system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

the inverse spectral problem for self adjoint hankel operators in 8 5 we have considered a geometric problem in the theory of stationary gaussian processes and we have reduced this problem to the problem of the description of the bounded linear operators on hilbert space that are unitarily equivalent to moduli of hankel operators in this chapter we are going to solve the latter problem which in turn will lead to a solution of the above geometric problem in prediction theory

symmetries in special classes of passive state signal systems abstract this article is devoted to a further development of the passive linear continuous time invariant s s state signal systems theory the main focus is on the connections between certain symmetry properties such as reality and reciprocity of the external characteristics of a s s system and the respective symmetry of the evolution of the inner state of the system these connections are investigated for the following classes of passive s s systems simple conservative controllable energy preserving observable co energy preserving optimal optimal and minimal balanced out of which the last three are introduced and studied here for the first time in each of these six classes a s s system is defined by its external characteristics up to unitary similarity our results are connected with the respective results in the input state output systems theory where the external characteristics of a system are scattering impedance or transmission matrices

transfer functions of regular linear systems part ii the system operator and the lax phillips semigroup this paper is a sequel to a paper by the second author on regular linear systems 1994 referred to here as part i we introduce the system operator of a well posed linear system which for a finite dimensional system described by x ax bu y cx du would be the s dependent matrix s s a si c b d in the general case s s is an unbounded operator and we show that it can be split into four blocks as in the finite dimensional case but the splitting is not unique the upper row consists of the uniquely determined blocks a si and b as in the finite dimensional case but the lower row is more problematic for weakly regular systems which are introduced and studied here there exists a special splitting of s s where the right lower block is the feedthrough operator of the system using s 0 we give representation theorems which generalize those from part i to well posed linear systems and also to the situation when the initial time is we also introduce the lax phillips semigroup t induced by a well posed linear system which is in fact an alternative representation of a system used in scattering theory our concept of a lax phillips semigroup differs in several respects from the classical one for example by allowing an index r which determines an exponential weight in the input and output spaces this index allows us to characterize the spectrum of a and also the points where s s is not invertible in terms of the spectrum of the generator of for various values of the system is dissipative if and only if with index zero is a contraction semigroup

bilinear transformation for discrete time positive real and negative imaginary systems this paper studies the connection between discrete time and continuous time negative imaginary systems first we analyze differences between two statements that are claimed to provide equivalent conditions for systems to be discrete time positive real our conclusion is that one is equivalent to the definition of discrete time positive real transfer matrices the other is not second by means of the bilinear transformation a connection between discrete time and continuous time negative imaginary transfer matrices is established third the concept of discrete time lossless negative imaginary systems is introduced and a discrete time lossless negative imaginary lemma is developed to characterize the lossless negative imaginary properties in terms of minimal state space realization some properties of discrete time lossless negative imaginary transfer matrices are also studied several numerical examples illustrate the developed theory

dynamical system design from a control perspective finite frequency positive realness approach nonminimum phase zeros are well known to limit the best achievable control performance when the control gain is allowed to be arbitrarily high on the other hand the phase crossover appears to be a limiting factor for performance when high gain controllers are not allowed in particular the positive realness in a finite frequency range seems crucial for achieving good performance in the presence of control constraints this paper will first give multiple reasons to support this conjecture and then develop a systematic method for designing mechanical systems to achieve the finite frequency positive real ffpr property specifically we present a state space characterization of the ffpr property by generalizing the well known kalman yakubovich popov lemma to deal with a class of frequency domain inequalities that are required to hold within a finite frequency interval the result is further extended for uncertain systems to give a sufficient condition for satisfaction of a robust ffpr property the nominal ffpr result is interpreted in the time domain in terms of input output signals finally we show that certain sensor actuator placement problems to achieve the ffpr property can be reduced to finite dimensional convex problems involving linear matrix inequalities the method is applied to the shape design of a swing arm for magnetic storage devices with the objective of maximizing the control bandwidth achievable with a limited actuator power

