robust finite time h control of singular stochastic systems via static output feedback abstract this paper addresses the problem of robust finite time stabilization of singular stochastic systems via static output feedback firstly sufficient conditions of singular stochastic finite time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time varying norm bounded disturbance then the results are extended to singular stochastic h finite time boundedness for the class of singular stochastic systems designed algorithm for static output feedback controller is provided to guarantee that the underlying closed loop singular stochastic system is singular stochastic h finite time boundedness in terms of strict linear matrix equalities with a fixed parameter finally an illustrative example is presented to show the validity of the developed methodology

energy of line graphs the energy of a graph is equal to the sum of the absolute values of its eigenvalues the energy of a matrix is equal to the sum of its singular values we establish relations between the energy of the line graph of a graph g and the energies associated with the laplacian and signless laplacian matrices of g

brief paper control for discrete singular hybrid systems the problems of stability state feedback control and static output feedback control for a class of discrete time singular hybrid systems are investigated in this paper a new sufficient and necessary condition for a class of discrete time singular hybrid systems to be regular causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict lmis respectively finally two illustrative examples are provided to demonstrate the applicability of the proposed approach

note on the energy of regular graphs abstract for a simple graph g the energy e g is defined as the sum of the absolute values of all the eigenvalues of its adjacency matrix a g let n m respectively be the number of vertices and edges of g one well known inequality is that e g 1 n 1 2 m 1 where 1 is the spectral radius if g is k regular we have e g k k n 1 n k denote e 0 k k n 1 n k balakrishnan r balakrishnan the energy of a graph linear algebra appl 387 2004 287 295 proved that for each 0 there exist infinitely many n for each of which there exists a k regular graph g of order n with k n 1 and e g e 0 and proposed an open problem that given a positive integer n 3 and 0 does there exist a k regular graph g of order n such that e g e 0 1 in this paper we show that for each 0 there exist infinitely many such n that e g e 0 1 moreover we construct another class of simpler graphs which also supports the first assertion that e g e 0

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

upper and lower bounds for the energy of bipartite graphs using lagrange s multiplier rule we find upper and lower bounds of the energy of a bipartite graph g in terms of the number of vertices edges and the spectral moment of fourth order moreover the upper bound is attained in a graph g if and only if g is the graph of a symmetric balanced incomplete block design bibd also we determine the graphs for which the lower bound is sharp

the energy of c4 free graphs of bounded degree abstract answering some questions of gutman we show that except for four specific trees every connected graph g of order n with no cycle of order 4 and with maximum degree at most 3 satisfies 1 n n where 1 n are the eigenvalues of g we give some general results and state two conjectures

fault detection filter design for markovian jump singular systems with intermittent measurements this paper addresses the problem of fault detection filter design for discrete time markovian jump singular systems with intermittent measurements the measurement transmission from the plant to the fault detection filter is assumed to be imperfect and a stochastic variable is utilized to model the phenomenon of data missing our attention is focused on the design of a fault detection filter such that the residual system is stochastically markovian jump admissible and satisfies some expected performances a new necessary and sufficient condition for a class of discrete time markovian jump singular systems to be stochastically markovian jump admissible is proposed in the form of strict linear matrix inequalities sufficient conditions are established for the existence of the fault detection filter finally a numerical example is provided to demonstrate the usefulness and applicability of the developed theoretical results

on graphs whose energy exceeds the number of vertices abstract let g be a graph on n vertices and let 1 2 n be the eigenvalues of a 0 1 adjacency matrix of g the energy of g is e i 1 n i we characterize several classes of graphs for which e n

h sub spl infin state feedback control for discrete singular systems deals with the problem of state feedback h sub spl infin control for discrete singular systems it is not assumed that the singular system under consideration is necessarily regular the problem we address is the design of a state feedback controller such that the resulting closed loop system is not only regular causal and stable but also satisfies a prescribed h sub spl infin norm bound condition in terms of certain matrix inequalities a necessary and sufficient condition for the solution to this problem is obtained and a suitable state feedback control law is also given

