h h consensus control for multi agent systems with missing measurements the finite horizon case abstract this paper deals with the h consensus control problem for a class of discrete time varying multi agent systems with both missing measurements and parameter uncertainties a directed graph is used to represent the communication topology of the multi agent network and a binary switching sequence satisfying a conditional probability distribution is employed to describe the missing measurements the purpose of the addressed problem is to design a time varying controller such that for all probabilistic missing observations and admissible parameter uncertainties the h consensus performance is guaranteed over a given finite horizon for the closed loop networked multi agent systems according to the given topology the measurement output available for the controller is not only from the individual agent but also from its neighboring agents by using the completing squares method and stochastic analysis techniques necessary and sufficient conditions are derived for the h consensus to be ensured and then the time varying controller parameters are designed by solving coupled backward recursive riccati difference equations rdes a simulation example is utilized to illustrate the usefulness of the proposed control protocol

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

predecessor property full combinatorial column rank and the height characteristics of an m matrix abstract for a loopless acyclic transitive directed graph we give a new result about the relation between the t predecessor property of subsets of its levels and the property of having full combinatorial column rank for certain blocks in its adjacency matrix as a corollary we give new lower bounds for the i th height characteristic number of a singular m matrix an open question about determining the height characteristics of singular m matrices with a prescribed singular graph is also posed

distributed linear estimation over sensor networks we consider a network of sensors in which each node may collect noisy linear measurements of some unknown parameter in this context we study a distributed consensus diffusion scheme that relies only on bidirectional communication among neighbour nodes nodes that can communicate and exchange data and allows every node to compute an estimate of the unknown parameter that asymptotically converges to the true parameter at each time iteration a measurement update and a spatial diffusion phase are performed across the network and a local least squares estimate is computed at each node the proposed scheme allows one to consider networks with dynamically changing communication topology and it is robust to unreliable communication links and failures in measuring nodes we show that under suitable hypotheses all the local estimates converge to the true parameter value

brief paper stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper is to study the discrete time stochastic h 2 h control with state and external disturbance dependent noise a necessary and sufficient condition for the existence of h 2 h control is presented which transforms the h 2 h controller design into solving four coupled matrix valued equations moreover a recursive algorithm for solving the four coupled matrix valued equations is also given

some remarks on general nonlinear stochastic h_ infty control with state control and disturbance dependent noise this technical note studies the nonlinear stochastic h control of ito type differential systems with all the state control input and external disturbance dependent noise x u v dependent noise for short a sufficient condition is given for the finite infinite horizon h control of such a system by means of an hamilton jacobi inequality hji instead of three coupled hamilton jacobi equations hjes as in previous literature

null controllability of linear systems with constrained controls the paper considers the problem of steering the state of a linear time varying system to the origin when the control is subject to magnitude constraints necessary and sufficient conditions are given for global constrained controllability as well as a necessary and sufficient condition for the existence of a control satisfying the constraints which steers the system to the origin from a specified initial epoch x 0 t 0 the global result does not require zero to be an interior point of the control set omega and the theorem for constrained controllability at x 0 t 0 only requires that omega be compact not that it contain zero the results are compared to those available in the literature furthermore numerical aspects of the problem are discussed as is a technique for determining a steering control

structured and simultaneous lyapunov functions for system stability problems abstract it is shown that many system stability and robustness problems can be reduced to the question of when there is a quadratic lyapunov function of a certain structure which establishes stability of x ax for some appropriate a the existence of such a lyapunov function can be determined by solving a convex program we present several numerical methods for these optimization problems a simple numerical example is given

some new results on closed loop stability in the presence of control saturation some new sufficient conditions for determining global asymptotic stability of an equilibrium point under control saturation are presented for an open loop stable system we show that there exists a class of linear time invariant state feedback matrices which globally stablizes an equilibrium under control saturation in addition we show that for open loop unstable plants an equilibrium can never be globally stabilized using a certain class of saturated linear time invariant state feedback finally we extend the stability results to nonlinear systems whose nonlinearities are globally lipschitz