proper efficiency and tradeoffs in multiple criteria and stochastic optimization the mathematical equivalence between linear scalarizations in multiobjective programming and expected value functions in stochastic optimization suggests to investigate and establish further conceptual analogies between these two areas in this paper we focus on the notion of proper efficiency that allows us to provide a first comprehensive analysis of solution and scenario tradeoffs in stochastic optimization in generalization of two standard characterizations of properly efficient solutions using weighted sums and augmented weighted tchebycheff norms for finitely many criteria we show that these results are generally false for infinitely many criteria in particular these observations motivate a slightly modified definition to prove that expected value optimization over continuous random variables still yields bounded tradeoffs almost everywhere in general further consequences and practical implications of these results for decision making under uncertainty and its related theory and methodology of

the role of critical exponents in blow up theorems the sequel abstract in 27 fujita showed that for positive solutions the initial value problem in r n for u t u u p with p 1 exhibited the following behavior if p p c 1 2 n then the initial value problem does not have any nontrivial non negative solution existing on r n 0 a global solution whereas if p p c there exist global small data positive solutions as well as solutions which are non global we call such a result a blow up theorem of fujita type in 50 levine discussed the various theorems of this type that had appeared in the literature prior to 1990 in this paper we revisit the literature since 1990

a lower bound for the balanced truncation error for mimo systems we show that for a class of systems which includes state space symmetric systems the balanced truncation error is bounded from below by twice the sum of the tail of the hankel singular values including multiplicities divided by the dimension of the input space

positive solutions of quasilinear parabolic systems with nonlinear boundary conditions abstract the aim of this paper is to investigate the existence uniqueness and asymptotic behavior of solutions for a coupled system of quasilinear parabolic equations under nonlinear boundary conditions including a system of quasilinear parabolic and ordinary differential equations also investigated is the existence of positive maximal and minimal solutions of the corresponding quasilinear elliptic system as well as the uniqueness of a positive steady state solution the elliptic operators in both systems are allowed to be degenerate in the sense that the density dependent diffusion coefficients d i u i may have the property d i 0 0 for some or all i our approach to the problem is by the method of upper and lower solutions and its associated monotone iterations it is shown that the time dependent solution converges to the maximal solution for one class of initial functions and it converges to the minimal solution for another class of initial functions and if the maximal and minimal solutions coincide then the steady state solution is unique and the time dependent solution converges to the unique solution applications of these results are given to three model problems including a porous medium type of problem a heat transfer problem and a two component competition model in ecology these applications illustrate some very interesting distinctive behavior of the time dependent solutions between density independent and density dependent diffusions

on decentralized integral controllability of stable negative imaginary systems and some related extensions abstract this paper exploits the decentralized integral controllability dic of stable negative imaginary ni systems with non singular dc gain matrix to develop a constant input tracking framework with failure tolerance property in the event of sensor and or actuator faults by virtue of the dic property of ni systems it is shown that a positive feedback interconnection of two ni systems of which one is a decentralized integrator system with non negative gains and the other one is a stable ni system having negative definite dc gain matrix is internally stable this is in contrast to the existing results where for internal stability at least one of the systems needs to be strictly negative imaginary sni further it is shown that in a positive feedback interconnection stable ni systems with negative definite dc gain matrix exhibit integral controllability ic property for any positive value of the integral gain k which is a distinct property of stable ni systems having negative definite dc gain matrix since the existing notion of ic for lti systems offers only a finite range of k using the dic property and the eigenvalue loci technique some new results and research directions for the ni systems have also been presented in this paper

model reduction by balanced truncation for systems with nuclear hankel operators we prove the h infinity error bounds for lyapunov balanced truncation and for optimal hankel norm approximation under the assumption that the hankel operator is nuclear this is an improvement of the result from glover curtain and partington siam j control optim 26 1998 pp 863 898 where additional assumptions were made the proof is based on convergence of the schmidt pairs of the hankel operator in a sobolev space we also give an application of this convergence theory to a numerical algorithm for model reduction by balanced truncation

