optimal control of a simple immigration emigration process through total catastrophes abstract this paper is concerned with the problem of controlling a simple immigration emigration process which represents a pest population by the introduction of total catastrophes which when they occur reduce the population size to zero the optimality criterion is that of minimizing the expected long run average cost per unit time the optimality of a control limit policy is obtained using the method of successive approximations an efficient markov decision algorithm that generates a sequence of strictly improved control limit policies is developed there is strong numerical evidence that the algorithm converges to the overall optimal policy

robust linear filtering for discrete time hybrid markov linear systems in this paper we consider the robust linear filtering of hybrid discrete time markovian jump linear systems we assume that only an output of the system is available and therefore the values of the jump parameter are not known it is desired to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the square error we consider uncertainties on the parameters of the possible modes of operation of the system a linear matrix inequalities lmi formulation is proposed to solve the problem for the case in which there are no uncertainties on the modes of operation of the system we show that the lmi formulation provides a filter with the same stationary mean square error as the one obtained from the riccati equation approach

distributed robust estimation over randomly switching networks using h consensus the paper considers a distributed robust estimation problem over a network with markovian randomly varying topology the objective is to deal with network variations locally by switching observer gains at affected nodes only we propose sufficient conditions which guarantee a suboptimal h level of relative disagreement of estimates in such observer networks when the status of the network is known globally these sufficient conditions enable the network gains to be computed by solving certain lmis when the nodes are to rely on a locally available information about the network topology additional rank constraints are used to condition the gains given this information the results are complemented by necessary conditions which relate properties of the interconnection graph laplacian to the mean square detectability of the plant through measurement and interconnection channels

on some time non homogeneous queueing systems with catastrophes computations for non homogeneous birth and death processes with catastrophes applications to queueing and population dynamics problems effect of the periodicity of the rates on the performance of systems with catastrophes non stationary queueing systems subject to catastrophes occurring with time varying intensity are considered the effect of a catastrophe is to make the queue instantly empty the transition probabilities the related moments and the first visit time density to zero state are analyzed particular attention is dedicated to queueing systems in the presence of catastrophes with periodic intensity function various applications are provided including the non stationary birth death process with immigration the queueing systems m t m t 1 and m t m t

eigenvalue localization and neville elimination abstract neville elimination is an elimination procedure alternative to gaussian elimination and very adequate when dealing with some special classes of matrices in this paper we present pivoting strategies such that the radii of the gersgorin circles of the schur complements through neville elimination with these pivoting strategies reduce their length and we consider classes of matrices important in many applications we include illustrative examples comparing the results with those obtained with gaussian elimination and showing that our hypotheses are necessary

analysis of the m g 1 queue in multi phase random environment with disasters this paper studies an m g 1 queue in a multi phase random environment when in operative phase i i 1 2 n the system is subject to disastrous interruptions causing all present customers waiting and served to leave the system at an exponential failure instant the server abandons the service and the system goes directly to repair phase after an exponential repair time the system moves to operative phase i with probability qi i 1 2 n using the supplementary variable technique we obtain the distribution for the stationary queue at an arbitrary epoch we also derive results of the cycle analysis the sojourn time distribution and the length of the server s working time in a service cycle in addition some special cases and numerical examples are presented

distributed robust filtering with h consensus of estimates the paper addresses a problem of design of distributed robust filters using the recent vector dissipativity theory the main result is a sufficient condition which guarantees a suboptimal h level of disagreement of estimates in a network of filters it involves solving a convex optimization feasibility problem subject to lmi constraints the special case of balanced interconnection graphs is also considered a gradient descent type algorithm is presented which allows the nodes to compute their estimator parameters in a decentralized manner the proposed approach is applied to the problem of observer based robust synchronization of a nonlinear network to an isolated node

technical communique a linear distributed filter inspired by the markovian jump linear system filtering problem in this paper we introduce a consensus based distributed filter executed by a sensor network inspired by the markovian jump linear system filtering theory we show that the optimal filtering gains of the markovian jump linear system can be used as an approximate solution of the optimal distributed filtering problem this parallel allows us to interpret each filtering gain corresponding to a mode of operation of the markovian jump linear system as a filtering gain corresponding to a sensor in the network the approximate solution can be implemented distributively and guarantees a quantifiable level of performance

an extension to balanced truncation with application to structured model reduction balanced truncation is a standard method for model reduction possessing many desirable properties such as preservation of model stability and a priori error bounds balanced truncation is conducted using controllability and observability gramians generalized gramians can be found by solving a set of linear matrix inequalities in this paper we show that these linear matrix inequalities can be extended so that the number of decision variables are at least doubled leading to the concept of extended gramians herein it is shown that the desirable properties of balanced truncation also hold with extended gramians the extended gramians are especially useful for improving error bounds and for models possessing additional structural constraints as is demonstrated by means of examples herein

the dominant degree and disc theorem for the schur complement of matrix the theory of schur complement plays an important role in many fields such as control theory and computational mathematics in this paper we obtain some estimates for the diagonally c diagonally and product c diagonally dominant degree on the schur complement of matrices which improve some relative results as application we present some bounds for the eigenvalues of schur complement by the entries of the original matrix instead of those of the schur complement particularly we obtain that the eigenvalues of the schur complements are located in the gerschgorin circles of the original matrices under certain conditions

observability through a matrix weighted graph observability of an array of identical linear time invariant systems with incommensurable output matrices is studied where an array is called observable when identically zero relative outputs imply synchronized solutions for the individual systems it is shown that the observability of an array is equivalent to the connectivity of its interconnection graph whose edges are assigned matrix weights moreover to better understand the relative behavior of distant units pairwise observability that concerns with the synchronization of a certain pair of individual systems in the array is studied this milder version of observability is shown to be closely related to certain connectivity properties of the interconnection graph as well pairwise observability is also analyzed using the circuit theoretic tool effective conductance the observability of a certain pair of units is proved to be equivalent to the nonsingularity of the matrix valued effective conductance between the associated pair of nodes of a resistive network with matrix valued parameters whose node admittance matrix is the laplacian of the array s interconnection graph