leader following consensus of a class of stochastic delayed multi agent systems with partial mixed impulses in this paper the exponential leader following consensus problem is investigated for a class of nonlinear stochastic networked multi agent systems with partial mixed impulses and unknown time varying but bounded delays the main feature of partial mixed impulses is that time varying impulses are not only composed of synchronizing and desynchronizing impulses simultaneously but they are also injected into a fraction of nodes in multi agent systems three kinds of partial mixed impulses are proposed fixed partial mixed impulses periodic partial mixed impulses and try once discard like partial mixed impulses by means of the lyapunov function theory and the comparison principle conditions are derived for ensuring global exponential leader following consensus under the presented three kinds of partial mixed impulses simulations of leader following consensus of robotic systems are provided to validate the effectiveness of the proposed results and to show the advantages of the proposed partial mixed impulses

robust stability of uncertain impulsive dynamical systems abstract this paper studies robust stability of uncertain impulsive dynamical systems by introducing the concepts of uniformly positive definite matrix functions and hamilton jacobi riccati inequalities several criteria on robust stability robust asymptotic stability and robust exponential stability are established an example is also worked through to illustrate our results

matrix roots of imprimitive irreducible nonnegative matrices abstract using matrix function theory perron frobenius theory combinatorial matrix theory and elementary number theory we characterize classify and describe in terms of the jordan canonical form the matrix p th roots of imprimitive irreducible nonnegative matrices preliminary results concerning the matrix roots of reducible matrices are provided as well

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks this paper is concerned with the distributed recursive filtering problem for a class of discrete time delayed stochastic systems subject to both uniform quantization and deception attack effects on the measurement outputs the target plant is disturbed by the multiplicative as well as additive white noises a novel distributed filter is designed where the available innovations are from not only the individual sensor but also its neighboring ones according to the given topology attention is focused on the design of a distributed recursive filter such that in the simultaneous presence of time delays deception attacks and uniform quantization effects an upper bound for the filtering error covariance is guaranteed and subsequently minimized by properly designing the filter parameters via a gradient based method at each sampling instant furthermore by utilizing the mathematical induction a sufficient condition is established to ensure the asymptotic boundedness of the sequence of the error covariance finally a simulation example is utilized to illustrate the usefulness of the proposed design scheme of distributed filters

consensus conditions of multi agent systems with time varying topologies and stochastic communication noises this paper investigates the average consensus problem of first order discrete time multi agent networks in uncertain communication environments each agent can only use its own and neighbors information to design its control input to attenuate the communication noises a distributed stochastic approximation type protocol is used by using probability limit theory and algebraic graph theory consensus conditions for this kind of protocols are obtained a for the case of fixed topologies a necessary and sufficient condition for mean square average consensus is given which is also sufficient for almost sure consensus b for the case of time varying topologies sufficient conditions for mean square average consensus and almost sure consensus are given respectively especially if the network switches between jointly containing spanning tree instantaneously balanced graphs then the designed protocol can guarantee that each individual state converges both almost surely and in mean square to a common random variable whose expectation is right the average of the initial states of the whole system and whose variance describes the static maximum mean square error between each individual state and the average of the initial states of the whole system

robust mathscr h _ infty filtering for a class of two dimensional uncertain fuzzy systems with randomly occurring mixed delays this paper is concerned with the robust mathscr h infty filtering problem for a class of 2 d uncertain fuzzy systems with randomly occurring mixed delays romds the underlying 2 d systems are described by the fornasini marchesini model and the uncertainty is expressed in a linear fraction form an improved takagi sugeno t s fuzzy model corresponding to the spatial promise variables is adopted to represent the complicated 2 d nonlinear system the mixed delays consisting of both discrete and distributed delays are allowed to appear in a random manner governed by two sets of bernoulli distributed white sequences with known probability a full order fuzzy filter is constructed to estimate the output signal such that in the presence of parameter uncertainties and romds the dynamics of the estimation errors is asymptotically stable with a prescribed mathscr h infty disturbance attenuation level based on the stochastic analysis technique and the lyapunov like functional sufficient conditions are established to ensure the existence of the desired filters and the explicit expressions of such filters are derived by means of the solution to a class of convex optimization problems that can be solved via standard software packages a numerical example is provided to demonstrate the effectiveness of the developed filter design algorithms and the filter performances with and without fuzzy rules are also compared

