an lmi approach to reliable guaranteed cost control of discrete time systems with actuator failure this paper is concerned with the reliable guaranteed cost control problem for discrete time systems with actuator failures and a given quadratic cost function the problem is to design a reliable guaranteed cost state feedback control law which can tolerate actuator failure such that the cost function of the closed loop system is guaranteed to be no more than a certain upper bound a sufficient condition for the existence of reliable guaranteed cost controllers is derived via the linear matrix inequality lmi approach and a design procedure of such controllers is presented furthermore a convex optimization problem with lmi constraints is formulated to design the optimal reliable guaranteed cost controller which minimizes the upper bound of the closed loop system cost

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

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

robust reliable passive control of uncertain stochastic switched time delay systems this paper investigates the problem of robust reliable passive control for a class of uncertain stochastic switched time delay systems with actuator failures the multiple lyapunov functions mlfs technique is exploited to derive a delay dependent sufficient condition for the stochastic switched time delay systems to be passive and exponentially stable under a state based switching law moreover the proposed approach is extended to investigate stochastic switched systems with structured uncertainties finally two numerical examples are presented to illustrate the effectiveness of the proposed method

on the coerciveness of some merit functions for complementarity problems over symmetric cones abstract one of the popular solution methods for the complementarity problem over symmetric cones is to reformulate it as the global minimization of a certain merit function an important question to be answered for this class of methods is under what conditions the level sets of the merit function are bounded the coerciveness of the merit function in this paper we introduce the generalized weak coerciveness of a continuous transformation under this condition we prove the coerciveness of some merit functions such as the natural residual function the normal map and the fukushima yamashita function for complementarity problems over symmetric cones we note that this is a much milder condition than strong monotonicity used in the current literature

a one step smoothing newton method for second order cone programming a new smoothing function for the second order cone programming is given by smoothing the symmetric perturbed fischer burmeister function based on this new function a one step smoothing newton method is presented for solving the second order cone programming the proposed algorithm solves only one linear system of equations and performs only one line search at each iteration this algorithm does not have restrictions regarding its starting point and is q quadratically convergent numerical results suggest the effectiveness of our algorithm

convergence of a smoothing type algorithm for the monotone affine variational inequality problem smoothing type algorithms have been applied to solve various optimization problems in the analysis on the global convergence most existing smoothing type algorithms need to assume that the solution set of the problem concerned is nonempty and bounded or some stronger conditions in this paper we investigate a smoothing type algorithm for solving the monotone affine variational inequality problem avip specially we reformulate the avip as a system of parameterized smooth equations and instead of solving the original avip we use a newton type method to solve the smooth equations we show that under mild assumptions the iteration sequence generated by the algorithm is bounded and the algorithm may find a maximally complementary solution to the avip in our analysis on the convergence we do not need to assume that the solution set of the avip is bounded

stabilization of switched linear systems in this note we study the stabilization problem of systems that switch among a finite set of controllable linear systems with arbitrary switching frequency for both cases of known and unknown switching functions feedback laws are designed to achieve exponential stability for the later case a method combining on line adaptive estimation and feedback stabilization is developed in the controller design

lowner s operator and spectral functions in euclidean jordan algebras we study analyticity differentiability and semismoothness of lowner s operator and spectral functions under the framework of euclidean jordan algebras in particular we show that many optimization related classical results in the symmetric matrix space can be generalized within this framework for example the metric projection operator over any symmetric cone defined in a euclidean jordan algebra is shown to be strongly semismooth the research also raises several open questions whose answers would be of strong interest for optimization research

robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching this paper is concerned with the problem of robust reliable control for a class of uncertain stochastic switched nonlinear systems under asynchronous switching where the switching instants of the controller experience delays with respect to those of the system a design scheme for the reliable controller is proposed to guarantee almost surely exponential stability for stochastic switched systems with actuator failures and the dwell time approach is utilized for the stability analysis then the approach is extended to take into account stochastic switched system with lipschitz nonlinearities and structured uncertainties finally a numerical example is employed to verify the proposed method

extension of primal dual interior point algorithms to symmetric cones in this paper we show that the so called commutative class of primal dual interior point algorithms which were designed by monteiro and zhang for semidefinite programming extends word for word to optimization problems over all symmetric cones the machinery of euclidean jordan algebras is used to carry out this extension unlike some non commutative algorithms such as the xs sx method this class of extensions does not use concepts outside of the euclidean jordan algebras in particular no assumption is made about representability of the underlying jordan algebra as a special case we prove polynomial iteration complexities for variants of the short semi long and long step path following algorithms using the nesterov todd xs or sx directions

