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

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

predicting epidemic threshold of correlated networks a comparison of methods abstract being able to theoretically predict the outbreak threshold of an epidemic is essential in disease control real world correlated networks are ubiquitous and their topological structure strongly affects the prediction accuracy of present day theoretical methods quantifying their accuracy and fitness in predicting outbreak thresholds of correlated networks is thus essential we use a susceptible infected removed sir model to examine four widely used theoretical methods the heterogeneous mean field h m f quenched mean field q m f dynamical message passing d m p and connectivity matrix c m methods to predict the outbreak threshold of a correlated network the potential topological structure of correlated network impacts on prediction accuracy of these four methods we emphasize that the quantitative changes of degree correlation degree distribution exponent and network size strongly affect the outbreak of sir spreading dynamics and compare the simulation results with the theoretical ones obtained from these four methods the extensive experiments in synthetic networks show that a the increasing degree correlation coefficients reduce outbreak threshold and suppress outbreak size b the increasing degree distribution exponents raise outbreak threshold but suppress outbreak size c the increasing network sizes decrease outbreak threshold but do not affect outbreak size d as for four theoretical methods c m and d m p are more likely to precisely predict outbreak threshold because they to some extent incorporate network topology with dynamical correlations the experimental results in 50 real world networks also prove the above conclusions

extended lmi characterizations for stability and performance of linear systems over the past ten years extensive research has been devoted to extended lmi characterizations for stability and performance of linear systems these characterizations constitute a valuable tool for reducing conservatism in hard problems like multi objective control and robust stability and performance analysis the present paper proposes a general projection lemma based methodology for deriving such extended lmis and hereby provides a straightforward and unified proof for all known literature results as well as some currently missing extended lmis

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

the generalized h 2 control problem abstract in this paper we consider the problem of finding an internally stabilizing controller such that the controlled or regulated signals have a guaranteed maximum peak value in response to arbitrary but bounded energy exogenous inputs more specifically we give a complete solution to the problem of finding a stabilizing controller such that the closed loop gain from l 2 0 to l 0 is below a specified level we consider both state feedback and output feedback problems in the state feedback case it is shown that if this synthesis problem is solvable then a solution can be chosen to be a constant state feedback gain necessary and sufficient conditions for the existence of solutions as well as a formula for a state feedback gain that solves this control problem are obtained in terms of a finite dimensional convex feasibility program after showing the separation properties of this synthesis problem the output feedback case is reduced to a state feedback problem it is shown that in the output feedback case generalized h 2 controllers can be chosen to be observer based controllers the theory is demonstrated with a numerical example

improved decay estimates in time dependent stokes flow abstract this paper investigates the time dependent stokes flow of a viscous fluid in a channel with nonzero net entry flow assuming the fluid to be initially at rest with entry flow at the finite end of a semi infinite channel energy bounds for the flow are derived it is shown that the flow decays exponentially in energy norm to a transient poiseuille flow as the distance from the finite end tends to infinity the problem was previously investigated by lin saacm 2 1992 249 264 for the case in which the net entry flow was zero our methods are patterned after those of lin but a somewhat better choice of arbitrary constants yields an improved decay rate for lin s problem

the scenario approach to robust control design this paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms this includes the wide class of np hard control problems representable by means of parameter dependent linear matrix inequalities lmis it is shown in this paper that by appropriate sampling of the constraints one obtains a standard convex optimization problem the scenario problem whose solution is approximately feasible for the original usually infinite set of constraints i e the measure of the set of original constraints that are violated by the scenario solution rapidly decreases to zero as the number of samples is increased we provide an explicit and efficient bound on the number of samples required to attain a priori specified levels of probabilistic guarantee of robustness a rich family of control problems which are in general hard to solve in a deterministically robust sense is therefore amenable to polynomial time solution if robustness is intended in the proposed risk adjusted sense

