corrections to bisection algorithm for computing the frequency response gain of sampled data systems infinite dimensional congruent transformation approach this paper derives a bisection algorithm for computing the frequency response gain of sampled data systems with their intersample behavior taken into account the properties of the infinite dimensional congruent transformation i e the schur complement arguments and the sylvester law of inertia play a key role in the derivation specifically it is highlighted that counting up the numbers of the negative eigenvalues of self adjoint operators is quite important for the computation of the frequency response gain this contrasts with the well known arguments on the related issue of the sampled data h sub spl infin problem where the key role is played by the positivity of operators and the loop shifting technique the effectiveness of the derived algorithm is demonstrated through a numerical example

incompressible limit of the compressible nematic liquid crystal flow abstract this paper is concerned with the incompressible limit of the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions in r n n 2 3 the local and global existence of strong solutions for the incompressible system with small initial data is rigorously proved via the incompressible limit furthermore the convergence rates are obtained in some sense

new conic sectors for sampled data feedback systems abstract new conic sectors are presented which can be used to analyze sampled data feedback systems first a cone is constructed which contains just the sampler next by using conic sector results for interconnected systems the cone is propagated to the entire sampled data operator the new cone result is less conservative has a smaller radius and removes the restriction of an open loop stable sampled data compensator

robust h observer design of linear time delay systems with parametric uncertainty abstract this paper deals with the problem of h observer design for a class of uncertain linear systems with delayed state and parameter uncertainties this problem aims at designing the linear state observers such that for all admissible parameter uncertainties the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified h norm upper bound constraint independently of the time delay the time delay is assumed to be unknown and the parameter uncertainties are allowed to be norm bounded and appear in all the matrices of the state space model an effective matrix inequality methodology is developed to solve the proposed problem we derive the conditions for the existence of the desired robust h observers and then characterize the analytical expression of these observers in terms of some free parameters a numerical example demonstrates the validity and applicability of the present approach

weak solution to the steady compressible flow of nematic liquid crystals abstract in this study three dimensional equations for the steady compressible flow of nematic liquid crystals are considered in a bounded domain for the adiabatic exponent 1 we establish the existence of a weak solution by three level approximation and adapting the weak convergence method

loop transfer recovery for linear systems with delays in the state and the output this paper presents robustness properties of the kalman filter and the associated lqg ltr method for linear time invariant systems having delays in both the state and the output a circle condition relating to the return difference matrix associated with the kalman filter is derived using this circle condition it is shown that the kalman filter guarantees 1 2 gain margin and 60 phase margin which are the same as those for non delay systems however it is shown that even for minimum phase plants the lqg ltr method cannot recover the target loop transfer function instead an upper bound on the recovery error is obtained by using an upper bound of the solution of the kalman filter riccati equations finally some dual properties between output delayed systems and input delayed systems are exploited

a sensitivity tradeoff for plants with time delay in this paper we show that the sensitivity function of a scalar feedback system must satisfy an integral constraint when the open loop transfer function is strictly proper and contains a time delay the integral constraint is identical to the classical bode sensitivity integral which holds provided the open loop gain has greater than a one pole rolloff the design implications of the two constraints are somewhat different however and this difference is discussed the relation between open loop phase and a conflict between bandwidth and sensitivity properties is explored

on spherically symmetric solutions of the compressible isentropic navier stokes equations we prove the global existence of weak solutions to the cauchy problem for the compressible isentropic navier stokes equations in n n 2 3 when the cauchy data are spherically symmetric the proof is based on the exploitation of the one dimensional feature of symmetric solutions and use of a new multidimensional property induced by the viscous flux the present paper extends lions existence theorem 15 to the case 1 n for spherically symmetric initial data where is the specific heat ratio in the pressure n 3 2 for n 2 and n 9 5 for n 3 dedicated to professor rolf leis on the occasion of his 70th birthday