stability robustness of a feedback interconnection of systems with negative imaginary frequency response a necessary and sufficient condition expressed simply as the dc loop gain i e the loop gain at zero frequency being less than unity is given in this note to guarantee the internal stability of a feedback interconnection of linear time invariant lti multiple input multiple output systems with negative imaginary frequency response systems with negative imaginary frequency response arise for example when considering transfer functions from force actuators to colocated position sensors and are commonly important in for example lightly damped structures the key result presented here has similar application to the small gain theorem which refers to the stability of feedback interconnections of contractive gain systems and the passivity theorem which refers to the stability of feedback interconnections of positive real or passive systems a complete state space characterization of systems with negative imaginary frequency response is also given in this note and also an example that demonstrates the application of the key result is provided

foundations of not necessarily rational negative imaginary systems theory relations between classes of negative imaginary and positive real systems in this technical note we lay the foundations of a not necessarily rational negative imaginary systems theory and its relations with positive real systems theory in analogy with the theory of positive real functions in our general framework negative imaginary systems are defined in terms of a domain of analyticity of the transfer function and of a sign condition that must be satisfied in such domain in this way we do not require to restrict the attention to systems with a rational transfer function in this work we also define various grades of negative imaginary systems and aim to provide a unitary view of the different notions that have appeared so far in the literature within the framework of positive real and in the more recent theory of negative imaginary systems and to show how these notions are characterized and linked to each other

existence and dynamics of quasilinear parabolic systems with time delays abstract this paper is concerned with a coupled system of quasilinear parabolic equations where the effect of time delays is taken into consideration in the reaction functions of the system the partial differential operators in the system may be degenerate and the reaction functions possess some mixed quasimonotone property including quasimonotone nondecreasing functions the aim of the paper is to show the existence and uniqueness of a global solution to the parabolic system the existence of positive quasisolutions or maximal minimal solutions of the corresponding elliptic system and the asymptotic behavior of the solution of the parabolic system in relation to the quasisolutions or maximal minimal solutions of the elliptic system applications are given to three reaction diffusion models arising from mathematical biology and ecology where the diffusion coefficients are density dependent and are degenerate this degenerate density dependent diffusion leads to some interesting distinct asymptotic behavior of the time dependent solution when compared with density independent diffusion

a step toward a unified treatment of continuous and discrete time control problems in this paper we introduce a new approach for a unified theory for continuous and discrete time optimal control problems based on the generalized cayley transformation we also relate the associated discrete and continuous generalized algebraic riccati equations we demonstrate the potential of this new approach by proving a new result for discrete algebraic riccati equations but we also discuss where this new approach as well as all other approaches still is nonsatisfactory we explain a discrepancy observed between the discrete and continuous case and show that this discrepancy is partly due to the consideration of the wrong analogues we also present an idea for an implication scheme that relates general theorems for discrete and continuous control problems

stability analysis and controller design for lur e system with hysteresis nonlinearities a negative imaginary theory based approach in this paper absolute stability condition is investigated when a hysteresis nonlinearity is connected to a linear subsystem via positive feedback in lur e system framework in particular the non

stability analysis of interconnected systems with mixed negative imaginary and small gain properties in this letter an analytical framework is proposed to examine stability of two stable linear time invariant systems interconnected in positive feedback where the systems have mixed properties of negative imaginary and small gain using the notion of dissipativity the interconnection of systems is guaranteed to be finite gain stable under the condition that the dc loop gain is contractive this work builds on griggs and exploits a new set of frequency dependent triplets that was introduced in above reference to mix two unconditional stability statements i e small gain and passivity unlike the above reference the present work explores the important question of how a conditional stability statement as needed when two negative imaginary systems are connected in a feedback loop can be mixed with an unconditional stability statement as needed when two contractive systems are connected in a feedback loop the usefulness of the proposed analytical framework is demonstrated via a numerical example

bilinear transformation of infinite dimensional state space systems and balanced realizations of nonrational transfer functions the bilinear transform maps the open right half plane to the open unit disk and is therefore a suitable tool for carrying over results for continuous time systems to discrete time systems and vice versa corresponding state space formulae are widely used and well understood for the case of finite dimensional systems in this paper infinite dimensional generalizations of these formulae are studied for a general class of infinite dimensional state space systems in particular it is shown that reachability and observability are carried over and that the reachability and observability gramians are preserved under this transformation young showed that a wide class of nonrational discrete time transfer functions admit a balanced state space representation it is shown that this result carries over to the continuous time situation via the bilinear transformation

