sense that a lyapunov function exists if and only if there exists a lyapunov function in spl sigma sub p sup z they prove this result in a constructive way showing that such a lyapunov function can always be obtained by smoothing a polyhedral function for which construction algorithms are available the authors show that unlike the polyhedral lyapunov functions these functions allow us to derive explicit formulas for the stabilizing controller

kernel dimension reduction in regression we present a new methodology for sufficient dimension reduction sdr our methodology derives directly from the formulation of sdr in terms of the conditional independence of the covariate x from the response y given the projection of x on the central subspace cf j amer statist assoc 86 1991 316 342 and regression graphics 1998 wiley we show that this conditional independence assertion can be characterized in terms of conditional covariance operators on reproducing kernel hilbert spaces and we show how this characterization leads to an m estimator for the central subspace the resulting estimator is shown to be consistent under weak conditions in particular we do not have to impose linearity or ellipticity conditions of the kinds that are generally invoked for sdr methods we also present empirical results showing that the new methodology is competitive in practice

laplacian eigenmaps for dimensionality reduction and data representation one of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data we consider the problem of constructing a representation for data lying on a low dimensional manifold embedded in a high dimensional space drawing on the correspondence between the graph laplacian the laplace beltrami operator on the manifold and the connections to the heat equation we propose a geometrically motivated algorithm for representing the high dimensional data the algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering some potential applications and illustrative examples are discussed

on switched regulator design of uncertain nonlinear systems using takagi sugeno fuzzy models this paper is concerned with the design of state feedback switched controllers for a class of uncertain nonlinear plants described by takagi sugeno t s fuzzy models the proposed methodology eliminates the need to find the membership function expressions to implement the control law which is relevant in cases where the membership function depends on uncertain parameters the design of the switched controllers is based on a minimum type lyapunov function and the minimization of the time derivative of this lyapunov function the conditions of the new stability criterion are represented by a kind of bilinear matrix inequalities bmis that has been solved by the path following method a numerical example and the nonlinear control design of a magnetic levitator with uncertainties illustrate the procedure

on the design and synthesis of limit cycles using switching linear systems this article deals with the design and synthesis of limit cycles for a class of switched linear systems this work is motivated by an application in the context of electrical networks but the methodologies can be applied in other engineering fields as well several methods for the design and synthesis of limit cycles are presented based on a monodromy matrix associated with a periodically switched system a design method and two feedback strategies are developed the first strategy is based on linear feedback design using pole placement the second strategy is based on the observation that certain state dependent switching strategies can be implemented by means of a simple nonlinear output feedback controller advantages of this latter strategy are not only the ease with which the switching strategy can be implemented but also the fact that classical techniques may also be used to ascertain the stability of the resulting limit cycle our next contribution is the development of a novel frequency domain

quadratic and h switching control for discrete time linear systems with multiplicative noises the goal of this paper is to study the switched stochastic control problem of discrete time linear systems with multiplicative noises we consider both the quadratic and the h criteria for the performance evaluation initially we present a sufficient condition based on some lyapunov metzler inequalities to guarantee the stochastic stability of the switching system moreover we derive a sufficient condition for obtaining a metzler matrix that will satisfy the lyapunov metzler inequalities by directly solving a set of linear matrix inequalities and not bilinear matrix inequalities as usual in the literature of switched systems we believe that this result is an interesting contribution on its own in the sequel we present sufficient conditions again based on lyapunov metzler inequalities to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and h performance costs are bounded above by a constant value these results are illu

stability analysis and control of a class of lpv systems with piecewise constant parameters stability criteria characterizing the asymptotic stability of a class of lpv systems with piecewise constant parameters under constant and minimum dwell time are derived it is shown that for such systems the conditions for the stability under minimum dwell time can be seen as a unifying stability concept lying in between quadratic and robust stability thereby including them as extremal cases the results are then extended to address the stabilization problem using a particular class of time dependent gain scheduled state feedback controllers several examples are given for illustration

stability of stochastic nonlinear switched systems with average dwell time this paper concerns the stability of nonlinear stochastic switched systems with delay by using the razumikhin method and the average dwell time approach some sufficient criteria of stability are derived it is shown that when the lyapunov like functions are decreasing in all active subsystems the switched system is pth moment exponentially stable moreover it is also shown that under some conditions the system can be pth moment stable and global asymptotically stable where the lyapunov like functions are increasing on some intervals the effectiveness of the proposed results is illustrated by two examples