relationship between nash equilibrium strategies and h_ 2 h_ infty control of stochastic markov jump systems with multiplicative noise this technical note is concerned with discussing the relationship between nash equilibrium strategies and the finite horizon h 2 h control of time varying stochastic systems subject to markov jump parameters and multiplicative noise it is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term furthermore necessary and sufficient conditions for the finite horizon h 2 h control of stochastic markov jump systems are presented via coupled matrix valued equations

a general collision avoiding flocking framework we prove a general result of collision avoiding flocking the underlying model allows several forms of coupling forces and the main result ensures flocking provided the initial state of the population does not show simultaneously very different velocities very spread positions or very close agents

on the existence of globally stable actuator saturation compensators although actuator saturation is a common nonlinear problem in practical control systems the condition under which compensators exist that globally stabilize systems subject to actuator saturation is still not well understood in this paper it is shown that actuator saturation compensators exist that globally stabilize systems containing up to one integrator for systems with two integrators it is established that the compensated system can only be lagrange stable the stability result presented in this paper can also be extended to analyse the stability of systems using existing compensation schemes thus providing a much needed justification for the use of these schemes in practice the results presented here are illustrated by examples

brief stability region for a class of open loop unstable linear systems theory and application a new method to calculate the stability region of scalar systems with one unstable pole subject to control limitations is derived and used to determine the conditions for a maximum stabilizer controller the results are illustrated by means of two numerical examples and experiments on the real compass d tokamak

on square roots of m matrices abstract the question of the existence and uniqueness of an m matrix which is a square root of an m matrix is discussed the results are then used to derive some new necessary and sufficient conditions for a real matrix with nonpositive off diagonal elements to be an m matrix

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

mixed control the discrete time case abstract a stochastic h and a mixed stochastic h 2 h control problem for discrete time systems are considered and solved conditions for existence of a solution are derived based on the solvability of an equivalent minimax problem in this framework it is possible to consider at the same time both stochastic and deterministic disturbances highlighting their mutual effects the controller can be designed by solving a system of three coupled riccati equations such equations display how the h 2 type minimization problem and the h type constraint influence each other

event triggered mean square consensus control for time varying stochastic multi agent system with sensor saturations in this technical note the consensus control problem is investigated for a class of discrete time varying stochastic multi agent system subject to sensor saturations an event based mechanism is adopted where each agent updates the control input signal only when the pre specified triggering condition is violated to reflect the time varying manner and characterize the transient consensus behavior a new index for mean square consensus is put forward to quantify the deviation level from individual agent to the average value of all agents states for a fixed network topology the aim of the proposed problem is to design time varying output feedback controllers such that at each time step the mean square consensus index of the closed loop multi agent system satisfies the pre specified upper bound constraints subject to certain triggering mechanism both the existence conditions and the explicit expression of the desired controllers are established by resorting to the solutions to a set of recursive matrix inequalities an illustrative simulation example is utilized to demonstrate the usefulness of the proposed algorithms

on pth roots of stochastic matrices in markov chain models in finance and healthcare a transition matrix over a certain time interval is needed but only a transition matrix over a longer time interval may be available the problem arises of determining a stochastic pth root of a stochastic matrix the given transition matrix by exploiting the theory of functions of matrices we develop results on the existence and characterization of matrix pth roots and in particular on the existence of stochastic pth roots of stochastic matrices our contributions include characterization of when a real matrix has a real pth root a classification of pth roots of a possibly singular matrix a sufficient condition for a pth root of a stochastic matrix to have unit row sums and the identification of two classes of stochastic matrices that have stochastic pth roots for all p we also delineate a wide variety of possible configurations as regards existence nature primary or nonprimary and number of stochastic roots and develop a necessary condition for existence of a stochastic root in terms of the spectrum of the given matrix