an observer based control scheme using negative imaginary theory this paper presents a full order state observer based scheme that transforms a causal lti minimally realized system into a strongly strict negative imaginary system by defining an auxiliary output based on the observed states the auxiliary output is used for closed loop control with positive feedback invoking the internal stability condition of negative imaginary theory a set of lmi conditions is derived that determines the value of a design parameter required for the proposed scheme to transform a given system with a minimal state space realization into a strongly strict negative imaginary system the proposed scheme is applicable for both stable unstable and square non square systems in this paper the framework is further explored for robustness analysis of uncertain systems and numerical examples are given to elucidate effectiveness of the proposed results

a mixed small gain and passivity theorem in the frequency domain abstract we show that the negative feedback interconnection of two causal stable linear time invariant systems with a mixed small gain and passivity property is guaranteed to be finite gain stable this mixed small gain and passivity property refers to the characteristic that at a particular frequency systems in the feedback interconnection are either both input and output strictly passive or both have gain less than one or are both input and output strictly passive and simultaneously both have gain less than one the mixed small gain and passivity property is described mathematically using the notion of dissipativity of systems and finite gain stability of the interconnection is proven via a stability result for dissipative interconnected systems

on generalized trade off directions in nonconvex multiobjective optimization trade off information related to pareto optimal solutions is important in multiobjective optimization problems with conflicting objectives recently the concept of trade off directions has been introduced for convex problems these trade offs are characterized with the help of tangent cones generalized trade off directions for nonconvex problems can be defined by replacing convex tangent cones with nonconvex contingent cones here we study how the convex concepts and results can be generalized into a nonconvex case giving up convexity naturally means that we need local instead of global analysis

lqg balancing for continuous time infinite dimensional systems in this paper we study the existence of linear quadratic gaussian lqg balanced realizations for continuous time infinite dimensional systems lqg balanced realizations are those for which the optimal cost operator for the system and its dual system are equal and diagonal the class of systems we consider is that of distributional resolvent linear systems which includes well posed linear systems as a subclass we prove the existence of lqg balanced realizations under a finite cost condition for both the system and its dual system we also show that an lqg balanced realization of a well posed transfer function is well posed we further show that approximately controllable and observable lqg balanced realizations are unique up to a unitary state space transformation finally we show that the spectrum of the product of the optimal cost operator of a system and its dual system is independent of the particular realization our method of proof shows the connections with coprime factorizations lyapunov balanced realizations and discrete time systems the main reason for studying lqg balanced realizations is that truncated lqg balanced realizations provide a good approximation of the original system we show that under certain conditions this is also true in the infinite dimensional case by proving an error bound in the gap metric

absolute stability analysis for negative imaginary systems this paper deals with absolute stability of a lur e system with positive feedback where the linear subsystem exhibits negative imaginary frequency response and the nonlinearity connected in feedback is time invariant memoryless and slope restricted the proposed absolute stability criterion requires the linear subsystem to belong to the strongly strict negative imaginary class along with that positive definiteness of a symmetric matrix needs to be ensured where the symmetric matrix is obtained by subtracting the dc gain matrix of the linear subsystem from a strictly positive diagonal matrix with elements indicating the reciprocal of the maximum slope bounds of the nonlinearities the stability criterion is proved using a lur e postnikov type lyapunov function numerical examples are presented to demonstrate the proposed results

a generalized negative imaginary lemma and riccati based static state feedback negative imaginary synthesis abstract in this paper we present a generalized negative imaginary lemma based on a generalized negative imaginary system definition then an algebraic riccati equation method is given to determine if a system is negative imaginary also a state feedback control procedure is presented that stabilizes an uncertain system and leads to the satisfaction of the negative imaginary property the controller synthesis procedure is based on the proposed negative imaginary lemma using this procedure the closed loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty such as in the case of unmodeled spill over dynamics in a lightly damped flexible structure a numerical example is presented to illustrate the usefulness of the results