probability guaranteed robust h performance analysis and state feedback design abstract this paper addresses the common engineering practice of specifying a required probability of attaining some performance level the problem setup is that of a robust h performance analysis state feedback synthesis of an affinely parameter dependent linear system except that the parameter hyper rectangle box is allowed to shrink representing a probability less than one in order to accommodate a polytopic performance goal that is better than the one attainable for the original parameter box a new version of the bounded real lemma brl which assigns a different lyapunov function to each of the vertices of the uncertainty polytope and includes a scalar free parameter seems to reduce the overdesign associated with the polytopic problem to the bare minimum the shrinking of the parameter box leads to bi linear matrix inequalities blmis since the final vertices are also unknown these blmis are solved iteratively three steps have sufficed both in the analysis and in the state feedback design examples a uniform distribution is assumed for all the system parameters following the uniformity principle the probability requirement is expressed by a set of linear matrix inequalities lmis that is derived by extending an existing second order cone method these lmis are concurrently solved with the blmis of the brl the features of the proposed method are demonstrated via two examples

parameter dependent lyapunov functions for state derivative feedback control in polytopic linear systems in some practical problems for instance the suppression of vibration in mechanical systems the state derivative signals are easier to obtain than the state signals using linear matrix inequalit

new approach to mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems this paper revisits the problem of mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems differing from previous results in the quadratic framework the filter design makes full use of the parameter dependent stability idea not only is the filter dependent of the parameters which are assumed to reside in a polytope and be measurable online but in addition the lyapunov matrices are different for the entire polytope domain as well as for different channels with respect to the mixed performances these ideas are realized by introducing additional slack variables to the well established performance conditions and by employing new bounding techniques which results in a much less conservative filter design method a numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method

stabilization of uncertain linear distributed delay systems with dissipativity constraints abstract this paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints specifically the nonlinear distributed kernel includes functions such as polynomials trigonometric and exponential functions by constructing a liapunov krasovskii functional related to the distributed kernels sufficient conditions for the existence of a state feedback controller which stabilizes the uncertain distributed delay systems with dissipativity constraints are given in terms of linear matrix inequalities lmis in contrast to existing methods the proposed scenario is less conservative or requiring less number of decision variables based on the application of a new derived integral inequality finally numerical examples are presented to demonstrate the validity and effectiveness of the proposed methodology

loose eigenstructure assignment via rank one lmi approach with application to transient response shaping in h control this article proposes a new regional eigenstructure assignment via rank one lmi approach a gain parameter condition for the regional eigenvalue eigenstructure assignment is newly derived this assignment condition is easily combined with h design by means of enhanced lmi characterisation in the present approach the desired assignment of closed loop eigenvalues i e poles are not previously fixed but constrained into individual assignment regions to bring us more design freedom than classical exact assignment the regional assignment discussed in this article never falls into an ordinary lmi root clustering because the union of assignment regions is disjoint in general each closed loop eigenvector is also constrained into individual alignment cone to show the practical use of the extra design freedom brought by regional assignment a transient response shaping in h design is also discussed a useful design algorithm based on linearisation algorithm is proposed

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

static output feedback control synthesis for linear systems with time invariant parametric uncertainties this technical note is concerned with the problem of designing robust static output feedback controllers for linear discrete and continuous time systems with time invariant polytopic uncertainties sufficient conditions for static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities furthermore the results are also extended to h2 static output feedback controller designs numerical examples are given to illustrate the effectiveness of the proposed design methods

parameterized lmis in control theory a wide variety of problems in control system theory fall within the class of parameterized linear matrix inequalities lmis that is lmis whose coefficients are functions of a parameter confined to a compact set such problems though convex involve an infinite set of lmi constraints and hence are inherently difficult to solve numerically this paper investigates relaxations of parameterized lmi problems into standard lmi problems using techniques relying on directional convexity concepts an in depth discussion of the impact of the proposed techniques in quadratic programming lyapunov based stability and performance analysis mu analysis and linear parameter varying control is provided illustrative examples are given to demonstrate the usefulness and practicality of the approach

