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

lmi based designs for robust state and output derivative feedback guaranteed cost controllers in reciprocal state space form in some practical problems state derivative variables are more easily obtained than state variables solution of guaranteed cost control problem using derivative feedback for continuous linear ti

gain scheduled output feedback controllers using inexact scheduling parameters for continuous time lpv systems this paper addresses the design problem of gain scheduled output feedback gsof controllers for continuous time linear parameter varying lpv systems in contrast to the conventional problem setting scheduling parameters are supposed to be provided with bounded absolute proportional uncertainties h type problem is tackled and a sufficient condition for our problem is given in terms of parameter dependent linear matrix inequalities pdlmis with a single line search parameter it is also proved that our method is no more conservative than an existing method in proportional uncertainty case

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

improved stability analysis and gain scheduled controller synthesis for parameter dependent systems we present new algorithms for robust stability analysis and gain scheduled controller synthesis for linear systems affected by time varying parametric uncertainties these new techniques can also be applied to parameter dependent nonlinear systems with real rational nonlinearities sufficient conditions for robust stability as well as conditions for the existence of a robustly stabilizing gain scheduled controller are given in terms of a finite number of linear matrix inequalities lmis explicit formulas for constructing robustly stabilizing gain scheduled controllers are given in terms of the feasible set of these lmis the improvement offered by our approach over existing methods for stability analysis and gain scheduled controller synthesis for parameter dependent linear systems are analyzed in theory numerical examples demonstrate that our approach can offer significant improvement in practice

stability analysis with dissipation inequalities and integral quadratic constraints this technical note considers the stability of a feedback connection of a known linear time invariant system and a perturbation the input output behavior of the perturbation is described by an integral quadratic constraint iqc iqc stability theorems can be formulated in the frequency domain or with a time domain dissipation inequality the two approaches are connected by a non unique factorization of the frequency domain iqc multiplier the factorization must satisfy two properties for the dissipation inequality to be valid first the factorization must ensure the time domain iqc holds for all finite times second the factorization must ensure that a related matrix inequality when feasible has a positive semidefinite solution this technical note shows that a class of frequency domain iqc multipliers has a factorization satisfying these two properties thus the dissipation inequality test with an appropriate factorization can be used with no additional conservatism

robust performance of linear parametrically varying systems using parametrically dependent linear feedback abstract in this paper a parameter dependent control problem for linear parametrically varying lpv systems is presented sufficient conditions are given that guarantee an lpv system is exponentially stable and achieves an induced l 2 norm performance objective from the disturbance to error signals the usefulness of parameter dependent controllers is motivated from a gain scheduling viewpoint the resulting synthesis problem is reformulated into a convex optimization problem which can be solved using efficient new algorithms

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

a hybridized iterative algorithm of the bicorstab and gpbicor methods for solving non hermitian linear systems in this study we derive a new iterative algorithm including its preconditioned version which is a hybridized variant of the biconjugate a orthogonal residual stabilized bicorstab method and the generalized product type solvers based on bicor gpbicor method the proposed method which is named gpbicor m similarly to the gpbicg m method proposed by fujino 2002 can be regarded as an extension of the bicorstab2 method introduced by zhao and huang 2013 inspired by fujino s idea for improving the bicgstab2 method in the established gpbicor m method the parameters computed by the bicorstab method are chosen at successive m iteration steps and afterwards the parameters of the gpbicor method are utilized in the subsequent iteration steps therefore the proposed method can inherit the low computational cost of bicorstab and the attractive convergence of gpbicor extensive numerical convergence results on selected real and complex matrices are shown to assess the performances of the proposed gpbicor m method also against other popular non hermitian krylov subspace 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

fixed structure lpv discrete time controller design with induced l2 norm and h2 performance abstracta new method for the design of fixed structure dynamic output feedback linear parameter varying lpv controllers for discrete time lpv systems with bounded scheduling parameter variations is presented sufficient conditions for the stability h2 and induced l2 norm performance of a given lpv system are represented through a set of linear matrix inequalities lmis these lmis are used in an iterative algorithm with monotonic convergence for lpv controller design extension to the case of uncertain scheduling parameter value is considered as well controller parameters appear directly as decision variables in the optimisation program which enables preserving a desired controller structure in addition to the low order efficiency of the proposed method is illustrated on a simulation example with an iterative convex optimisation scheme used for the improvement of the control system performance

filter design for lpv systems using quadratically parameter dependent lyapunov functions this paper considers design problems of robust gain scheduled h and h 2 filters for linear parameter varying lpv systems whose state space matrices are represented as parametrically affine matrices using quadratically parameter dependent lyapunov functions and proposes methods of filter design via parametrically affine linear matrix inequalities lmis for robust filters our design methods theoretically encompass those that use constant lyapunov functions several numerical examples are included that demonstrate the effectiveness of gain scheduled and robust filters using our proposed methods compared with robust filters using existing methods