brief paper discrete time switching linear system with constraints characterization and computation of invariant sets under dwell time consideration this paper introduces the concepts of dwell time invariant contractive dt invariant contractive set constraint admissible dt invariant contractive cadt invariant contractive set for a discrete time switching system under dwell time switching main contributions of this paper include a characterization for a dt contractive set an algorithm for the computation of the maximal cadt invariant set a necessary and sufficient condition for asymptotic stability of the origin of switching systems under dwell time switching and computation of the minimal dwell time needed for asymptotic stability of the origin

output feedback control for switched linear systems subject to actuator saturation this article is devoted to the output feedback control problem for switched linear systems subject to actuator saturation we consider both continuous and discrete time switched systems using the minimal switching rule nonlinear output feedbacks expressed in the form of quasi linear parameter varying system are designed to satisfy a pre specified disturbance attenuation level defined by the regional 2 l2 gains over a class of energy bounded disturbances the conditions are expressed in bilinear matrix inequalities and can be solved by line search coupled with linear matrix inequalities optimisation a spherical inverted pendulum example is used to illustrate the effectiveness of the proposed approach

on the growth of logarithmic differences difference quotients and logarithmic derivatives of meromorphic functions a crucial ingredient in the recent discovery by ablowitz halburd herbst and korhonen 2000 2007 that a connection exists between discrete painleve equations and finite order nevanlinna theory is an estimate of the integrated average of log f z 1 f z on z r we obtained essentially the same estimate in our previous paper 2008 independent of halburd et al 2006 we continue our study in this paper by establishing complete asymptotic relations amongst the logarithmic differences difference quotients and logarithmic derivatives for finite order meromorphic functions in addition to the potential applications of our new estimates in integrable systems they are also of independent interest in particular our findings show that there are marked differences between the growth of meromorphic functions with nevanlinna order less than and greater than one we have established a difference analogue of the classical wiman valiron type estimates for meromorphic functions with order less than one which allow us to prove that all entire solutions of linear difference equations with polynomial coefficients of order less than one must have positive rational order of growth we have also established that any entire solution to a first order algebraic difference equation with polynomial coefficients must have a positive order of growth which is a difference analogue of a classical result of polya

necessary and sufficient condition for stability of switched uncertain linear systems under dwell time constraint in this technical note a necessary and sufficient stability criterion for switched linear systems under dwell time constraint is proposed by employing a class of time scheduled homogeneous polynomial lyapunov functions with a sufficiently large degree the key feature of this nonconservative condition lies in its convexity in the system matrices which explicitly facilitates its further extension to uncertain systems then in order to obtain numerically testable condition a family of lmi conditions are presented with the aid of the idea of dividing the dwell time interval into a finite number of segments it is proved that the non conservativeness can be maintained with a sufficiently large interval dividing parameter in the end the result is straightforwardly extended to the uncertain case in virtue of the convexity in the system matrices numerical examples are presented to illustrate our findings

linear differential equations with coefficients in weighted bergman and hardy spaces complex linear differential equations of the form with coefficients in weighted bergman or hardy spaces are studied it is shown for example that if the coefficient a j z of belongs to the weighted bergman space a 1 k j where a 0 for all j 0 k 1 then all solutions are of order of growth at most a measured according to the nevanlinna characteristic in the case when a 0 all solutions are shown to be not only of order of growth zero but of bounded characteristic conversely if all solutions are of order of growth at most a 0 then the coefficient aj z is shown to belong to a pj for all p j 0 1 k j and j 0 k 1 analogous results when the coefficients belong to certain weighted hardy spaces are obtained the non homogeneous equation associated to is also briefly discussed

co design of aperiodic sampled data min jumping rules for linear impulsive switched impulsive and sampled data systems abstract co design conditions for the design of a jumping rule and a sampled data control law for impulsive and impulsive switched systems subject to aperiodic sampled data measurements are provided semi infinite discrete time lyapunov metzler conditions are first obtained as these conditions are difficult to check and generalize to more complex systems an equivalent formulation is provided in terms of clock dependent infinite dimensional matrix inequalities these conditions are then in turn approximated by a finite dimensional optimization problem using a sum of squares based relaxation it is proven that the sum of squares relaxation is non conservative provided that the degree of the polynomials is sufficiently large it is emphasized that acceptable results are obtained for low polynomial degrees in the considered examples

convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode dependent dwell time abstract alternative conditions for establishing dwell time stability properties of linear switched systems are considered unlike the hybrid conditions derived in geromel and colaneri 2006 the considered ones are affine in the system matrices allowing then for the consideration of uncertain switched systems with time varying uncertainties the low number of decision variables moreover permits to easily derive convex stabilization conditions using a specific class of state feedback control laws the resulting conditions are enforced using sum of squares programming which are shown to be less complex numerically that approaches based on piecewise linear functions or looped functionals previously considered in the literature the sums of squares conditions are also proven to 1 approximate arbitrarily well the conditions of geromel and colaneri 2006 and 2 be invariant with respect to time scaling emphasizing that the complexity of the approach does not depend on the size of the dwell time several comparative examples illustrate the efficiency of the approach

stabilization of continuous time switched nonlinear systems abstract the paper considers three problems for continuous time nonlinear switched systems the first result of this paper is a open loop stabilization strategy based on dwell time computation the second considers a state switching strategy for global stabilization the strategy is of closed loop nature trajectory dependent and is designed from the solution of what we call nonlinear lyapunov metzler inequalities from which the stability condition is expressed finally results on the stabilization of nonlinear time varying polytopic systems are provided

stabilization of markovian systems via probability rate synthesis and output feedback this technical note is concerned with the stabilization problem of markovian jump linear systems via designing switching probability rate matrices and static output feedback gains a novel necessary and sufficient condition is established to characterize the switching probability rate matrices that guarantee the mean square stability of markovian jump linear systems based on this a necessary and sufficient condition is provided for the existence of desired controller gains and probability rate matrices extensions to the polytopic uncertain case are also provided all the conditions are formulated in terms of linear matrix inequalities with some equality constraints which can be solved by two modified cone complementarity linearization algorithms examples are given to show the effectiveness of the proposed method

a nonconservative lmi condition for stability of switched systems with guaranteed dwell time ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems several methods have been proposed in the literature to address this problem but unfortunately they provide sufficient conditions only this technical note proposes the use of homogeneous polynomial lyapunov functions in the non restrictive case where all the subsystems are hurwitz showing that a sufficient condition can be provided in terms of an lmi feasibility test by exploiting a key representation of polynomials several properties are proved for this condition in particular that it is also necessary for a sufficiently large degree of these functions as a result the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well some examples illustrate the proposed approach

differential linear matrix inequality in optimal sampled data control this paper addresses the design of optimal sampled data output feedback full order controllers for linear continuous time invariant systems first h2 and h performance indices are determined and expressed through differential linear matrix inequalities dlmis second in each scenario the optimal sampled data controller of the aforementioned class is determined from a convex programming problem expressed by dlmis theoretical achievements are based on the direct application of the celebrated bellman s principle of optimality expressed in terms of the dynamic programming equation associated to the time interval corresponding to two successive sampling instants the design problems to be dealt with are convex and are solved by converting all constraints to lmi and adopting a piecewise linear solution the possibility of aperiodic sampling is considered and briefly discussed finally academic examples are solved for illustration

affine characterizations of minimal and mode dependent dwell times for uncertain linear switched systems an alternative approach for minimum and mode dependent dwell time characterization for switched systems is derived while minimum dwell time results require the subsystems to be asymptotically stable mode dependent dwell time results can consider unstable subsystems and dwell times within a possibly unbounded range of values the proposed approach is related to lyapunov looped functionals a new type of functionals leading to stability conditions affine in the system matrices unlike standard results for minimum dwell time these conditions are expressed as infinite dimensional lmis which can be solved using recent polynomial optimization techniques such as sum of squares the specific structure of the conditions is finally utilized in order to derive dwell time stability results for uncertain switched systems several examples illustrate the efficiency of the approach

the set of stable switching sequences for discrete time linear switched systems in this paper we study the characterization of the asymptotical stability for discrete time switched linear systems we first translate the system dynamics into a symbolic setting under the framework of symbolic topology then by using the ergodic measure theory a lower bound estimate of hausdorff dimension of the set of asymptotically stable sequences is obtained we show that the hausdorff dimension of the set of asymptotically stable switching sequences is positive if and only if the corresponding switched linear system has at least one asymptotically stable switching sequence the obtained result reveals an underlying fundamental principle a switched linear system either possesses uncountable numbers of asymptotically stable switching sequences or has none of them provided that the switching is arbitrary we also develop frequency and density indexes to identify those asymptotically stable switching sequences of the system