stability analysis for stochastic hybrid systems this survey addresses stability analysis for stochastic hybrid systems shs which are dynamical systems that combine continuous change and instantaneous change and that also include random effects we re emphasize the common features found in most of the models that have appeared in the literature which include stochastic switched systems markov jump systems impulsive stochastic systems switching diffusions stochastic impulsive systems driven by renewal processes diffusions driven by levy processes piecewise deterministic markov processes general stochastic hybrid systems and stochastic hybrid inclusions then we review many of the stability concepts that have been studied including lyapunov stability lagrange stability asymptotic stability and recurrence next we detail lyapunov based sufficient conditions for these properties and additional relaxations of lyapunov conditions many other aspects of stability theory for shs like converse lyapunov theorems and robustness theory are not fully developed hence we also formulate some open problems to serve as a partial roadmap for the development of the underdeveloped pieces

a robust stabilizing law for switched linear systems in this paper we address some robustness issues for a class of switched linear systems with non linear perturbations we illustrate through an example that the well known state space partition based switching law may lead to chattering in the event that the systems undergo perturbations to overcome this we propose a state feedback switching law with a non zero level set we prove that this switching law can prevent the system from chattering in addition this switching law makes the perturbed systems bounded with bounded perturbations and practically convergent with convergent perturbations we also propose an observer based switching law to steer the switched system stable with nice robustness performances

a predictor corrector smoothing newton method for symmetric cone complementarity problems abstract in this paper we present a predictor corrector smoothing newton method for solving nonlinear symmetric cone complementarity problems sccp based on the symmetrically perturbed smoothing function under a mild assumption the solution set of the problem concerned is just nonempty we show that the proposed algorithm is globally and locally quadratic convergent also the algorithm finds a maximally complementary solution to the sccp numerical results for second order cone complementarity problems soccp a special case of sccp show that the proposed algorithm is effective

delay dependent robust stabilization of uncertain systems with multiple state delays this paper deals with the problem of robust stabilization for uncertain systems with multiple state delays the parameter uncertainties are time varying and unknown but are norm bounded and the delays are time varying a new method for achieving robust stabilization is presented for a class of uncertain time delay systems via linear memoryless state feedback control the results depend on the size of the delays and are given in terms of several linear matrix inequalities

reliable dissipative control for stochastic impulsive systems this paper deals with the problem of reliable dissipative control for a class of stochastic hybrid systems the systems under study are subject to markovian jump parameter uncertainties possible actuator failure and impulsive effects which are often encountered in practice and the sources of instability our attention is focused on the design of linear state feedback controllers and impulsive controllers such that for all admissible uncertainties as well as actuator failure occurring among a prespecified subset of actuators the stochastic hybrid system is stochastically robustly stable and strictly q s r dissipative the sufficient conditions are obtained by using linear matrix inequality lmi techniques the main results of this paper extend the existing results on h control

finite time stability and stabilization of switched nonlinear systems with asynchronous switching abstract this paper is concerned with the problem of finite time stability and stabilization for switched nonlinear systems with asynchronous switching firstly when not all subsystems are finite time stable fts we propose a finite time stability criteria to show that if the constraint condition between the settling time and the average dwell time is satisfied finite time stability of the system is guaranteed then we extend the result to the case which lipschitzian perturbations exist in the subsystems when asynchronous switching is considered and not all closed loop subsystems are finite time stabilizable we recur to the generalized inverse of matrices to design a state feedback controller to stabilize the original system finally an example of two container liquid level system is provided to illustrate the effectiveness of developed result

a novel result on stability analysis for uncertain neutral stochastic time varying delay systems generalized finsler lemma is applied to deduce delay dependent stability conditions the case is considered that the discrete delay is different from the neutral delay model transformation cross terms estimation and free weighting matrices are avoided the conditions show less conservatism and involves fewer computational variables numerical examples show that the proposed approach improves some existing ones this paper is concerned with the mean square exponential stability analysis for uncertain neutral linear stochastic time varying delay systems by lyapunov krasovskii theory and linear matrix inequality method under the generalized finsler lemma gfl framework delay dependent mean square exponential stability criteria are established without involving model transformation cross terms bounding technique or additional free weighting matrix moreover gfl is also employed to obtain stability criteria for a class of uncertain linear stochastic neutral systems with different discrete and neutral delays numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing results

the exponential stability and asynchronous stabilization of a class of switched nonlinear system via the t s fuzzy model in this paper we investigate the problem of exponential stability and asynchronous stabilization for a class of switched nonlinear systems the takagi and sugeno t s fuzzy model is employed to approximate the subnonlinear dynamic systems with two level functions namely crisp switching functions and local fuzzy weighting functions we introduce continuous time switched fuzzy systems which inherently contain the features of the switched hybrid systems and t s fuzzy systems by the use of delicately constructed piecewise lyapunov like functions plfs and minimum dwell time method we obtain the exponential stability of the switched fuzzy systems which allows us to have stable and unstable nonlinear subsystems in practice for the control problem it inevitably takes some time to identify the system modes and apply the matched controller the asynchronous phenomena between the system modes switching and the controllers switching generally exists based on the result of stability the fuzzy state feedback controller under asynchronous switching is proposed for switched fuzzy systems in addition the lower bound of minimum dwell time can be obtained using convex optimization such that the switched fuzzy system can be exponentially stabilized if its minimum dwell time is larger than the bound the stability results and control laws of the switched fuzzy systems are formulated in the form of linear matrix inequalities that are numerically feasible finally two illustrated numerical examples are presented to show the effectiveness of the obtained theoretical results