a new robust d stability condition for real convex polytopic uncertainty abstract the problem of robust d stability analysis with respect to real convex polytopic uncertainties is tackled a new lmi based sufficient condition for the existence of parameter dependent lyapunov functions is proposed this condition generalises previously published conditions numerical comparisons with quadratic stability results as well as previous results based on parameter dependent lyapunov functions illustrate the relevance of this new condition finally this result appears to be promising for robust multi objective performance analysis and control synthesis purposes

parameter dependent state observer design for affine lpv systems in this paper the design of a parameter dependent state observer that allows to estimate the state of an affine linear parameter varying lpv system is investigated the observer has the property of being parameter dependent since the corresponding state space matrices are scheduled using an interpolation method moreover the stability of the estimation error is based on the existence of an affine parameter dependent lyapunov function the main contribution of this paper is that the problem of the observer design and the existence of such a lyapunov function is interpreted as a flexible lmi feasibility condition some illustrative examples are presented at the end of this paper

robust synthesis for linear parameter varying systems using integral quadratic constraints a robust synthesis algorithm is developed for a class of uncertain linear parameter varying lpv systems the uncertain system is described as an interconnection of a nominal lpv system and a block structured uncertainty the nominal part is a gridded lpv system with state matrices that are arbitrary functions of the parameter the input output behavior of the uncertainty is described by integral quadratic constraints iqcs the robust synthesis problem leads to a non convex optimization the proposed algorithm is a coordinate wise descent similar to the well known dk iteration for synthesis it alternates between an lpv synthesis step and an iqc analysis step both steps can be efficiently solved as semidefinite programs the derivation of the synthesis algorithm is less obvious for lpv systems as compared to its lti counterpart due to the lack of a valid frequency response interpretation the main contribution is the construction of the iterative synthesis algorithm using time domain dissipation inequalities and a scaled system analogous to that appearing in synthesis it is shown that the proposed algorithm ensures that the robust performance is non increasing at each iteration step the effectiveness of the proposed method is demonstrated on a simple numerical example

distributed lpv state feedback control under control input saturation developed in this note is a scheduled state feedback controller synthesis method for discrete time linear parameter varying lpv systems subjected to control input saturation constraints the static state feedback gain is scheduled with an exact replica of the parameter matrix the saturation effect is modeled by introducing time varying parameters as functions of the control inputs which are also used to schedule the controller the synthesis method is then specialized to distributed state feedback by imposing a particular structure on the feedback gain matrix an explicit formula is also derived for the computation of the distributed control input from a nonlinear equation the viability of the proposed method is tested in a simulation environment for a ramp meter traffic flow control problem

generalized robust gain scheduled pid controller design for affine lpv systems with polytopic uncertainty in the paper a generalized guaranteed cost output feedback robust gain scheduled pid controller synthesis is presented for affine linear parameter varying systems under polytopic model uncertainty the controller synthesis is generalized in a sense that it covers robust robust gain scheduled and robust switched with arbitrary switching algorithm pid controller design the proposed centralized decentralized controller method is based on bellman lyapunov equation guaranteed cost and parameter dependent quadratic stability the proposed sufficient robust stability and performance conditions are derived in the form of bilinear matrix inequalities bmi which can efficiently be solved or further linearized as the main result the suggested performance and stability conditions without any restriction on the controller structure are convex functions of the scheduling and uncertainty parameters hence there is no need for applying multi convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method the viability of the novel design technique is demonstrated and evaluated through numerical examples

a synthesis framework for robust gain scheduling controllers we present a general framework for the systematic synthesis of robust gain scheduling controllers by convex optimization techniques and for uncertain dynamical systems described by standard linear fractional representations we distinguish between linear time varying parameters which are assumed to be available online as scheduling parameters for the controller and genuine uncertainties not necessarily time varying parametric or linear that are not available online under the rough hypothesis that the control channel is not affected by the unmeasurable uncertainties and that the properties of the uncertainties and scheduling variables are captured by suitable families of integral quadratic constraints this paper reveals how controller synthesis can be turned into a genuine semi definite program the design framework is shown to encompass a rich class of concrete scenarios

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

structural stabilization of uncertain systems necessity of the matching condition this paper investigates one aspect of the problem of stabilizing an uncertain linear system that is the systems under consideration contain uncertain parameters which are unknown but bounded the question arises as to whether such a system can be stabilized via feedback control in some of the previous papers in this area the system is assumed to satisfy a so called matching condition this type of assumption is used to assure that the uncertain system can be stabilized it is known however that the matching condition is not a necessary condition for stabilizability this paper introduces a strengthened notion of stabilizability referred to as structural stabilizability via a nominally determined quadratic lyapunov function it is then shown that if a system is to have this stronger property the matching condition must necessarily be satisfied