simultaneous quadratic stabilization for a class of non linear systems with input saturation using dynamic surface control in this paper a new method to estimate the initial condition set which guarantees the quadratic stability for a class of non linear systems via dynamic surface control dsc in the presence of input saturation has been proposed the estimated set is enlarged to allow some degree of input saturation while achieving the simultaneous quadratic stability of the system in the domain a convex optimization problem to obtain ellipsoidal initial condition sets via a linear matrix inequality lmi approach as well as an illustrative example will be presented

a note on square roots of nonnegative matrices abstract the max times algebra is the set r of nonnegative reals with operations a b max a b and a b a b we discuss the property of matrices to be squares of max times or conventional nonnegative matrices we prove that there exists a matrix having a conventional nonnegative square root but no max times square root also we present a set s of cardinality three for which there is a nonnegative matrix m with spectrum s and every such m has both conventional and max times square roots these results answer two questions from the recent paper by tam and huang

output feedback h2 h consensus control for stochastic time varying multi agent systems with x u v dependent noises abstract in this paper the output feedback h 2 h consensus control problem is investigated for discrete time varying stochastic multi agent systems with state control and disturbance dependent noises also called x u v dependent noises two new concepts for the h 2 and h consensus requirements are proposed to quantify the transient behavior of the consensus over a finite horizon for the addressed time varying multi agent systems we aim to design an output feedback consensus controller such that the closed loop multi agent systems achieve the prescribed h 2 and h consensus performances over a finite horizon by using the completing squares method and stochastic analysis techniques sufficient conditions are derived for the existence of the desired output feedback h 2 h consensus controller in terms of the solution to two coupled backward recursive riccati difference equations rdes moreover an iterative algorithm is proposed for solving the rdes by resorting to the moore penrose pseudo inverse a numerical example is utilized to illustrate the effectiveness of the proposed h 2 h consensus control strategy

factoring a band matrix over a semiring abstract matrix factorization problems over various semirings naturally arise in different contexts of modern pure and applied mathematics these problems are very hard in general and cause computational difficulties in applications we give a survey of what is known on the algorithmic complexity of boolean tropical nonnegative and positive semidefinite factorizations and we examine the behavior of the corresponding rank functions on matrices of bounded bandwidth we show that the boolean tropical and t norm versions of matrix factorization become polynomial time solvable when restricted to this class of matrices and we also show that the nonnegative rank of a tridiagonal matrix is easy to compute we recall several open problems from earlier papers on the topic and formulate a number of further questions

on matrices with cyclic structure abstract the relations between several necessary conditions for a square complex matrix a to be m cyclic are examined these conditions are known to be equivalent if a is an irreducible nonnegative matrix whose index of imprimitivity is m in particular we find that if the digraph of a contains at least one cycle with nonzero signed length then the following conditions are each equivalent to the m cyclicity of a i a is diagonally similar to e 2 i m a ii all cycles in the digraph of a have signed length an integral multiple of m in the course of our investigations we lay down the groundwork of the theory of cyclically m partite or linearly partite digraphs and characterize these digraphs in terms of the signed lengths of their cycles the characterization of diagonal similarity between matrices in terms of matrix cycle products due to saunders and schneider plays a key role in our development our investigations also lead to a new illuminating conceptual proof for the second part of the frobenius theorem on an irreducible nonnegative matrix the connection between the m cyclicity of a square complex matrix and that of its associated collection of elementary jordan blocks is studied in the second half of this paper in particular for an m cyclic collection u it is found that the problem of determining all m tuples k 1 k m of positive integers for which there exists an m cyclic matrix a in the superdiagonal k 1 k m block form such that u a u is equivalent to determine all row sum vectors of 0 1 matrices that have a prescribed column sum vector and each of whose column vectors has cyclically consecutive equal components as a by product we also obtain an equivalent condition on m given square complex matrices b 1 b m so that there exist complex rectangular matrices a 1 a m that satisfy b j a j a m a 1 a j 1 for j 1 m thus completing the work of flanders for the case m 2