properties and stability analysis of discrete time negative imaginary systems abstract this paper is concerned with discrete time negative imaginary dt ni functions first a new definition of dt ni functions is introduced then by means of the relations between discrete time positive real and dt ni functions two different versions of dt ni lemmas are established to characterize the dt ni properties based on state space realizations also a necessary and sufficient condition is presented to guarantee the internal stability of positive feedback interconnected dt ni systems meanwhile some other properties of dt ni functions are studied several numerical examples are presented to illustrate the main results of this paper compared to the previous results our results remove the symmetric assumption in rational case

a negative imaginary lemma and the stability of interconnections of linear negative imaginary systems the note is concerned with linear negative imaginary systems first a previously established negative imaginary lemma is shown to remain true even if the system transfer function matrix has poles on the imaginary axis this result is achieved by suitably extending the definition of negative imaginary transfer function matrices secondly a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems meanwhile some properties of linear negative imaginary systems are developed finally an undamped flexible structure example is presented to illustrate the theory

strictly negative imaginary state feedback control with a prescribed degree of stability abstract this paper presents conditions for the synthesis of a strictly negative imaginary closed loop system with a prescribed degree of stability under the assumption of full state feedback a perturbation method is used to ensure the closed loop system has both the strict negative imaginary property and a prescribed degree of stability this approach involves the real schur decomposition of a matrix followed by the solution to two lyapunov equations also we present and clarify the perturbation properties of strictly negative imaginary systems

on non proper negative imaginary systems abstract this paper studies non proper negative imaginary systems first the concept of negative imaginary transfer functions that may have poles at the origin and infinity is introduced then a generalized lemma is presented to provide a sufficient condition to characterize the non proper negative imaginary properties of systems the generalized lemma is given in terms of complex variable s in the quarter domain of analyticity compared to previous results our result removes the symmetric restriction also a new relationship is established between lossless negative imaginary and lossless positive real transfer function matrices by using a minor decomposition the results in this paper give us the possibility to address non proper and non symmetric descriptor systems with negative imaginary frequency response several examples are presented to illustrate the results

admissible factorizations of hankel operators induce well posed linear systems abstract one of the basic axioms of a well posed linear system says that the hankel operator of the input output map of the system factors into the product of the input map and the output map here we prove the converse every factorization of the hankel operator of a bounded causal time invariant map from l 2 to l 2 which satisfies a certain admissibility condition induces a stable well posed linear system in particular there is a one to one correspondence between the set of all minimal stable well posed realizations of a given stable causal time invariant input output map or equivalently of a given h transfer function and all minimal stable admissible factorizations of the hankel operator of this input output map

on lti output strictly negative imaginary systems abstract this paper deals with the notion of output strictly negative imaginary systems a definition is given for the class of output strictly negative imaginary systems and a lemma is proposed to test the necessary and sufficient conditions required to satisfy output strictly negative imaginary system properties a set theoretic relationship is established between the existing class of strictly negative imaginary systems and the newly defined output strictly negative imaginary systems class a stability analysis result for interconnected systems with positive feedback is presented while one of the systems is negative imaginary and the other one is output strictly negative imaginary contrary to the existing results where at least one of the systems in the interconnection belongs to the strictly negative imaginary class several numerical examples have been studied to demonstrate the proposed results

strictly positive real transfer functions revisited the two most commonly used definitions of strictly positive real spr transfer functions are reviewed contrary to what has been suggested in the literature it is proven that the least restrictive weak definition of the two is clearly related to the yacubovich kalman lemma the relationship between time and frequency domain conditions pertaining to the weak definition of spr systems is established

on positive realness negative imaginariness and h control of state space symmetric systems this paper studies positive realness and negative imaginariness of state space symmetric systems first a necessary and sufficient condition is provided for a state space symmetric system to be respectively positive real and negative imaginary then an explicit formulation for the infimum of h norm under a mixed h and negative imaginary performance and an explicit solution for the associated optimal static output feedback control gain are developed based on symmetric negative imaginary theorem finally three examples are provided to illustrate the main results of the paper