improved synthesis conditions for mixed h2 h gain scheduling control subject to uncertain scheduling parameters abstractthe vast majority of the existing work in gain scheduling gs control literature assumes perfect knowledge of scheduling parameters generally this assumption is not realistic since for practical control applications measurement noises are unavoidable in this paper novel synthesis conditions are derived to synthesise robust gs controllers with mixed h2 h performance subject to uncertain scheduling parameters the conditions are formulated in terms of parameterised bilinear matrix inequalities pbmis that depend on varying parameters inside multi simplex domain the conditions provide practical gs controllers independent of the derivatives of scheduling parameters that is the designed controllers are feasible for implementation since bilinear matrix inequality problems are intractable an iterative pbmi algorithm is developed to solve the developed synthesis conditions by the virtue of this algorithm conservativeness reduction is achieved with few iterations examples are presented to il

alternative proofs for improved lmi representations for the analysis and the design of continuous time systems with polytopic type uncertainty a predictive approach in a previous paper jia et al 2002 several new linear matrix inequality lmi conditions have been obtained to reduce the conservativeness for the analysis and the design of continuous time systems with polytopic type uncertainty the results are quite attractive but their proofs are technical the aim of this note is to provide a different route to reach the results to this end the concepts of standard spl epsi and spl lambda blocks are introduced and the corresponding equivalent forms are also defined based on which the improved representations of given linear matrix inequalities can be predicted by replacing directly the standard blocks with their equivalent forms under two newly established exchange criteria while the correctness of the predicted results can be tested by the well known projection lemma

mixed h2 h multi channel linear parameter varying control in discrete time this paper develops a new method for the synthesis of linear parameter varying lpv controllers in discrete time lpv plants under consideration have a linear fractional transformation lft representation in contrast to earlier results which are restricted to single objective lpv problems the proposed method can handle a set of h2 h specifications that can be defined channel wise this practically attractive extension is derived by using specific transformations of both the lyapunov and scaling multiplier variables in tandem with appropriate linearizing transformations of the controller data and of the controller scheduling function it is shown that the controller gain scheduling function can be constructed as an affine matrix valued function in the polytopic coordinates of the scheduled parameter hence is easily implemented on line finally these manipulations give rise to a tractable and practical lmi formulation of the multi objective lpv control problem

robust analysis and control of parameter dependent uncertain descriptor systems in this paper we address the robust admissibility analysis and control of descriptor systems with parameter dependent possibly time varying uncertainties first we propose a new necessary and sufficient condition for the admissibility of linear time invariant lti descriptor systems this condition uses a strict linear matrix inequality lmi formulation and involves two additional matrix variables usually called slack variables then we present an extension of this condition to robust admissibility of time varying parameter dependent descriptor systems using parameter dependent lyapunov functions and employing two slack variables this extension states robust admissibility lmi conditions that are less restrictive as supported by our numerical examples than the existing ones our robust admissibility analysis result which can be directly used for state estimation cannot be so for state feedback control design this is due to the absence of duality between state estimation and state feedback control in the case of parameter dependent systems with uncertain parameters as recently reported in the literature in order to overcome this problem we also present in this paper a new robust admissibility analysis result involving only one slack variable which we apply to state feedback control design

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

h_ infty controller design using an alternative to youla parameterization all h controllers of a siso lti system are parameterized thanks to the relation between bounded real lemma and positive real lemma this new parameterization shares the same features with youla parameterization namely on the convexity of h norm constraints for the closed loop transfer functions however it can deal with low order controllers and can be extended easily for the systems with polytopic uncertainty the effectiveness of the proposed method is shown via an academic example

decay estimates for homogeneous boussinesq equations in a semi infinite pipe abstract in this paper we establish the spatial decay bounds for homogeneous boussinesq equations in a semi infinite pipe flow assuming that the entrance velocity and magnetic field data are restricted appropriately and it converges to laminar flow as the distance down the pipe tends to infinity we derive a second order differential inequality that leads to an exponential decay estimate for the energy e z t defined in 27 we also indicate how to establish the explicit bound for the total energy

generalized kalman yakubovich popov lemma for 2 d fm lss model this paper is concerned with the generalized kalman yakubovich popov kyp lemma for 2 d fornasini marchesini local state space fm lss systems by carefully analyzing the feature of the states in 2 d fm lss models a linear matrix inequality lmi characterization for a rectangular finite frequency region is constructed and then by combining this characterization with s procedure a generalized kyp lemma is proposed for 2 d fm lss models as applications of the developed kyp lemma new conditions are further derived for designing controllers guaranteeing finite frequency positive realness of the closed loop systems where both state feedback and dynamic output feedback control laws are considered finally two illustrative examples clearly show the effectiveness of the proposed results the main contribution of the paper is trifold 1 a novel characterization for a finite frequency region has been developed 2 a generalized kyp lemma has been proposed including the existing bounded realness and positive realness results as special cases and 3 systematic methods for finite frequency positive real control of 2 d systems have been presented