signless laplacians of finite graphs we survey properties of spectra of signless laplacians of graphs and discuss possibilities for developing a spectral theory of graphs based on this matrix for regular graphs the whole existing theory of spectra of the adjacency matrix and of the laplacian matrix transfers directly to the signless laplacian and so we consider arbitrary graphs with special emphasis on the non regular case the results which we survey old and new are of two types a results obtained by applying to the signless laplacian the same reasoning as for corresponding results concerning the adjacency matrix b results obtained indirectly via line graphs among other things we present eigenvalue bounds for several graph invariants an interpretation of the coefficients of the characteristic polynomial a theorem on powers of the signless laplacian and some remarks on star complements

using a mixed integer quadratic programming solver for the unconstrained quadratic 0 1 problem in this paper we consider problem p of minimizing a quadratic function q x x tqx ctx of binary variables our main idea is to use the recent mixed integer quadratic programming miqp solvers but for this we have to first convexify the objective function q x a classical trick is to raise up the diagonal entries of q by a vector u until q diag u is positive semidefinite then using the fact that xi2 xi we can obtain an equivalent convex objective function which can then be handled by an miqp solver hence computing a suitable vector u constitutes a preprocessing phase in this exact solution method we devise two different preprocessing methods the first one is straightforward and consists in computing the smallest eigenvalue of q in the second method vector u is obtained once a classical sdp relaxation of p is solved we carry out computational tests using the generator of pardalos and rodgers 1990 and we compare our two solution methods to several other exact solution methods furthermore we report computational results for the max cut problem

on the integral weighted oriented unicyclic graphs with minimum skew energy abstract let g be a weighted oriented graph which is obtained from a simple weighted undirected graph by assigning an orientation to each of its edges for a weighted oriented graph g the undirected graph obtained from g by removing the orientation and the weight of each of its arcs is called the underlying graph of g denoted by g by u n m m n we denote the set of all connected integral weighted oriented unicyclic graphs with order n in which each arc is assigned a positive integral weight and the sum of the weights of all arcs is equal to the specified integer m in this paper we investigate the minimal skew energies of integral weighted unicyclic oriented graphs showing that the underlying graph of the oriented graph with minimum skew energy among all graphs over u n m n 6 is s n 3 the graph obtained from a triangle by attaching n 3 pendent edges in exactly one of its vertices moreover we show that its weight sequence has form w 1 a a a k a 1 a 1 a 1 n 3 k w 2 w 3 in which the arc lying on the cycle c 3 and incident to no pendent arcs has weight w 1 and the two largest weights correspond the other two arcs of c 3 where positive integer numbers w 1 w 2 w 3 a and k satisfy 1 w 1 a a 1 w 2 w 3 a w 1 and m w 1 ka n k 3 a 1 w 2 w 3 in addition we determine the weight sequence above for n m 3 n 1

more on borderenergetic graphs abstract the energy e g of a graph g is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix if a graph g of order n has the same energy as the complete graph k n i e if e g 2 n 1 then g is said to be borderenergetic we obtain three asymptotically tight bounds on the edge number of borderenergetic graphs then by using disconnected regular graphs we construct connected non complete borderenergetic graphs

graphs with least eigenvalue 2 ten years on abstract the authors monograph spectral generalizations of line graphs was published in 2004 following the successful use of star complements to complete the classification of graphs with least eigenvalue 2 guided by citations of the book we survey progress in this area over the past decade some new observations are included

asymptotic energy of lattices abstract the energy of a simple graph g arising in chemical physics denoted by e g is defined as the sum of the absolute values of eigenvalues of g as the dimer problem and spanning trees problem in statistical physics in this paper we propose the energy per vertex problem for lattice systems in general for a type of lattice in statistical physics to compute the entropy constant with toroidal cylindrical mobius band klein bottle and free boundary conditions are different tasks with different hardness and may have different solutions we show that the energy per vertex of plane lattices is independent of the toroidal cylindrical mobius band klein bottle and free boundary conditions in particular the asymptotic formulae of energies of the triangular 3 3 4 2 and hexagonal lattices with toroidal cylindrical mobius band klein bottle and free boundary conditions are obtained explicitly