comments on robust tracking control for rigid robotic manipulators in the original paper by m zhihong and m palaniswami ibid vol 39 p 154 9 1994 a robust tracking control using a nominal feedback controller and a variable structure compensator for a rigid robotic manipulator with uncertain dynamics was presented it is assumed that the model uncertainty is bounded the author claims that this assumption is not necessarily correct and that the results obtained are therefore untenable

robust stabilization of sampled data systems to structured lti perturbations sampled data systems with stable structured lti linear time invariant perturbations in the half plane algebra applied to the continuous time plant are considered necessary and sufficient conditions are derived for robust l sub 2 stability of such systems an example is provided to illustrate the results which shows that the small gain theorem can be an extremely conservative robustness test in this sampled data context

nonparabolic dissipative systems modeling the flow of liquid crystals we study a simplified system which retains most of the interesting mathematical properties of the original ericksen leslie equations for the flow of liquid crystals this is a coupled nonparabolic dissipative dynamic system we derive several energy laws which enable us to prove the global existence of the weak solutions and the classical solutions we also discuss uniqueness and some stability properties of the system 1995 john wiley sons inc

nonlinear theory of defects in nematic liquid crystals phase transition and flow phenomena this is a summary of some recent mathematical advances in the theory of defects in nematic liquid crystals it also includes some new results concerning disclinations line defects which have not been published elsewhere

on designing observers for time delay systems with non linear disturbances in this paper the observer design problem is studied for a class of time delay non linear systems the system under consideration is subject to delayed state and non linear disturbances the time delay is allowed to be time varying and the non linearities are assumed to satisfy global lipschitz conditions the problem addressed is the design of state observers such that for the admissible time delay as well as non linear disturbances the dynamics of the observation error is globally exponentially stable an effective algebraic matrix inequality approach is developed to solve the non linear observer design problem specifically some conditions for the existence of the desired observers are derived and an explicit expression of desired observers is given in terms of some free parameters a simulation example is included to illustrate the practical applicability of the proposed theory

logarithmic integrals interpolation bounds and performance limitations in mimo feedback systems we study performance limitation issues found in linear multivariable feedback systems our main contributions include bode and poisson type integral inequalities and performance limits for the sensitivity and complementary sensitivity functions these results characterize and quantify explicitly how open loop unstable poles and nonminimum phase zeros may impose inherent limitations on feedback design and fundamental limits on the best achievable performance the role of time delay is also studied in this context most notably we show that the performance and design limitations in multivariable systems intrinsically depend on the locations as well as directions of unstable poles and nonminimum phase zeros and in particular on how pole and zero directions are aligned the latter is characterized by angles measuring the mutual orientation between zero and pole directions and it is shown to play a crucial role in multivariable system design

global classical solutions to the one dimensional free boundary problem for compressible non isothermal liquid crystal flow with large data abstract in this paper we study the free boundary problem of compressible non isothermal liquid crystal flow in dimension one for the vacuum interface condition that is the density is assumed to vanish and connect to vacuum continuously we prove global existence and uniqueness of classical solutions to the liquid crystal system with large initial data

on the gain margin improvement using dynamic compensation based on generalized sampled data hold functions this paper shows that the use of dynamic compensation based on generalized sampled data hold functions gshf can arbitrarily improve the gain margin for continuous time nonminimum phase linear systems the gshf compensator is a particular periodic digital controller the effect of sampling period on the gain margin is analyzed furthermore it is proved that under a mild condition the gain margin improvement can be achieved without forcing the sampling period small an important advantage of periodic compensation over lti compensation is found to be the capability of reducing conflict between gain margin and sensitivity

a free boundary problem for compressible hydrodynamic flow of liquid crystals in one dimension abstract in this paper we consider the free boundary problem for a simplified version of ericksen leslie equations modeling the compressible hydrodynamic flow of nematic liquid crystals in dimension one we obtain both existence and uniqueness of global classical solutions provided that the initial density is away from vacuum