robust static output feedback control for linear discrete time systems with time varying uncertainties this paper is concerned with the problem of designing robust static output feedback controllers for linear discrete time systems with timevarying polytopic uncertainties sufficient conditions for robust static output feedback stabilizing controller designs are given in terms of solutions to a set of linear matrix inequalities and the results are extended to h2 and h static output feedback controller designs numerical examples are given to illustrate the effectiveness of the proposed design methods 2007 elsevier b v all rights reserved

h sub spl infin design with pole placement constraints an lmi approach this paper addresses the design of state or output feedback h sub spl infin controllers that satisfy additional constraints on the closed loop pole location sufficient conditions for feasibility are derived for a general class of convex regions of the complex plane these conditions are expressed in terms of linear matrix inequalities lmis and the authors formulation is therefore numerically tractable via lmi optimization in the state feedback case mixed h sub 2 h sub spl infin synthesis with regional pole placement is also discussed finally the validity and applicability of this approach are illustrated by a benchmark example

brief paper stability and h2 objective characterizations in control a comparative study this paper is concerned with stability and h 2 objective characterizations in control new forms of alternative lmi characterizations are presented for continuous time stability and h 2 objective a key relationship between the alternative characterizations for continuous time systems and the existing discrete time versions is illustrated the existing enhanced lmi characterization for continuous time systems called the reciprocal projection lemma is revisited and an alternative proof is provided with a new interpretation an e embedded lmi characterization is presented for a comparative study with the reciprocal projection lemma and for numerical analysis on the conservativeness of synthesis conditions through an application in control it is discussed that when applied to multi objective problems in control the alternative characterizations in this paper lead to an lmi solution with further significant conservativeness reduction compared to the reciprocal projection lemma in addition through the comparison with the existing dilated lmi condition it is shown that the dilated condition is an equivalent continuous time counterpart of the existing discrete time versions

synthesis of strictly positive real ℋ2 controllers using dilated lmis abstractthis paper considers strictly positive real spr controller design via direct minimisation of an upper bound on the closed loop h2 norm to realise a tractable design problem an observer

behavior of susceptible infected susceptible epidemics on heterogeneous networks with saturation we investigate saturation effects in susceptible infected susceptible models of the spread of epidemics in heterogeneous populations the structure of interactions in the population is represented by networks with connectivity distribution p k including scale free sf networks with power law distributions p k approximately k gamma considering cases where the transmission of infection between nodes depends on their connectivity we introduce a saturation function c k which reduces the infection transmission rate lambda across an edge going from a node with high connectivity k a mean field approximation with the neglect of degree degree correlation then leads to a finite threshold lambda c 0 for sf networks with 2 gamma 3 we also find in this approximation the fraction of infected individuals among those with degree k for lambda close to lambda c we investigate via computer simulation the contact process on a heterogeneous regular lattice and compare the results with those obtained from mean field theory with and without neglect of degree degree correlations

robust filtering for uncertain nonlinearly parameterized plants we address the robust filtering problem for a wide class of systems whose state space data assume a very general nonlinear dependence in the uncertain parameters our resolution methods rely on new linear matrix inequality characterizations of spl hscr sub 2 and spl hscr sub spl infin performances which in conjunction with suitable linearization transformations of the variables give rise to practical and computationally tractable formulations for the robust filtering problem

h state feedback controller design for continuous time t s fuzzy systems in finite frequency domain this paper is concerned with finite frequency h state feedback controller designs for continuous time takagi sugeno t s fuzzy systems a parallel distributed compensation pdc controller is designed in finite frequency domain with the aid of the generalized kalman yakubovich popov gkyp lemma the design problem is formulated as solving a set of linear matrix inequalities lmis simulation examples illustrate that the finite frequency design approach proposed in this paper receives better results than those of existing full frequency approaches