on the minimum energy of regular graphs abstract the energy of a graph g e g is the sum of absolute values of the eigenvalues of its adjacency matrix gutman et al proved that for every cubic graph of order n e g n here we improve this result by showing that if g is a connected subcubic graph of order n 8 then e g 1 01 n also we prove that if g is a traceable subcubic graph of order n 8 then e g 1 1 n let g be a connected cubic graph of order n 8 it is shown that e g n 2 it was proved that if g is a connected cubic graph of order n then e g 1 65 n also in this paper we would like to present the best lower bound for the energy of a connected cubic graph we introduce an infinite family of connected cubic graphs whose for each element of order n say g e g 1 24 n and conjecture that if 6 n then minimum energy occurs just for each element of this family we conjecture that there exists n such that for every connected cubic graph g of order n n e g 1 24 n

sharp bounds on the distance spectral radius and the distance energy of graphs the d eigenvalues 1 2 p of a graph g are the eigenvalues of its distance matrix d and form the d spectrum of g denoted by specd g the greatest d eigenvalue is called the d spectral radius of g denoted by 1 the d energy ed g of the graph g is the sum of the absolute values of its d eigenvalues in this paper we obtain some lower bounds for 1 and characterize those graphs for which these bounds are best possible we also obtain an upperbound for ed g and determine those maximal d energy graphs

all hypoenergetic graphs with maximum degree at most 3 abstract the energy e g of a graph g is defined as the sum of the absolute values of its eigenvalues a connected graph g of order n is said to be hypoenergetic if e g n all connected hypoenergetic graphs with maximum degree 3 have been characterized in addition to the four earlier known hypoenergetic trees we now show that complete bipartite graph k 2 3 is the only hypoenergetic cycle containing hypoenergetic graph by this the validity of a conjecture by majstorovic et al has been confirmed

technical communique new bounded real lemma for discrete time singular systems in this paper the problem of bounded real lemma for discrete time singular system with strict matrix inequalities is investigated it is proved that the bounded real lemma for discrete singular system can be described by a strict matrix inequality the results lead to more tractable and reliable computation when applying them to design control systems

some new lower bounds for energy of graphs the energy of a graph g denoted by e g is defined as the sum of the absolute values of all eigenvalues of g in this paper we present some new lower bounds for energy of non singular graphs connected non singular graphs and connected unicyclic non singular graphs in terms of number of vertices number of edges maximum degree and zagreb indices

robust sliding mode control for uncertain time delay systems an lmi approach this note is devoted to robust sliding mode control for time delay systems with mismatched parametric uncertainties a delay independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities based on which the corresponding reaching motion controller is also developed the results are illustrated by an example

on state feedback h control for discrete time singular systems this technical note deals with the state feedback h control problem for linear time invariant discrete time singular systems relied on the use of auxiliary matrices and a positive scalar a novel necessary and sufficient condition for the bounded real lemma is derived for discrete time singular systems the characterization is reduced to a strict linear matrix inequality lmi when the scalar is fixed and the resulting lmi is non conservative as long as the scalar is chosen sufficiently large moreover the result is further expanded to h controller design and a numerically efficient and reliable design procedure is given since no particular restriction is imposed on the auxiliary matrices the proposed result outperforms the existing methods in the literature numerical examples are included to illustrate the effectiveness of the present result

descriptor variable systems and optimal state regulation linear systems of the form e dot x ax bu with e singular are treated it is desired to find a control which drives the system asymptotically to the origin minimizing a quadratic cost functional no restrictions are placed on initial conditions the cost associated with the impulsive behavior of the system is examined as well as existence and uniqueness of the optimal control through a sequence of coordinate transformations it is proven that the optimal control can be found by solving a reduced order riccati equation

on the energy of 0 1 matrices the energy of a matrix is the sum of its singular values we study the energy of 0 1 matrices and present two methods for constructing balanced incomplete block designs whose incidence matrices have the maximum possible energy amongst the family of all 0 1 matrices of given order and total number of ones we also find a new upper bound for the energy of p q bipartite graphs