robust stability and performance analysis of sampled data systems the authors consider the robust stability and performance analysis of a general linear interconnection of a continuous time plant and a discrete time controller via sample and hold devices they obtain necessary and sufficient conditions for the robust stability of the feedback system consisting of an uncertain plant represented as a known linear time invariant nominal model with time varying norm bounded uncertainty and a shift invariant discrete time controller these results show that the condition arising from the small gain theorem is necessary and sufficient when the uncertainties belong to a class of linear systems also similar results are derived for a case of structured uncertainty both l sub 2 and l sub infinity signal norms are considered robust performance analysis problem is solved by converting it to a robust stability analysis problem

performance analysis of sampled data control systems abstract this brief paper considers multivariable sampled data systems with bandlimited exogenous inputs a procedure is given for the computation of the l 2 induced input to output norm of such a system in addition sufficient conditions are given for input output stability the digital implementation of an analog controller will generally degrade the performance of the closed loop system in light of this two examples are given to illustrate how this degradation is quantified as a function of the sampling period in general this allows the determination of the minimum sampling rate required to recover the performance designed for using the original continuous time setup

robustness of zero shifting via generalized sampled data hold functions in this paper we study robustness and sensitivity properties of a sampled data feedback system with a generalized sampled data hold function gshf we argue that shifting non minimum phase zeros using gshf control can lead to difficulties unless the zero is outside the closed loop bandwidth

lqg ltr methods for linear systems with delay in state the lqg ltr linear quadratic gaussian loop transfer recovery method is discussed along with related frequency domain properties for linear systems with delay in state based on the frequency domain inequality and a robust stability condition the guaranteed stability margin of lq regulators and the guaranteed nondivergence margin of kalman filters are obtained to improve the robustness of lqg regulators the asymptotic property of the filter gain is investigated and a loop transfer recovery procedure is suggested with an illustration

robust stability of sampled data systems under possibly unstable additive multiplicative perturbations applies the fr operator technique to the robust stability problem of sampled data systems against additive multiplicative perturbations where a reasonable class of perturbations consists of unstable as well as stable ones assuming that the number of unstable modes of the plant does not change we show that a small gain condition in terms of the fr operator representation which is actually equivalent to a small gain condition in terms of the l sub 2 induced norm is still necessary and sufficient for the sampled data system to be robustly stable against h periodic perturbations in spite of their possible instability the result is derived by a nyquist type of arguments next a necessary and sufficient condition for robust stability against linear time invariant lti perturbations is also given furthermore we show that if the plant is either single input or single output the condition can be reduced to a readily testable form finally we clarify when the small gain condition becomes a particularly poor measure for robust stability

global solution to the incompressible flow of liquid crystals abstract the initial boundary value problem for the three dimensional incompressible flow of liquid crystals is considered in a bounded smooth domain the existence and uniqueness is established for both the local strong solution with large initial data and the global strong solution with small data it is also proved that when the strong solution exists a weak solution must be equal to the unique strong solution with the same data

dynamics of the ericksen leslie equations with general leslie stress ii the compressible isotropic case in this article the non isothermal compressible ericksen leslie system for nematic liquid crystals subject to general leslie stress is considered it is shown that this system is locally well posed within the l q setting and that for initial data close to equilibria points which are identical with the ones for the incompressible situation the solution exists globally moreover any global solution which does not develop singularities converges to an equilibrium in the topology of the natural state manifold note that no structural assumptions on the leslie coefficients are imposed and in particular parodi s relation is not being assumed the results can be viewed as an extension of the studies in hieber and pruss math ann 369 977 996 2017 for the incompressible case to the compressible situation