low complexity polytopic invariant sets for linear systems subject to norm bounded uncertainty we propose a novel algorithm to compute low complexity polytopic robust control invariant rci sets along with the corresponding state feedback gain for linear discrete time systems subject to norm bounded uncertainty additive disturbances and state input constraints using a slack variable approach we propose new results to transform the original nonlinear problem into a convex lmi problem whilst introducing only minor conservatism in the formulation through numerical examples we illustrate that the proposed algorithm can yield improved maximal minimal volume rci set approximations in comparison with the schemes given in the literature

technical communique robust h2 control of continuous time markov jump linear systems this paper is concerned with the problem of designing robust h 2 state feedback controllers for continuous time markov jump linear systems subject to polytopic type parameter uncertainty based on the parameter dependent lyapunov function approach a new method for designing robust h 2 controllers is presented in terms of solutions to a set of linear matrix inequalities a numerical example is given to illustrate the effectiveness of the proposed design method

spatial decay estimates in time dependent double diffusive darcy plane flow this paper considers the time dependent double diffusive convective darcy flow in a semi infinite channel an exponential decay estimate in terms of the distance from the finite end of the channel is obtained from a second order differential inequality for a weighted energy integral the paper also indicates how to bound the total weighted energy

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

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

relaxed observer based controller design method of discrete time multiplicative noised lpv systems via an extended projective lemma the aim of this paper is to discuss a relaxed observer based control problem of multiplicative noised linear parameter varying lpv systems with unmeasurable states for discussing the problem po

a new polytopic approach for the unknown input functional observer design in this paper a constructive procedure to design functional unknown input observers for nonlinear continuous time systems is proposed under the polytopic takagi sugeno framework an equivalent rep

controller design for affine fuzzy systems via characterization of dilated linear matrix inequalities we study the design of a state feedback controller for a class of nonlinear systems described by continuous time affine fuzzy models by introducing extra slack variables the lyapunov matrix and the system matrix are decoupled such that the controller parametrization is independent of the lyapunov matrix a novel quadratic stability analysis condition for affine fuzzy systems is derived in the formulation of linear matrix inequalities lmis which is equivalent to existing results using the analytical results and a diffeomorphic state transformation a stabilizing condition under which the affine fuzzy system is quadratically stabilizable is derived and can be solved by means of an lmi technique in conjunction with a search for scaling parameters in contrast to existing work the stabilizability condition we derive leads to less conservative lmi characterizations the result is also extended to h state feedback synthesis finally a numerical example illustrates the merits of the new results

robust observer design for unknown inputs takagi sugeno models this paper deals with the observer design for takagi sugeno t s fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system sufficient conditions to design an unknown input t s observer are given in linear matrix inequality lmi terms both continuous time and discrete time cases are studied relaxations are introduced by using intermediate variables extension to the case of unmeasured decision variables is also given a numerical example is given to illustrate the effectiveness of the given results

epidemic spreading in a variety of scale free networks we have shown that the epidemic spreading in scale free networks is very sensitive to the statistics of degree distribution characterized by the index gamma the effective spreading rate lambda the social strategy used by individuals to choose a partner and the policy of administrating a cure to an infected node depending on the interplay of these four factors the stationary fractions of infected population f gamma as well as the epidemic threshold properties can be essentially different we have given an example of the evolutionary scale free network which is disposed to the spreading and the persistence of infections at any spreading rate lambda 0 for any gamma probably it is impossible to obtain a simple immunization program that can be simultaneously effective for all types of scale free networks we have also studied the dynamical solutions for the evolution equation governed by the epidemic spreading in scale free networks and found that for the case of vanishingly small cure rate delta 1 the initial configuration of infected nodes would feature the solution for very long times

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

technical communique new dilated lmi characterizations for continuous time multiobjective controller synthesis this paper provides new dilated linear matrix inequality lmi characterizations for continuous time controller synthesis the dilated lmis enable us to parametrize controllers without involving the lyapunov variables in the parametrizations taking advantage of this feature we can readily design multiobjective controllers with non common lyapunov variables whereas we are forced to employ a common one in the well known lyapunov shaping paradigm in particular it is shown that the proposed dilated lmi based approach to h 2 d stability synthesis encompasses the corresponding lyapunov shaping paradigm as a special case in this sense the results of this paper can be viewed as partial counterparts of those obtained in the discrete time setting