mobius transformations of matrix polynomials we discuss mobius transformations for general matrix polynomials over arbitrary fields analyzing their influence on regularity rank determinant constructs such as compound matrices and on structural features including sparsity and symmetry results on the preservation of spectral information contained in elementary divisors partial multiplicity sequences invariant pairs and minimal indices are presented the effect on canonical forms such as smith forms and local smith forms on relationships of strict equivalence and spectral equivalence and on the property of being a linearization or quadratification are investigated we show that many important transformations are special instances of mobius transformations and analyze a mobius connection between alternating and palindromic matrix polynomials finally the use of mobius transformations in solving polynomial inverse eigenproblems is illustrated

trade off rates in the hyperplane method for multiobjective optimization problems abstract recently as a generalization of the well known scalarizing methods for characterizing pareto optimal solutions of multiobjective optimization problems a fully integrated scalarizing method called the hyperplane method has been introduced by the authors in this paper a meaningful formula which relates the trade off rates within the pareto optimal solution set to the lagrange multipliers of the hyperplane problems is derived by realizing that trade off information is significantly useful in almost all the interactive multiobjective decision making methods moreover it is shown that such a formula can be regarded as a generalized version of the trade off rate formulae for all of the well known scalarizing problems finally various aspects of the results developed in this paper are illustrated by a numerical example

balanced realization of separable denominator multidimensional systems we present a general framework for internal balancing and model order reduction for an important class separable denominator of multidimensional systems it is shown that the internally balanced realizations for denominator separable n dimensional digital systems can be obtained by solving certain coupled lyapunov equations the proposed balancing and order reduction technique is illustrated by applying it to obtain low order approximations of gaussian and laplacian gaussian infinite impulse response filters

interconnections of nonlinear systems with mixed small gain and passivity properties and associated input output stability results abstract a negative feedback interconnection consisting of two causal nonlinear systems is shown to be input output stable when a mixed small gain and passivity assumption is placed on each of the systems the mixed small gain and passivity property captures the well known notions of passivity and small gain associated with systems the property can be appropriately reduced to an input and output strictly passive system description or alternatively can be reduced to a description of a system with small gain more importantly the property captures the concept of a blending of the small gain and passivity ideas this concept of blending can be visualized for example by considering linear time invariant systems that exhibit passivity type properties at say low frequencies and lose these passivity type properties but have small gain at high frequencies

singular reaction diffusion equations of porous medium type abstract a class of reaction diffusions equations with nonlinear boundary conditions and porous medium type of diffusion is investigated by the method of upper and lower solutions the diffusion term in the equation includes the so called slow diffusion m 1 fast diffusion 0 m 1 and super diffusion m 0 and the reaction term may involve a singular function the aim of this paper is to show the existence of a global time dependent solution the existence of positive minimal and maximal steady state solutions including the uniqueness of the positive solution and the asymptotic behavior of the time dependent solution in relation to the positive steady state solutions of particular concern is the convergence of the time dependent solution to a unique positive steady state solution and the global attraction property of the reaction diffusion problem applications are given to several specific problems which are of considerable interest in the current literature

necessary and sufficient conditions on negative imaginariness for interval siso transfer functions and their interconnection this article is concerned with the study of the negative imaginariness of interval transfer functions necessary and sufficient conditions for strictly negative imaginary interval transfer functions subject to parameter uncertainty are first derived based on kharitonov s theorem then certain properties of the interconnection system with negative imaginary interval transfer functions are analyzed finally an example is provided to illustrate the main results of the article

discrete time negative imaginary systems abstract in this paper we introduce the notion of a discrete time negative imaginary system and we investigate its relations with discrete time positive real system theory in the framework presented here discrete time negative imaginary systems are defined in terms of a sign condition that must be satisfied in a domain of analyticity of the transfer function in analogy with the case of discrete time positive real functions as well as analogously to the continuous time case this means in particular that we do not need to restrict our notions and definitions to systems with rational transfer functions we also provide a discrete time counterpart of the different notions that have appeared so far in the literature within the framework of strictly positive real and in the more recent theory of strictly negative imaginary systems and to show how these notions are characterized and linked to each other stability analysis results for the feedback interconnection of discrete time negative imaginary systems are also derived