h filtering for descriptor systems with strict lmi conditions in this paper the problem of h filtering for descriptor systems with strict linear matrix inequalities lmis is investigated the necessary and sufficient conditions for the solvability and the expression of the solution are obtained for both continuous time and discrete time descriptor systems the proposed continuous time filters extend the results presented by xu and lam 2006 by removing semi definite conditions and introducing new formulation for the filter parameters which does not require determination of intermediate variables for discrete time descriptors differing from existing methods that provide sufficient conditions only two necessary and sufficient conditions are introduced new proposed design methods propose less conservative results comparing with existing works two numerical examples are presented to demonstrate the applicability of the proposed methods

further enhancement on robust h_ infty control design for discrete time singular systems this note deals with the robust h control design for uncertain discrete time singular systems necessary and sufficient conditions for the admissibility for these systems are formulated in strict linear matrix inequalities lmis formulation then both state feedback and static output feedback controllers are studied and robust necessary and sufficient design conditions are expressed in terms of strict bilinear matrix inequalities bmis robust h controllers are designed for uncertain singular systems including uncertainties on matrix e lmi design conditions are also proposed an illustrative example is provided to show the effectiveness of the proposed approach

the energy of unitary cayley graphs abstract a graph g of order n is called hyperenergetic if e g 2 n 2 where e g denotes the energy of g the unitary cayley graph x n has vertex set z n 0 1 2 n 1 and vertices a and b are adjacent if gcd a b n 1 these graphs have integral spectrum and play an important role in modeling quantum spin networks supporting the perfect state transfer we show that the unitary cayley graph x n is hyperenergetic if and only if n has at least two prime factors greater than 2 or at least three distinct prime factors in addition we calculate the energy of the complement of unitary cayley graph and prove that x n is hyperenergetic if and only if n has at least two distinct prime factors and n 2 p where p is a prime number by extending this approach for every fixed k n we construct families of k hyperenergetic non cospectral integral circulant n vertex graphs with equal energy

bounds of graph energy in terms of vertex cover number abstract the energy e g of a graph g is the sum of the absolute values of all eigenvalues of g in this paper we give a lower bound and an upper bound for graph energy in terms of vertex cover number for a graph g with vertex cover number it is proved that 2 2 c e g 2 where c is the number of odd cycles in g and is the maximum vertex degree of g the lower bound is attained if and only if g is the disjoint union of some complete bipartite graphs with perfect matchings and some isolated vertices the upper bound is attained if and only if g is the disjoint union of copies of k 1 together with some isolated vertices

beyond graph energy norms of graphs and matrices abstract in 1978 gutman introduced the energy of a graph as the sum of the absolute values of graph eigenvalues and ever since then graph energy has been intensively studied since graph energy is the trace norm of the adjacency matrix matrix norms provide a natural background for its study thus this paper surveys research on matrix norms that aims to expand and advance the study of graph energy the focus is exclusively on the ky fan and the schatten norms both generalizing and enriching the trace norm as it turns out the study of extremal properties of these norms leads to numerous analytic problems with deep roots in combinatorics the survey brings to the fore the exceptional role of hadamard matrices conference matrices and conference graphs in matrix norms in addition a vast new matrix class is studied a relaxation of symmetric hadamard matrices the survey presents solutions to just a fraction of a larger body of similar problems bonding analysis to combinatorics thus open problems and questions are raised to outline topics for further investigation

strongly regular graphs with maximal energy the energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix koolen and moulton have proved that the energy of a graph on n vertices is at most n 1 n 2 and that equality holds if and only if the graph is strongly regular with parameters n n n 2 n 2 n 4 n 2 n 4 such graphs are equivalent to a certain type of hadamard matrices here we survey constructions of these hadamard matrices and the related strongly regular graphs

on reachable set estimation of singular systems in this paper the problem of reachable set estimation of singular systems is investigated based on the lyapunov method a sufficient condition is established in terms of a linear matrix inequality lmi to guarantee that the reachable set of singular system is bounded by the intersection of ellipsoids then the result is extended to the problem for singular systems with time varying delay by utilizing the reciprocally convex approach the effectiveness of the obtained results in this paper is illustrated by numerical examples

on the energy of some circulant graphs we give an explicit construction of circulant graphs of very high energy this construction is based on gauss sums we also show the littlewood conjecture can be used to establish new result for a certain class of circulant graphs