global weak solutions to the equations of compressible flow of nematic liquid crystals in two dimensions we consider weak solutions to a simplified ericksen leslie system of two dimensional compressible flow of nematic liquid crystals an initial boundary value problem is first studied in a bounded domain by developing new techniques and estimates to overcome the difficulties induced by the supercritical nonlinearity nabla mathbf d 2 mathbf d in the equations of angular momentum on the direction field and adapting the standard three level approximation scheme and the weak convergence arguments for the compressible navier stokes equations we establish the global existence of weak solutions under a restriction imposed on the initial energy including the case of small initial energy then the cauchy problem with large initial data is investigated and we prove the global existence of large weak solutions by using the domain expansion technique and the rigidity theorem provided that the second component of initial data of the direction field satisfies some geometric angle condition

stability conditions for linear retarded functional differential equations abstract the purpose of this note is to study the exponential stability for the linear retarded functional differential equation x t 1 0 d x t r where the delay function r 0 is continuous and is of bounded variation on the interval 1 0 it is shown that the spectral limit function for the equation above has a continuous dependence on the pair r the set of all functions of bounded variation for which the equation above is exponentially stable for every delay function r the so called region of stability globally in the delays is a cone therefore for a fixed r the set of all which make our equation exponentially stable that is the region of stability for the delay function r contains a cone a discussion of the characterization of these regions of stability as well as of the largest cone contained in each region of stability for a fixed delay function r is given some remarks are made with respect to a similar question for the equation x t ax t 1 0 d x t r where a is a real n by n matrix is bounded variation on 1 0 and r as before several examples illustrate the results obtained

existence conditions and properties of the frequency response operators of continuous time periodic systems the definition of the frequency response operator via the steady state analysis in finite dimensional linear continuous time periodic fdlcp systems is revisited it is shown that the frequency response operator is guaranteed to be well defined only densely on the linear space l2 which is different from the usual understanding fortunately however it turns out that this frequency response operator can have an extension onto l2 so that the equivalence between the time domain h2 norm respectively the l2 induced norm and the frequency domain h2 norm respectively the h infty norm of the frequency response operator is recovered under some stronger assumptions it is also shown that the frequency response operator can be viewed as a bounded operator from l1 to l1 which can also be established via the steady state analysis

generalization of integral constraints on sensitivity to time delay systems extends results on integral constraints to time delay systems key technical issues in this extension include properties of nonminimum phase zeros the convergence of blaschke products and the poisson integral the results have implications for scalar and multivariable control system design as well as in filtering problems

incompressible limit of the compressible nematic liquid crystal flows in a bounded domain with perfectly conducting boundary abstract in this paper we study the asymptotic behavior of the regular solution to a simplified ericksen leslie model for the compressible nematic liquid crystal flow in a bounded smooth domain in r 2 as the mach number tends to zero the evolution system consists of the compressible navier stokes equations coupled with the transported heat flow for the averaged molecular orientation we suppose that the navier stokes equations are characterized by a navier s slip boundary condition while the transported heat flow is subject to neumann boundary condition by deriving a differential inequality with certain decay property the low mach limit of the solutions is verified for all time provided that the initial data are well prepared

integral constraints on sensitivity vectors for multivariable linear systems this paper develops integral constraints on sensitivity vectors for multivariable feedback systems due to either unstable poles or non minimum phase zeros of the plant the results presented cover the continuous rational or distributed case and are based on the use of directions corresponding to zeros or poles of the plant the integral constraints are in vector form and give new insights into the inherent trade offs in sensitivity reduction for multivariable systems and the cost of decoupling

global solution to the 3d inhomogeneous nematic liquid crystal flows with variable density abstract in this paper we investigate the global existence and uniqueness of solution to the 3d inhomogeneous incompressible nematic liquid crystal flows with variable density in the framework of besov spaces it is proved that there exists a global and unique solution to the nematic liquid crystal flows if the initial data 0 1 u 0 n 0 e 3 m b p 1 3 p 1 r 3 b p 1 3 p 1 r 3 b p 1 3 p r 3 with 1 p 6 and satisfies 0 1 m b p 1 3 p 1 u 0 b p 1 3 p 1 n 0 e 3 b p 1 3 p c for some small c 0 depending only on p here m b p 1 3 p 1 r 3 is the multiplier space of besov space b p 1 3 p r 3 using the lagrangian approach in danchin and mucha 2012 2013 7 8 is the key to our results