h consensus control with spectrum constraints for stochastic multi agent systems subject to x u v dependent noises abstract this paper is concerned with the problem of h consensus control with spectrum constraints for continuous time multi agent systems mass with x u v dependent noises by means of the spectrum technique the definition of stability is introduced and the relationship between the convergence rate of state responses and the stability is discussed for the closed loop system the aim of the addressed problem is to design a static output feedback controller such that the closed loop system is stable and the prescribed h performance requirement is satisfied in virtue of the stochastic analysis method and kronecker product sufficient conditions are obtained for the existence of h consensus controller two examples are provided to illustrate the availability of the proposed techniques

static h2 and h output feedback of discrete time lti systems with state multiplicative noise abstract a parameter dependent approach for designing static output feedback controller for linear time invariant systems with state multiplicative noise is introduced which achieves a minimum bound on either the stochastic h 2 or the h performance levels a solution is obtained also for the case where in addition to the stochastic parameters the system matrices reside in a given polytope in this case a parameter dependent lyapunov function is described which enables the derivation of the required constant feedback gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope the stochastic parameters appear in both the dynamics and the input matrices of the state space model of the system the problems are solved using the expected value of the standard performance indices over the stochastic parameters the theory developed is demonstrated by a simple example

stabilizing randomly switched systems this article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals the switching signal is modeled as a jump stochastic not necessarily markovian process independent of the system state it selects at each instant of time the active subsystem from a family of systems sufficient conditions for stochastic stability almost sure in the mean and in probability of the switched system are established when the subsystems do not possess control inputs and not every subsystem is required to be stable these conditions are employed to design stabilizing feedback controllers when the subsystems are affine in control the analysis is carried out with the aid of multiple lyapunov like functions and the analysis results together with universal formulae for feedback stabilization of nonlinear systems constitute our primary tools for control design

nonnegative square roots of matrices abstract by the square root of a square matrix a we mean a matrix b that satisfies b 2 a in this paper we begin a study of the entrywise nonnegative square roots of nonnegative matrices adopting mainly a graph theoretic approach to start with we settle completely the question of existence and uniqueness of nonnegative square roots for 2 by 2 nonnegative matrices by the square of a digraph h denoted by h 2 we mean the digraph with the same vertex set as h such that i j is an arc if there is a vertex k such that i k and k j are both arcs in h we call a digraph h a square root of a digraph g if h 2 g it is observed that a necessary condition for a nonnegative matrix to have a nonnegative square root is that its digraph has a square root and also that a digraph g has a square root if and only if there exists a nonnegative matrix a with digraph g such that a has a nonnegative square root we consider when or whether certain kinds of digraphs including digraphs that are disjoint union of directed paths and circuits permutation digraphs or a special kind of bigraphs have square roots we also consider when certain kinds of nonnegative matrices including monomial matrices rank one matrices and nilpotent matrices with index two have nonnegative square roots a known characterization of loopless digraphs to have square roots due to f escalantge l montejano and t rojano is extended and amended to digraphs possibly with loops some natural open questions are also posed

leader follower consensus of time varying nonlinear multi agent systems a distributed consensus protocol is developed for a class of homogeneous time varying nonlinear multi agent systems in this paper the agents dynamics are supposed to be in the strict feedback form and satisfy lipschitz conditions with time varying gains it is firstly shown that the leader follower consensus problem is equivalent to a conventional stabilization control problem of augmented high dimensional multi variable systems by introducing an appropriate state transformation the stabilization control problem is then converted into a design problem of an appropriate time varying parameter which plays a key role to cope with the time varying nonlinear terms in the concerned systems it is proved that the exponential consensus of the multi agent system can be achieved with the proposed consensus protocol a simulation example is given to illustrate the effectiveness of the proposed consensus protocol

commuting matrices equilibrium points for control systems with single saturated input in this paper commutative matrices of multiple input multiple output mimo linear systems are considered the existence of the feedback matrices of a commutative state matrix set in the mimo closed loops is reduced to the existence of an invariant subspace of a matrix a the existence of feedback matrices in systems in open loop is equivalent to the existence of the solution of matrix equations denoted by kronecker products by defining new equilibrium points the relationship between equilibrium points are discussed for a linear system with a single saturated input four criteria for equilibrium points are outlined for such linear systems finally four interesting examples including their corresponding simulink plots are shown to illustrate the above results