brief paper a controller design based on a functional h filter for descriptor systems the time and frequency domain cases in this paper we investigate the time and frequency domain designs of a controller based on a functional filter for both continuous time and discrete time multivariable descriptor systems the order of this controller is equal to the dimension of the state to be estimated and the control gain is designed using h techniques the time procedure is based on the unbiasedness of the estimation error using a sylvester equation then a new method for avoiding the derivative of the disturbance vector in the observation error dynamics is proposed this problem is solved by means of linear matrix inequalities lmis the frequency domain procedure design is derived from time domain results where we propose some suitable matrix fraction descriptions mfds and most importantly the factorization approach permits us to give a polynomial parameterization of the functional h filter based controller

lower bounds of graph energy in terms of matching number abstract the energy e g of a graph g is the sum of the absolute values of all eigenvalues of g we are interested in the relation between the energy of a graph g and the matching number g of g it is proved that e g 2 g for every graph g and e g 2 g 5 5 c 1 g if the cycles of g if any are pairwise vertex disjoint where c 1 g denotes the number of odd cycles in g besides we prove that e g r g 1 2 if g has at least one odd cycle and it is not of full rank where r g is the rank of g

on stabilization methods of descriptor systems abstract numerically reliable computational methods are proposed for the stabilization of a linear descriptor system with or without simultaneous elimination of its impulsive behavior two basic stabilization approaches are discussed the first approach relies on methods which represent generalizations of direct stabilization techniques for standard state space systems the second approach is based on a recursive generalized schur algorithm for pole assignment both approaches are based exclusively on numerically reliable procedures and can serve for robust software implementations

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

dilated lmi characterisations for linear time invariant singular systems this article explores based on projection lemma dilated linear matrix inequality lmi characterisations for linear time invariant singular systems the deduced formulations cover not only the existing results reported in the literature but also complete some missing lmi conditions this article also lightens the mutual relations of these characterisations and clarifies the relation between the dilated lmis for the conventional state space systems and those for singular systems the well known results for the state space setting reported in the literature can be reviewed as special cases

brief paper convex relaxations for mixed integer predictive control the main objective in this work is to compare different convex relaxations for model predictive control mpc problems with mixed real valued and binary valued control signals in the problem description considered the objective function is quadratic the dynamics are linear and the inequality constraints on states and control signals are all linear the relaxations are related theoretically and the quality of the bounds and the computational complexities are compared in numerical experiments the investigated relaxations include the quadratic programming qp relaxation the standard semidefinite programming sdp relaxation and an equality constrained sdp relaxation the equality constrained sdp relaxation appears to be new in the context of hybrid mpc and the result presented in this work indicates that it can be useful as an alternative relaxation which is less computationally demanding than the ordinary sdp relaxation and which often gives a better bound than the bound from the qp relaxation furthermore it is discussed how the result from the sdp relaxations can be used to generate suboptimal solutions to the control problem moreover it is also shown that the equality constrained sdp relaxation is equivalent to a qp in an important special case

a lower bound for the energy of symmetric matrices and graphs the energy of a symmetric matrix is the sum of the absolute values of its eigenvalues we introduce a lower bound for the energy of a symmetric matrix partitioned into blocks this bound is related to the spectrum of its quotient matrix furthermore we study necessary conditions for the equality applications to the energy of the generalized composition of a family of arbitrary graphs are obtained a lower bound for the energy of a graph with a bridge is given some computational experiments are presented in order to show that in some cases the obtained lower bound is incomparable with the well known lower bound 2m where m is the number of edges of the graph

a note on sum of powers of the laplacian eigenvalues of bipartite graphs abstract for a graph g and a real number 0 the graph invariant s g is the sum of the th power of the non zero laplacian eigenvalues of g in this note we obtain some bounds of s g for a connected bipartite graph g which improve some known results of zhou b zhou on sum of powers of the laplacian eigenvalues of graphs linear algebra appl 429 2008 2239 2246

approximating quadratic programming with bound and quadratic constraints we consider the problem of approximating the global maximum of a quadratic program qp subject to bound and simple quadratic constraints based on several early results we show that a 4 7 approximate solution can be obtained in polynomial time