singularity formation to the two dimensional compressible non isothermal nematic liquid crystal flows in a bounded domain abstract we study the singularity formation of strong solutions to the two dimensional 2d compressible non isothermal nematic liquid crystal flows in a bounded domain under a geometric condition of the initial orientation field we show that the strong solution exists globally if the temporal integral of the maximum norm of the divergence of the velocity is bounded our method relies on critical sobolev inequalities of logarithmic type and delicate energy estimates

on multi dimensional compressible flows of nematic liquid crystals with large initial energy in a bounded domain abstract we study the global existence of weak solutions to a multi dimensional simplified ericksen leslie system for compressible flows of nematic liquid crystals with large initial energy in a bounded domain r n where n 2 or 3 by exploiting a maximum principle nirenberg s interpolation inequality and a smallness condition imposed on the n th component of initial direction field d 0 to overcome the difficulties induced by the supercritical nonlinearity d 2 d in the equations of angular momentum and then adapting a modified three dimensional approximation scheme and the weak convergence arguments for the compressible navier stokes equations we establish the global existence of weak solutions to the initial boundary problem with large initial energy and without any smallness condition on the initial density and velocity

closed loop properties of the infinite time linear quadratic optimal regulator for systems with delays the infinite time linear quadratic optimal control problem for systems with delays is discussed from the viewpoint of closed loop properties the kalman equation and the circle condition for the optimal closed loop control law are derived and the optimal closed loop poles are characterized via the hamiltonian matrix

lqg ltr methods for linear input delayed systems this paper presents robustness properties of lq regulators for linear time invariant systems with delay in the input the kalman inequality concerning the return difference matrix is derived and the stability margins of lq regulators are investigated when the open loop systems are stable in order to obtain the stability margins of lq regulators an upper bound of the solution of lq riccati equations is derived finally the lqg ltr method for the robustness improvement of lqg regulators is obtained and illustrated with an example

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

liquid crystal flows in two dimensions this paper is concerned with a simplified hydrodynamic equation proposed by ericksen and leslie modeling the flow of nematic liquid crystals in dimension two we establish both interior and boundary regularity theorems for such a flow under smallness conditions as a consequence we establish the existence of global in time weak solutions on a bounded smooth domain in mathbb r 2 which are smooth everywhere with possible exceptions of finitely many singular times

weak strong uniqueness property for the compressible flow of liquid crystals abstract weak strong uniqueness property in the class of finite energy weak solutions is established for two different compressible liquid crystal systems by the method of relative entropy to overcome the difficulties caused by the molecular direction with inhomogeneous dirichlet boundary condition new techniques are introduced to build up the relative entropy inequalities

spectral analysis and singular value computations of the noncompact frequency response and compression operators in sampled data systems this paper is motivated by the problem of computing the frequency response gain of general sampled data systems with noncompact frequency response operators we first show that with the j unitary transformation the computation in the noncompact operator case can be reduced in principle to that in the compact operator case to which an existing efficient and reliable bisection method can be applied at the same time however we point out that there arise some critical problems in this reduction to the compact case which could be serious enough to invalidate the apparent success in the reduction through some spectral analysis of operators involving or related to the frequency response operators we eventually prove that these critical problems can be circumvented after all and we give an explicit result that shows how to compute the frequency response gain with a bisection method dealing only with finite dimensional matrices extending the arguments we also give a bisection method to compute the singular values of the frequency response operators and the associated compression operators

generalized sample hold functions frequency domain analysis of robustness sensitivity and intersample difficulties over the past 5 years there has been substantial interest in the use of generalized sample hold functions for control in this correspondence the authors use a tool which is novel in this context namely amplitude modulation theory the authors employ this tool to analyze the quantitative and qualitative features of the intersample behavior in a frequency domain setting this offers new theoretical and practical insights into the method the authors conclusion is that the perceived benefits come at substantial cost which makes its practical use questionable