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

convex lifted conditions for robust l 2 stability analysis and l 2 stabilization of linear discrete time switched systems with minimum dwell time constraint stability analysis of discrete time switched systems under minimum dwell time is studied using a new type of lmi conditions these conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed in geromel and colaneri 2006b the convexification of the conditions is performed by a lifting process which introduces a moderate number of additional decision variables the convexity of the conditions can be exploited to extend the results to uncertain systems control design and 2 gain computation without introducing additional conservatism several examples are presented to show the effectiveness of the approach

adaptive asymptotic tracking control of uncertain time driven switched linear systems this technical note establishes a novel result for adaptive asymptotic tracking control of uncertain switched linear systems the result exploits a recently proposed stability condition for switched systems in particular a time varying positive definite lyapunov function is used to develop a novel piecewise continuous model reference adaptive law and a dwell time switching law in contrast with previous research where asymptotic tracking was possible only in the presence of a common lyapunov function for the reference models in this work asymptotic tracking is shown in a more general setting additionally in the presence of persistence of excitation the controller parameter estimation errors will converge to zero asymptotically the main contribution of this work consists in establishing a symmetry between adaptive control of classical non switched linear systems and adaptive control of switched linear systems a practical example with an electro hydraulic system is adopted to illustrate the results

central subspace dimensionality reduction using covariance operators we consider the task of dimensionality reduction informed by real valued multivariate labels the problem is often treated as dimensionality reduction for regression drr whose goal is to find a low dimensional representation the central subspace of the input data that preserves the statistical correlation with the targets a class of drr methods exploits the notion of inverse regression ir to discover central subspaces whereas most existing ir techniques rely on explicit output space slicing we propose a novel method called the covariance operator inverse regression coir that generalizes ir to nonlinear input output spaces without explicit target slicing coir s unique properties make drr applicable to problem domains with high dimensional output data corrupted by potentially significant amounts of noise unlike recent kernel dimensionality reduction methods that employ iterative nonconvex optimization coir yields a closed form solution we also establish the link between coir other drr techniques and popular supervised dimensionality reduction methods including canonical correlation analysis and linear discriminant analysis we then extend coir to semi supervised settings where many of the input points lack their labels we demonstrate the benefits of coir on several important regression problems in both fully supervised and semi supervised settings

design of stabilizing switching laws for mixed switched affine systems this technical note presents stability analysis and stabilization for a general class of switched systems characterized by nonlinear functions the proposed approach is composed of approximating the switched nonlinear system with a switched affine system that has a mixture of controlled and autonomous switching behavior utilizing a joint polyhedral partitioning approach a stabilizing switching law based on quadratic lyapunov functions and with considering the autonomous switching between polyhedral regions is proposed to ensure the decrease of the overall lyapunov function two approaches are proposed 1 guarantee continuity of the lyapunov function over boundaries of polyhedral regions and 2 relax the continuity requirement by using additional matrix inequalities the second approach is less conservative but with more variables and matrix inequalities than in the first method with fixing one scalar variable the stabilization conditions will have the form of linear matrix inequalities lmis further the sufficient conditions for stabilizing the original switched nonlinear system using the proposed switching schemes are presented finally through two examples the performance of the proposed stabilization methods is demonstrated

finite order meromorphic solutions and the discrete painleve equations let w z be a finite order meromorphic solution of the second order difference equation w z 1 w z 1 r z w z where r z w z is rational in w z and meromorphic in z then either w z satisfies a difference linear or riccati equation or else equation can be transformed to one of a list of canonical difference equations this list consists of all known difference painleve equation of the form together with their autonomous versions this suggests that the existence of finite order meromorphic solutions is a good detector of integrable difference equations