stabilization of singular markovian jump systems with generally uncertain transition rates this note is devoted to investigating the stability and stabilization problems for continuous time singular markovian jump systems smjss with generally uncertain transition rates gutrs in this gutr singular model each transition rate can be completely unknown or only its estimate value is known in terms of a set of coupled linear matrix inequalities lmis a sufficient condition is established to ensure the systems to be regular impulse free and stochastically stable moreover the corresponding sufficient condition on the existence of a mode dependent state feedback controller is derived to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method

the linear quadratic optimal regulator for descriptor systems in this paper we investigate the linear quadratic optimal regulator problem for the continuous time descriptor system e dot x ax bu where e is in general a singular matrix we solve first a general finite horizon problem by applying the calculus of variations to derive the optimal trajectory of the vector consisting of the concatenated descriptor codescriptor and control vectors from this trajectory the optimal feedback gain relating the control and descriptor variable can be computed by transforming to a coordinate system which can be computed by performing a singular value decomposition of e we derive several riccati differential equations all of which have the same solution this solution gives the optimal cost the steady state optimal feedback gain can be computed by solving an eigenvalue eigenvector problem formulated from the untransformed system parameters in general there does not exist a unique optimal feedback gain but rather the gain is constrained to lie in a linear variety whose dimension is equal to the number of inputs times the rank deficiency of e

3 regular digraphs with optimum skew energy abstract the skew energy of a digraph d is defined as the sum of the singular values of its skew adjacency matrix s d in this paper we first interpret the entries of the power of the skew adjacency matrix of a digraph in terms of the number of its walks and then focus on the question posed by adiga et al c adiga r balakrishnan wasin so the skew energy of a graph linear algebra appl 432 2010 1825 1835 of determining all 3 regular connected digraphs with optimum skew energy

controller design for discrete time descriptor models a systematic lmi approach this paper provides a systematic way to generalize the controller design for discrete time nonlinear descriptor models the controller synthesis is done using a takagi sugeno representation of the descriptor models and linear matrix inequalities we propose approaches to exploit the discrete time nature of the problem by using delayed lyapunov functions which allow delayed controller gains in addition the well known finsler s lemma is used to avoid the explicit substitution of the closed loop dynamics examples are provided to show the effectiveness of the proposed results

new results on output feedback h_ infty control for linear discrete time systems this note investigates the problem of output feedback h control for linear discrete time systems three types of h controllers are considered namely static output feedback controllers dynamic output feedback controllers and observer based output feedback controllers new design conditions for the three type of output feedback controllers are introduced in terms of unified linear matrix inequality lmi representations which guarantee the prescribed h performances of the closed loop systems in contrast to the existing lmi conditions for designing the output feedback h controllers the improvement of the proposed results over the existing ones is shown by theoretical proof and numerical example

a sharp lower bound for the least eigenvalue of the signless laplacian of a non bipartite graph we prove that the minimum value of the least eigenvalue of the signless laplacian of a connected non bipartite graph with a prescribed number of vertices is attained solely in the unicyclic graph obtained from a triangle by attaching a path at one of its endvertices

quadratic unitary cayley graphs of finite commutative rings abstract the purpose of this paper is to study spectral properties of a family of cayley graphs on finite commutative rings let r be such a ring and r be its set of units let q r u 2 u r and t r q r q r we define the quadratic unitary cayley graph of r denoted by g r to be the cayley graph on the additive group of r with respect to t r that is g r has vertex set r such that x y r are adjacent if and only if x y t r it is well known that any finite commutative ring r can be decomposed as r r 1 r 2 r s where each r i is a local ring with maximal ideal m i let r 0 be a local ring with maximal ideal m 0 such that r 0 m 0 3 mod 4 we determine the spectra of g r and g r 0 r under the condition that r i m i 1 mod 4 for 1 i s we compute the energies and spectral moments of such quadratic unitary cayley graphs and determine when such a graph is hyperenergetic or ramanujan

the energy of a graph abstract the energy e g of a simple graph g is defined to be the sum of the absolute values of the eigen values of g if g is a k regular graph on n vertices then e g k k n 1 n k b 2 and this bound is sharp it is shown that for each 0 there exist infinitely many n for each of which there exists a k regular graph g of order n with k e g b 2 two graphs with the same number of vertices are equienergetic if they have the same energy we show that for any positive integer n 3 there exist two equienergetic graphs of order 4n that are not cospectral