global solvability of nonlinear diffusion equations with forcing at the boundary abstract under the influence of a sufficiently weak nonlinear source term it is by now well known that a degenerate diffusion equation is globally solvable a similar result is known when the nonlinear source is present as a forcing term at the boundary such results are usually established via comparison with solutions of a related differential equation or some other form of the maximum principle however these techniques do not appear to apply in general situations when forcing occurs on only part of the boundary and convection is present in this work we obtain the global existence of solutions for such problems by deriving a differential inequality involving thelr 1norms of solutions the result is similar to that described above for equations with a nonlinear source term and furthermore establishes the global existence of small solutions even for strong forcings the technique also applies to a more general class of problems involving nonlinear reaction diffusion and convection

quasilinear parabolic and elliptic equations with nonlinear boundary conditions abstract this paper is concerned with a class of quasilinear parabolic and elliptic equations in a bounded domain with both dirichlet and nonlinear neumann boundary conditions the equation under consideration may be degenerate or singular depending on the property of the diffusion coefficient the consideration of the class of equations is motivated by some heat transfer problems where the heat capacity and thermal conductivity are both temperature dependent the aim of the paper is to show the existence and uniqueness of a global time dependent solution of the parabolic problem existence of maximal and minimal steady state solutions of the elliptic problem including conditions for the uniqueness of a solution and the asymptotic behavior of the time dependent solution in relation to the steady state solutions applications are given to some heat transfer problems and an extended logistic reaction diffusion equation

quasilinear parabolic and elliptic systems with mixed quasimonotone functions abstract this paper deals with a class of quasilinear parabolic and elliptic systems with mixed quasimonotone reaction functions the boundary condition in the system may be dirichlet nonlinear or a combination of these two types the elliptic operators in the system are allowed to be degenerate the aim is to show the existence and uniqueness of a classical solution to the parabolic system the existence of maximal and minimal solutions or quasisolutions of the elliptic system and the asymptotic behavior of the solution of the parabolic system this consideration leads to a global attractor of the parabolic system as well as an one sided stability of the maximal and minimal solutions applications of these results are given to three models arising from biology and ecology where diffusion coefficients are density dependent and are degenerate these applications exhibit quite distinct dynamical behavior of the population species between degenerate density dependent diffusion and constant diffusion

enforcing negative imaginary dynamics on mathematical system models flexible structures with collocated force actuators and position sensors lead to negative imaginary dynamics however in some cases the mathematical models obtained for these systems for example using system identification methods may not yield a negative imaginary system this paper provides two methods for enforcing negative imaginary dynamics on such mathematical models given that it is known that the underlying dynamics ought to belong to this system class the first method is based on a study of the spectral properties of hamiltonian matrices a test for checking the negativity of the imaginary part of a corresponding transfer function matrix is first developed if an associated hamiltonian matrix has pure imaginary axis eigenvalues the mathematical model loses the negative imaginary property in some frequency bands in such cases a first order perturbation method is proposed for iteratively collapsing the frequency bands whose negative imaginary property is violated and finally displacing the

global existence for nonlinear diffusion equations solutions of nonlinear possibly degenerate reaction diffusion models are known to exist for all time if the asymptotic growth of the reaction term is not greater than that of the diffusion term via concavity methods it is also known that negating such a condition results in solutions which blow up in finite time on the other hand two recent studies regarding the case of linear diffusion have reported on the ability for convective terms in a model to create global existence of solutions where no such result is true in their absence in this paper we develop a theory of global existence for a general class of reaction diffusion convection models which only requires a similar balance of diffusion and reaction our result extends previous work to models including convection but it does not reveal the exact role of convection in yielding global solutions further analysis of a slightly simplified model establishes the global existence of all solutions if the reaction term grows asymptotically at a rate less than that of either diffusion or convection