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

robust observed state feedback design for discrete time systems rational in the uncertainties design of controllers in the form of a state feedback coupled to a state observer is studied in the context of uncertain systems the classical approach by luenberger is revisited results provide a heuristic design procedure that mimics the independent state feedback observer gains design by minimizing the coupling of observation error dynamics on the ideal state feedback dynamics the proposed design and analysis conditions apply to linear systems rationally dependent on uncertainties defined in the cross product of polytopes convex linear matrix inequality results are given thanks to the combination of a new descriptor multi affine representations of systems and the s variable approach stability and h performances are assessed by multi affine parameter dependent lyapunov matrices for both cases of constant and time varying uncertainties or combinations of the two numerical complexity issues and ways to keep it as limited as possible are discussed and illustrated on an academic example

on bounded real matrix inequality dilation we discuss a variation of dilated matrix inequalities for the conventional bounded real matrix inequality and other similarly structured inequalities here system matrices are separated from lyapunov matrix to allow the use of different lyapunov matrices in multi objective and robust problems the search involves a bounded scalar parameter that enters the problem nonlinearly and is dealt with a line search to demonstrate the benefits of the new dilated matrix inequalities over the conventional ones an example of controller synthesis with 2 gain performance measure control for a system with polytopic uncertainty robust problem has been studied it is shown that for the resulting robust problem the performance obtained via the dilated form is at least equal to that of the conventional one also the connection between the proposed dilated form and the full block s procedure is discussed

spatial decay in a double diffusive convection problem in darcy flow this paper deals with a model of time dependent double diffusive convection in darcy flow in particular it is concerned with the spatial decay of solutions when the flow is confined to a semi infinite cylinder decay bounds for an energy expression are derived

spatial decay bounds in time dependent pipe flow of an incompressible viscous fluid in this paper the authors investigate the flow of an incompressible viscous fluid in a semi infinite cylindrical pipe if the net entrance flow is nonzero then the fluid velocity will not tend to zero as the distance from the entrance end tends to infinity when the fluid adheres at the cylinder wall and the fluid is initially at rest assuming that the entrance velocity data are small enough and that the fluid flow converges to a laminar flow as the distance down the pipe tends to infinity it is shown that the convergence in energy measure is at least exponential

periodically time varying memory state feedback controller synthesis for discrete time linear systems in this paper we deal with discrete time linear periodic time invariant systems with polytopic type uncertainties and propose a new linear matrix inequality lmi based method for robust state feedback controller synthesis in stark contrast with existing approaches that are confined to memoryless static controller synthesis we explore dynamical controller synthesis and reveal a particular periodically time varying memory state feedback controller ptvmsfc structure that allows lmi based synthesis in the context of robust controller synthesis we prove rigorously that the proposed design method encompasses the well known extended lmi based static controller synthesis methods as particular cases through numerical experiments we demonstrate that the suggested design method is indeed effective in achieving less conservative results under both periodic and time invariant settings we finally derive a viable test to verify that the designed robust ptvmsfc is exact in the sense that it attains the best achievable robust performance this exactness verification test works fine in practice and we will show via a numerical example that exact robust control is indeed attained by designing ptvmsfcs even for such a problem where the standard memoryless static state feedback fails

robust and reduced order filtering new lmi based characterizations and methods this paper addresses several challenging problems of robust filtering we derive new linear matrix inequality lmi characterizations of minimum variance or h sub 2 performance and demonstrate that they allow the use of parameter dependent lyapunov functions while preserving tractability of the problem the resulting conditions are less conservative than earlier techniques which are restricted to fixed not parameter dependent lyapunov functions the remainder of the paper discusses reduced order filter problems new lmi based nonconvex optimization formulations are introduced for the existence of reduced order filters and several efficient optimization algorithms of local and global optimization are proposed nontrivial and less conservative relaxation techniques are presented as well the viability and efficiency of the proposed approaches are then illustrated through computational experiments and comparisons with existing methods