on the minimal energy of graphs abstract the energy of a graph is the sum of the absolute values of the eigenvalues of the graph which is used to approximate the total electron energy of the molecule in this paper we determine the n e graphs with minimal energy for e n 1 and n 2 which is giving a complete solution to the conjecture for e n 1 and e n 2 proposed by caporossi et al in 4 moreover we determine the graphs with the minimal and second minimal energies for n 1 e 3 n 2 3 and the unique graph with minimal energy for 3 n 5 2 e 2 n 4 among all quasi trees with n vertices and e edges respectively

robust admissibility of uncertain switched singular systems this article investigates the robust admissibility of uncertain discrete time switched singular systems first the admissibility is introduced by using the switched lyapunov function for singular systems sufficient conditions for robust admissibility of uncertain switched singular systems are presented in strict linear matrix inequalities formulation robust admissibility condition designs for both state feedback and static output control feedback are then derived numerical examples are provided to illustrate our approach

lmi based robust mixed integer model predictive control for hybrid systems this paper proposes a linear matrix inequality lmi approach to mixed integer model predictive control mpc of uncertain hybrid systems with binary and real valued control inputs the stability c

optimal unbiased reduced order filtering for discrete time descriptor systems via lmi abstract in this paper the reduced order unbiased optimal h filtering problem for discrete time descriptor linear systems is considered necessary and sufficient conditions for the existence of unbiased causal time invariant filters are obtained solutions of the filtering problems are given in terms of linear matrix inequalities lmis parametrization of all optimal causal unbiased filters is provided the proposed method generalizes the existing results in the standard case

robust finite time h control for discrete time singular markovian jump systems with time varying delay and actuator saturation in this paper the problem of robust finite time h control for discrete time singular markovian jump systems with time varying delay and actuator saturation is studied first sufficient conditions that guarantee the systems singular stochastic finite time boundedness are derived via constructing a delay dependent lyapunov krasonskii functional and linear matrix inequalities lmi approaches then the results are extended to singular stochastic finite time h boundedness furthermore with these conditions and convex optimization arithmetic the design method of h controller and conditions that ensure the h disturbance attenuation level are obtained finally some numerical examples are presented to illustrate the validity and efficiency of the proposed methods

graph energy change due to edge deletion the energy of a graph is the sum of the singular values of its adjacency matrix we are interested in how the energy of a graph changes when edges are deleted examples show that all cases are possible increased decreased unchanged our goal is to find possible graph theoretical descriptions and to provide an infinite family of graphs for each case the main tool is a singular value inequality for complementary submatrices and its equality case

technical communique stabilization of discrete time singular systems a matrix inequalities approach this paper is concerned with the state feedback stabilization problem of discrete time singular systems the singular system under consideration is not assumed to be regular the problem we address is to design state feedback controllers such that the resulting closed loop system is regular causal and stable conditions for the existence of solutions to this problem are obtained expressed in terms of certain matrix inequalities when these conditions are satisfied the explicit formula of desired state feedback controllers is also given without resorting to decomposing the system matrices

edge addition singular values and energy of graphs and matrices the energy of a graph matrix is the sum of the absolute values of its eigenvalues we investigate the result of duplicating removing an edge to the energy of a graph we also deal with the problem that which graphs g have the property that if the edges of g are covered by some subgraphs then the energy of g does not exceed the sum of the subgraphs energies the problems are addressed in the general setting of energy of matrices which leads us to consider the singular values too among the other results it is shown that the energy of a complete multipartite graph increases if a new edge added or an old edge is deleted

on the discrete time bounded real lemma with application in the characterization of static state feedback h controllers abstract this paper deals with the discrete time bounded real lemma and its application in the characterization of all static state feedback h controllers for discrete time systems we first present two versions of the discrete time bounded real lemma the results apply to non minimal stable state space realizations and are given in terms of either the positive semi definite strong solution or the positive semi definite stabilizing solution of a discrete algebraic riccati equation based on the discrete time bounded real lemma we obtain a characterization of all static state feedback h controllers for discrete time systems as an application of the parameterization of all static state feedback h controllers we develop a solution to the discrete time h control problem via static output feedback also a numerical procedure is proposed to determine an output feedback gain