absolute stability in linear delay differential systems ill posedness and robustness the author considers matrix delay differential systems which are polynomial in several delay operators using a necessary and sufficient criterion for stability independent of delay or absolute stability the author shows that system stability for all values of the delay vector lying in a sector will imply absolute stability we then show that absolute stability is ill posed with respect to arbitrarily small perturbations of the delay ratios if a certain extended delay differential system which is formed from the original is not also absolutely stable

inherent design limitations for linear sampled data feedback systems there is a well developed theory describing inherent design limitations for linear time invariant feedback systems consisting of an analogue plant and analogue controller this theory describes limitations on achievable performance present when the plant has non minimum phase zeros unstable poles and or time delays the parallel theory for linear time invariant discrete time systems is less interesting because it describes system behaviour only at sampling instants this paper develops a theory of design limitations for sampled data feedback systems wherein the response of the analogue system output is considered this is done using the fact that the steady state response of a hybrid feedback system to a sinusoidal input consists of a fundamental component at the frequency of the input together with infinitely many harmonics at frequencies spaced integer multiples of the sampling frequency away from the fundamental this fact allows fundamental sensitivity and complementary sensitivity functions that re

technical communique robust h observer design of linear state delayed systems with parametric uncertainty the discrete time case in this note we consider the problem of h observer design for a class of uncertain linear discrete time systems with delayed state and parameter uncertainties the goal of this problem is to design a linear state observer such that for the positive integer state time delay and all admissible norm bounded parameter uncertainties the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified h norm upper bound constraint the observer structure does not depend on the parameter uncertainties a simple effective algebraic methodology is developed to derive the conditions for the existence of the desired robust h observers and the analytical expression of these observers is then characterized in terms of the matrix riccati like equations inequalities we provide a numerical example to demonstrate the validity and the applicability of the proposed approach

multivariable gain phase and sensitivity integral relations and design trade offs we present several extensions of the classical bode integral relations to multivariable systems the main contributions are an extended gain phase integral formula and an extended sensitivity integral relation these results are useful for analyzing fundamental design limitations that arise in linear multivariable feedback systems in particular they provide important insights into feedback properties which are unique to multivariable systems and which cannot be inferred from the previously known integral relations applicable to single input single output systems both results show that design limitations in multivariable systems depend strongly upon certain directionality properties

ripple free deadbeat control for sampled data systems in this paper the ripple free deadbeat control problem for sampled data systems is considered this control objective is to settle the error to zero for all time after some finite settling time in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled data systems the necessary and sufficient conditions to solve this problem are derived and related to the system type and a method of constructing the ripple free deadbeat control system is presented

brief upper and lower bounds of the frequency response gain of sampled data systems this paper gives three independent methods to compute the upper and lower bounds of the norm of the frequency response operator of sampled data systems they are useful first in its own right as an approximate method and more importantly as a method to provide an effective set of the initial upper and lower bounds for the recently developed bisection algorithm it is also shown that our arguments have very close relationships to the sampled data h 2 and h problems

logarithmic integrals and system dynamics an analogue of bode s sensitivity integral for continuous time time varying systems a new time domain interpretation of bode s integral is presented this allows for a generalization to the class of time varying systems which possess an exponential dichotomy it is shown that the sensitivity function is constrained on average by the spectral values in the dichotomy spectrum of the antistable component of the open loop dynamics

global low energy weak solutions of the equations of three dimensional compressible magnetohydrodynamics we prove the global in time existence of weak solutions of the equations of compressible magnetohydrodynamics in three space dimensions with initial data small in l2 and initial density positive and essentially bounded a great deal of information concerning partial regularity is obtained velocity vorticity and magnetic field become relatively smooth in positive time h1 but not h2 and singularities in the pressure cancel those in a certain multiple of the divergence of the velocity thus giving concrete expression to conclusions obtained formally from the rankine hugoniot conditions