a state dependent queueing system with asymptotic logarithmic distribution abstract a markovian single server queueing model with poisson arrivals and state dependent service rates characterized by a logarithmic steady state distribution is considered the laplace transforms of the transition probabilities and of the densities of the first passage time to zero are explicitly evaluated the performance measures are compared with those ones of the well known m m 1 queueing system finally the effect of catastrophes is introduced in the model and the steady state distribution the asymptotic moments and the first visit time density to zero state are determined

eigenvalue localization and pivoting strategies for gaussian elimination we show pivoting strategies such that the radii of the gersgorin circles of the schur complements through gaussian elimination with these pivoting strategies reduce their length the results will be illustrated with classes of matrices important in many applications

design of distributed decentralized estimators for formations with fixed and stochastic communication topologies this paper proposes a solution to the problem of synthesizing distributed decentralized estimators for a formation of agents the collected dynamics of the formation are modeled by a discrete lti system in the considered estimation structure each agent of the formation carries an estimate of the entire formation state agents of the formation can communicate information between each other through unidirectional links modeled with a fixed or a stochastic communication topology the design procedures are based on a set of convex optimization problems with linear matrix inequalities and result in the suboptimal choice of estimator gains which stabilize the estimation error dynamics and minimize a norm of the estimation error correlation matrix

on the uniform algebraic observability of multi switching linear systems the main objective of this paper is the characterisation of the notion of uniform algebraic observability for multi switching linear systems in particular it is shown that a multi switching linea

decentralized determinantal assignment problem fixed and almost fixed modes and zeros the decentralized determinantal assignment problem ddap is defined as the unifying description for the study of pole and zero assignment problems under decentralized output state feedback dof dsf and decentralized squaring down dsd respectively ddap is reduced to a linear problem of zero assignment of polynomial combinants and a multilinear problem of restricted decomposability of multivectors the decentralization characteristic dc and the decentralized polynomial grassmann representative d s gr of ddap are defined the fixed zero polynomial of ddap is then determined as the zero polynomial of d s gr the canonical d s gr cd r s gr and the decentralized plucker matrix dpm of ddap are introduced and necessary conditions for arbitrary assignment of the non fixed zeros are given in terms of the dpm the family of strongly zero non assignable sna systems is defined and for such systems the notion of the fixed zero is extended to that of the almost fixed zero afz an

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

a newton like method for solving rank constrained linear matrix inequalities this paper presents a newton like algorithm for solving systems of rank constrained linear matrix inequalities though local quadratic convergence of the algorithm is not a priori guaranteed or observed in all cases numerical experiments including application to an output feedback stabilization problem show the effectiveness of the algorithm

transient solution of an m m 1 queue with catastrophes abstract a transient solution for the system size in the m m 1 queueing model with the possibility of catastrophes at the service station is derived in the direct way asymptotic behavior of the probability of the server being idle and mean queue size are discussed steady state probabilities are also obtained

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

technical communique fixed modes in multivariable systems using constrained controllers a general expression is derived relating an arbitrary output feedback controller to the resulting closed loop characteristic polynomial in terms of suitably defined zero polynomials of the system this expression is then used to characterize the fixed modes of a multivariable system with respect to controllers of any desired structure

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

large deviations for markov processes with resetting markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches foraging and population dynamics here we study the large deviations of time additive functions or observables of markov processes with resetting by deriving a renewal formula linking generating functions with and without resetting we are able to obtain the rate function of such observables characterizing the likelihood of their fluctuations in the long time limit we consider as an illustration the large deviations of the area of the ornstein uhlenbeck process with resetting other applications involving diffusions random walks and jump processes with resetting or catastrophes are discussed

eigenvalue localization refinements for the schur complement abstract the theory of schur complement plays an important role in many fields as well as the theory of h matrices in this paper we obtain some bounds for the eigenvalues of schur complement by the entries of the original matrix instead of those of the schur complement for some special h matrices also we show how this result for a wider class can be applied for estimating bounds for the eigenvalues of schur complement of an sdd matrix

further results on h matrices and their schur complements abstract it is well known d carlson t markham schur complements of diagonally dominant matrices czech math j 29 104 1979 246 251 1 that the schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant also if a matrix is an h matrix then its schur complement is an h matrix too j liu y huang some properties on schur complements of h matrices and diagonally dominant matrices linear algebra appl 389 2004 365 380 8 recent research showed that the same type of statement holds for some special subclasses of h matrices see for example liu et al j liu y huang f zhang the schur complements of generalized doubly diagonally dominant matrices linear algebra appl 378 2004 231 244 the aim of this paper is to show that the proof of these results can be significantly simplified by using scaling approach as in zhang et al f zhang et al the schur complement and its applications springer new york 2005 and to give another invariance result of this type

pivoting strategies leading to diagonal dominance by rows pivoting strategies for gaussian elimination leading to upper triangular matrices which are diagonally dominant by rows are studied forward error analysis of triangular systems whose coefficient matrices are diagonally dominant by rows is performed we also obtain small bounds of the backward errors for the pivoting strategies mentioned above our examples of matrices include h matrices and some generalizations of diagonally dominant matrices and scaled partial pivoting for the 1 norm is an example of these pivoting strategies in the case of an n times n m matrix a pivoting strategy of computational complexity o n 2 is proposed which satisfies all the results of the paper