stabilization of switched linear systems with time delay in detection of switching signal a feedback stabilization problem for switched linear systems with time delay in detection of switching signal is formulated first online state feedback controller design method for asymptotic stability and exponential stability is given then offline state feedback controller design method for asymptotic stability and exponential stability is given as well

finite time stabilization for a class of switched time delay systems under asynchronous switching switched control systems can be used to describe many practical processes with switching phenomena such as power electronics mechanical systems etc in this paper the problem of finite time stabilization under asynchronous switching is dealt with for a class of switched time delay systems with nonlinear disturbances firstly the nonlinear uncertainties are transformed into the linear time varying forms via the differential mean value theorem under some assumptions secondly by applying the average dwell time method and convexity principle a finite time stability condition for the unforced switched time delay system is established finally an asynchronous switching state feedback controller is designed which renders the considered system finite time stable a numerical example is provided to show the effectiveness of the developed results

on the stability of uncertain polynomials with dependent coefficients a sufficient condition is given for reducing the conservatism of the stability bounds for a family of polynomials with dependent coefficients including nonlinear coefficients it is also proved that if a finite family of stable polynomials has the same even part then the polynomial with the even part and the odd part formed by adding any positive multiple of the even parts and odd parts respectively of the given family is also stable similar results holds if the given family of polynomials has the same odd part a numerical example with nonlinear coefficients is given to illustrate the technique and it is observed that the stability bounds obtained are larger than those acquired by kharitonov s theorem

stability analysis of a class of hybrid stochastic retarded systems under asynchronous switching the stability of a class of hybrid stochastic retarded systems hsrss with an asynchronous switching controller is investigated in this model the controller design relies on the observed jumping parameters which are however delayed and thus can not be measured in real time precisely this delayed time interval referred to as the asynchronous switching interval is markovian and dependent on the actual switching signal the sufficient conditions under which the system is either stochastically asymptotic stable or input to state stable are obtained by applying the extended razumikhin type theorem to the asynchronous switching interval these results are less conservative as it is only required that the designed lyapunov function is non decreasing it is shown that the stability of the considered system can be guaranteed by a sufficiently small mode transition rate of the underlying markov process which is a conclusion similar to that in asynchronous deterministic switched systems the effectiveness and correctness of the obtained results are finally verified by a numerical example

some p properties for nonlinear transformations on euclidean jordan algebras in this article we introduce the concepts of p and p0 properties for a nonlinear transformation defined on a euclidean jordan algebra and study existence of solution in the associated complementarity problems in particular we show in this general setting that if a transformation has the p0 and r0 properties then all associated complementarity problems have solutions we also describe a necessary condition for a transformation to have the global uniqueness of solution property

brief paper reliable control of uncertain nonlinear systems this paper is concerned with the reliable controller design problem for a class of uncertain nonlinear systems for the primary contingency problem a procedure of designing reliable nonlinear controllers is presented in terms of solutions of hamilton jacobi inequalities the resulting closed loop nonlinear system is reliable in the sense that the performance i e internal stability and h attenuation of the closed loop system is guaranteed not only when all sensors and actuators are operational but also when some sensor and actuator outages occur

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

a nonsmooth version of newton s method newton s method for solving a nonlinear equation of several variables is extended to a nonsmooth case by using the generalized jacobian instead of the derivative this extension includes the b derivative version of newton s method as a special case convergence theorems are proved under the condition of semismoothness it is shown that the gradient function of the augmented lagrangian forc2 nonlinear programming is semismooth thus the extended newton s method can be used in the augmented lagrangian method for solving nonlinear programs

robust reliable h control for uncertain nonlinear systems via lmi approach this paper investigates the robust reliable h control for a class of uncertain nonlinear system at first a criterion for nonlinear system without uncertainties is proposed to guarantee global exponential stabilization and disturbance attenuation next the criterion for uncertain nonlinear systems with parameter uncertainties is obtained by simple derivation linear matrix inequality lmi optimization approach is used to design the robust reliable h state feedback control two numerical examples are given to illustrate the effectiveness of the main results

a regularized smoothing newton method for symmetric cone complementarity problems this paper extends the regularized smoothing newton method in vector complementarity problems to symmetric cone complementarity problems sccp which includes the nonlinear complementarity problem the second order cone complementarity problem and the semidefinite complementarity problem as special cases in particular we study strong semismoothness and jacobian nonsingularity of the total natural residual function for sccp we also derive the uniform approximation property and the jacobian consistency of the chen mangasarian smoothing function of the natural residual based on these properties global and quadratical convergence of the proposed algorithm is established