brief paper generalized sampled data hold functions with asymptotic zero order hold behavior and polynomic reconstruction we present a generalized sampled data hold function that combines arbitrary z domain zero placement ability with zero order hold behavior under constant input thus exhibiting minimal intersample ripple by design our hold can be regarded as a generalization of the fractional order hold with a polynomial instead of a simple linear pattern and therefore with as many tuning parameters as desired moreover the polynomial approach turns out to provide a simple mechanism of control energy minimization among other benefits all these features help to achieve qualitatively better perfect model referencing because problematic sampling z zeros or the intersample issues of the conventional generalized holds need no longer be endured

multivariable feedback sensitivity and decentralized control in this paper the problem of sensitivity reduction by feedback is studied and related to a problem of decentralized control a plant will be represented by an n times n matrix of frequency responses which may be unstable or irrational the object will be to find conditions on p s under which a diagonal feedback f s can make the sensitivity parallel i p s f s 1 parallel arbitrarily small over some specified frequency interval j omega 0 j omega 0 without violating a global sensitivity bound parallel i p s f s 1 parallel leq m m geq some const 1 for re s geq 0 it will be shown that such a diagonal feedback of the high gain type can be constructed whenever p 1 s is analytic in re s geq 0 p s satisfies an attenuation condition near s infty and p s approaches diagonal dominance at high frequencies it will also be shown that these conditions on the plant can be interpreted as conditions for the existence of a decentralized wide band control scheme

well posedness for the heat flow of harmonic maps and the liquid crystal flow with rough initial data we investigate the well posedness of 1 the heat flow of harmonic maps from mathbb r n to a compact riemannian manifold n without boundary for initial data in bmo and 2 the hydrodynamic flow u d of nematic liquid crystals on mathbb r n for initial data in bmo 1 bmo

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

l sub 2 induced norms and frequency gains of sampled data sensitivity operators this paper develops exact computable formulas for the frequency gain and l sub 2 induced norm of the sensitivity operator in a sampled data control system with sampled data we refer to a system that combines both continuous time and discrete time signals which is studied in continuous time the expressions are obtained using lifting techniques in the frequency domain and have application in performance and stability robustness analysis taking into account full intersample information

global classical solution to a one dimensional compressible non newtonian fluid with large initial data and vacuum abstract because of the stronger nonlinearity and degeneracies of the density due to the momentum equation and appearance of vacuum there are few results until now about global existence of classical solution to a compressible non newtonian fluid in this paper the global in time existence and uniqueness of classical solution to the initial boundary value problem is established for a one dimensional compressible non newtonian fluid with large initial data and vacuum our analysis is based on some delicate energy estimates together with the iterate method being used ingeniously

global low energy weak solution and large time behavior for the compressible flow of liquid crystals abstract in this paper we consider the weak solution of the simplified ericksen leslie system modeling compressible nematic liquid crystal flows in r 3 when the initial data are of small energy and initial density is positive and essentially bounded we prove the existence of a global weak solution in r 3 the large time behavior of a global weak solution is also established

long time behavior of solution for the compressible nematic liquid crystal flows in r 3 abstract in this paper we investigate the global existence and long time behavior of classical solution for the compressible nematic liquid crystal flows in three dimensional whole space first of all the global existence of classical solution is established under the condition that the initial data are close to the constant equilibrium state in h n r 3 n 3 framework then one establishes algebraic time decay for the classical solution by weighted energy method finally the algebraic decay rate of classical solution in l p r 3 norm with 2 p and optimal decay rate of their spatial derivative in l 2 r 3 norm are obtained if the initial perturbation belong to l 1 r 3 additionally