the energy of graphs and matrices abstract given a complex m n matrix a we index its singular values as 1 a 2 a and call the value e a 1 a 2 a the energy of a thereby extending the concept of graph energy introduced by gutman let 2 m n a be an m n nonnegative matrix with maximum entry and a 1 n extending previous results of koolen and moulton for graphs we prove that e a a 1 m n m 1 a 2 2 a 1 2 m n n m m 2 furthermore if a is any nonconstant matrix then e a 1 a a 2 2 1 2 a 2 a finally we note that wigner s semicircle law implies that e g 4 3 o 1 n 3 2 for almost all graphs g

an argument principle based framework for structural and spectral characteristics in linear dynamical systems abstractby means of the argument principle in complex analysis the paper proposes a novel complex geometric framework about structural features in terms of controllability observability and stability stabilisability and spectral ones in terms of bounded positive realness for transfer functions in linear dynamical systems the proposed criteria render alternative complex frequency domain interpretations about the structural and spectral essentials moreover the criteria are implementable graphically with locus plotting independent of singularities distribution locus orientation specification singularity related locus encirclement counting and prior frequency sweeping the criteria are also utilisable numerically via complex argument increment integration without locus plotting independent of iterative algorithms in either ways the criteria are numerically tractable and opt for robustness analysis and synthesis numerical examples are included to illustrate the main results

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

energy of a vertex abstract in this paper we develop the concept of energy of a vertex introduced in arizmendi and juarez romero 2018 we derive basic inequalities continuity properties give examples and extend the definition to locally finite graphs

large scale binary quadratic optimization using semidefinite relaxation and applications in computer vision many problems can be formulated as binary quadratic programs bqps which are in general np hard finding a solution when the problem is of large size to be of practical interest typically requires relaxation semidefinite relaxation usually yields tight bounds but its computational complexity is high in this work we present a semidefinite programming sdp formulation for bqps with two desirable properties first it produces similar bounds to the standard sdp formulation second compared with the conventional sdp formulation the proposed sdp formulation leads to a considerably more efficient and scalable dual optimization approach we then propose two solvers namely quasi newton and smoothing newton methods for the simplified dual problem both of them are significantly more efficient than standard interior point methods empirically the smoothing newton solver is faster than the quasi newton solver for dense or medium sized problems while the quasi newton solver is preferable for large sparse structured problems

applications of a theorem by ky fan in the theory of graph energy abstract the energy of a graph g is equal to the sum of the absolute values of the eigenvalues of g which in turn is equal to the sum of the singular values of the adjacency matrix of g let x y and z be matrices such that x y z the ky fan theorem establishes an inequality between the sum of the singular values of z and the sum of the sum of the singular values of x and y this theorem is applied in the theory of graph energy resulting in several new inequalities as well as new proofs of some earlier known inequalities

on the average energy of circulant graphs we obtain upper and lower bounds on the average energy of circulant graphs with n vertices and regularity d the average is taken over all representations of such graphs by circulant adjacency matrices

technical communique novel bounded real lemma for discrete time descriptor systems application to h control design this paper concerns the bounded real lemma for discrete time descriptor systems a new formulation of the bounded real lemma for these systems is given it extends the recent results presented in zhang xia and shi 2008 and gives necessary and sufficient conditions in strict lmi linear matrix inequality which is more suitable for the control design than those presented in zhang xia and shi 2008 an application to the h control design is given a numerical example is presented to show the applicability of our approach

exponential stability of descriptor systems with large delay period based on a switching method this paper addresses the problem of exponential stability for a class of descriptor systems with interval time varying delays the time varying delays contain a large delay period ldp which is often present in practical control systems such descriptor system with ldp has been modeled as a switched descriptor system with delay which may include an unstable subsystem caused by large delay bound by adopting the switching technique and constructing a novel lyapunov krasovskii functional stability criteria are proposed under the restriction frequency and the rate of ldp to ensure that the descriptor system is regular impulse free and exponentially stable finally an integrated circuit example and a numerical simulation are given to illustrate the effectiveness and applicability of the proposed method