negative imaginary synthesis via dynamic output feedback and static state feedback a riccati approach abstract this paper is concerned with the study of strictly negative imaginary sni systems and the problem of synthesizing a controller rendering a linear fractional system sni first a set of necessary and sufficient conditions are developed for an sni lemma without imposing minimality assumptions the proposed lemma supports both the analysis and synthesis of sni systems then a set of sufficient conditions based on the solution of algebraic riccati equations is provided for the solution of the sni synthesis problem finally an illustrative example demonstrates the usefulness of the results given herein

robust output feedback consensus for networked negative imaginary systems a robust output feedback consensus problem for networked homogeneous negative imaginary ni systems is investigated in this technical note by virtue of ni systems theory a set of reasonable yet elegant conditions are derived for output consensus under fraktur l 2 external disturbances as well as ni model uncertainty as a byproduct this technical note also reaffirms a previous result by li et al which shows the robustness of networked systems is always worse than that of single agent systems furthermore the eventual convergence sets are also characterized for several special ni systems that are commonly studied in the literature it is shown how the results in this work embed and generalize earlier results for these classes of systems we show that the natural convergence set boils down to the centroid of the initial pattern when the initial conditions of the controllers are zero numerical examples are given to showcase the main results

nyquist plots finite gain phase margins dissipativity abstract the relation between the small gain theorem and infinite phase margin is classical in this paper we formulate a novel supply rate called the not out of phase supply rate to first prove that infinite gain margin i e non intersection of the nyquist plot of a transfer function and the negative half of the real axis is equivalent to dissipativity with respect to this supply rate capturing non intersection of half line makes the supply rate system dependent a novel feature unobserved in the supply rates considered in the literature so far we then show that the traditional finite and positive gain phase margin conditions for stability are equivalent to dissipativity with respect to a frequency weighted convex combination of the not out of phase supply rate and the small gain supply rate both frequency weightings and combining two supply rates performance indices have been investigated in the literature in different contexts but only as sufficient conditions

traveling wave profiles for nonlinear equations abstract exact traveling wave profiles are here obtained for a general reaction diffusion convection equation a two phase flow equation a generalized harry dym equation a generalized korteweg de vries kdv equation a modified mkdv equation a branching network model equation a nagumo equation and a third order equation of fluid mechanics

tradeoff directions in multiobjective optimization problems multiobjective optimization problems mop typically have conflicting objectives wherein a gain in one objective is at the expense of another tradeoff directions which measure the change in some objectives relative to changes in others provide important information as to the best direction of improvement from the current solution in this paper we present a general definition of tradeoffs as a cone of directions and provide a general method of calculating tradeoffs at every pareto optimal point of a convex mop this extends current definitions of tradeoffs which assume certain conditions on the feasible set and the objective functions two comprehensive numerical examples are provided to illustrate the tradeoff directions and the methods used to calculate them

feedback stability of negative imaginary systems this paper extends the robust feedback stability theorem of negative imaginary systems by removing restrictive assumptions on the instantaneous gains of the systems that were imposed in the earlier literature and it further generalizes this robust analysis result into the case that allows negative imaginary systems to have poles at the origin in doing so we extend the class of negative imaginary systems for which this robust stability theorem is applicable we also show that this new generalized necessary and sufficient result specializes to the earlier theorems under the same assumptions we additionally prove that the previously known dc gain condition is not only necessary and sufficient for robust feedback stability under the earlier specified instantaneous gain assumptions but is also necessary and sufficient for robust feedback stability under new different and equally simple assumptions the general robust feedback stability theorem for negative imaginary systems with free body dynamics i e poles at the origin derived in this paper also specializes to the case that is only applicable for the negative imaginary system without poles at the origin since the results for negative imaginary systems with free body dynamics developed in this paper depend on the existence of a matrix psi with certain properties we also propose a systematic construction of this matrix psi and show that construction of one such psi is sufficient for determining the feedback stability of the closed loop system finally examples are used to demonstrate the applicability of the results