brief damping of harmonic disturbances in sampled data systems parameterization of all optimal controllers optimal damping of harmonic disturbances of known frequencies is studied for sampled data systems a sampled data output feedback controller is designed to minimize the intersample variations of the controlled variable the set of all stabilizing optimal controllers is obtained in terms of the youla parameterization and a set of interpolation conditions at the disturbance frequencies which ensure that the stationary cost is minimized

uniform well posedness and low mach number limit to the compressible nematic liquid crystal flows in a bounded domain abstract we prove global in time and uniform in of the strong solutions to the 3 d compressible nematic liquid crystal flows in a bounded domain where is the mach number consequently we obtain the strong solution of compressible nematic liquid crystal model that converges to that of incompressible nematic liquid crystal model this is the first result on the low mach number limit for compressible nematic liquid crystal flows in 3 d bounded domain our proof relies on the dedicated estimates on the solutions and the subtle use of the boundary conditions

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

frequency responses for sampled data systems their equivalence and relationships abstract there are two ways to introduce the notion of frequency response for sampled data systems one is based on the so called lifting and the other based on an interpretation of steady state response in terms of impulse modulation this paper proves the equivalence of these two notions in particular it establishes a more direct link of the second approach to the h norm and also provides the first approach with a natural interpretation of steady state response as an infinite sum of sinusoidal signals this study also leads to a comprehensive account of impulse modulation from the lifting viewpoint

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

design of ripple free multivariable robust servomechanisms the application of standard robust servomechanism theory to sampled data systems guarantees asymptotic tracking at sampling instances and between sampling instants the output will normally contain ripple in this note the robust servomechanism theory is extended to sampled data systems and a technique is proposed for ripple free tracking of sinusoids and polynomials it is shown that a continuous internal model is necessary and sufficient to provide ripple free response

periodic discrete time systems stability analysis and robust control using zero placement a simple method based on floquet theory for obtaining the characteristic equation and hence stability of periodic discrete time systems is presented using this method it is shown that 2 periodic controllers can be used to relocate the zeros of siso plants some examples are considered to illustrate the use of 2 periodic controllers for robust control of finite gain margin problems

on a key sampling formula relating the laplace and l transforms this note provides a new rigorous derivation of a key sampling formula for discretizing an analogue system the required conditions are formulated in time domain and give a clear characterization of the classes of signals and systems to which the formula applies

input output stability of sampled data systems the authors study the l sub p input output stability of a continuous time controller using the usual arrangement of periodic sampling and zero order hold it is noted that even if the hybrid system is exponentially stable this arrangement does not yield l sub p 1

strong solutions of the compressible nematic liquid crystal flow abstract we study strong solutions of the simplified ericksen leslie system modeling compressible nematic liquid crystal flows in a domain r 3 we first prove the local existence of a unique strong solution provided that the initial data 0 u 0 d 0 are sufficiently regular and satisfy a natural compatibility condition the initial density function 0 may vanish on an open subset i e an initial vacuum may exist we then prove a criterion for possible breakdown of such a local strong solution at finite time in terms of blow up of the quantities l t l x and d l t 3 l x

feedback properties of multivariable systems the role and use of the return difference matrix for linear time invariant multivariable feedback systems the feedback properties of plant disturbance attenuation sensor noise response stability margins and sensitivity to plant and sensor variation are quantitatively related to the bode magnitude versus frequency plots of the singular values of the return difference matrix i l and of the associated inverse return difference matrix i l 1 implied fundamental limits of feedback performance are quantitatively described and design tradeoffs are discussed the penalty function in the stochastic linear quadratic gaussian lqg optimal control problem is found to be a weighted sum of the singular values with the weights determined by the quadratic cost and noise intensity matrices this enables systematic tuning of lqg cost and noise matrices so that the resulting optimal return difference and inversereturn difference meet inequality constraints derived from design specifications on feedback properties the theory has been used to synthesize a multivariable automatic controller for the longitudinal dynamics of an advanced fighter aircraft