robust stabilization of discrete time linear systems with norm bounded time varying uncertainty abstract this paper presents an algorithm for the stabilization of a class of discrete time uncertain systems suffering from uncertainty of the norm bounded time varying type the stabilizing control gain matrix is obtained by solving a certain discrete riccati equation the solution of this riccati equation is also a lyapunov matrix which is used to establish the stability of closed loop system the results presented in this paper generalize those obtained in previous works for continuous time uncertain systems

designing stabilizing controllers for uncertain systems using the riccati equation approach a useful technique for determining a linear feedback control law stabilizes an uncertain system is the riccati equation approach of i r petersen and c v hollot 1986 they consider systems with time varying uncertainty in the system matrix and obtain the constant feedback gains for the linear stabilizing controller in terms of the solutions of a riccati equation the technique is extended to include problems with time varying uncertainty in the input connection matrix several examples are included to demonstrate the efficacy of this result

linear quadratic differential games with cheap control abstract this paper considers a linear quadratic differential game in which the weighting on the minimizing control is allowed to approach zero it is shown that if a certain minimum phase condition is satisfied then the value of the game will approach zero as the weighting on the minimizing control approaches zero

output feedback disk pole assignment for systems with positive real uncertainty in this paper the problem of pole assignment in a disk by output feedback for continuous or discrete time uncertain systems is addressed a necessary and sufficient condition for quadratic d stabilizability by output feedback is presented this condition is expressed in terms of two parameter dependent riccati equations whose solutions satisfy two extra conditions an output d stabilization algorithm is derived and a controller formula given some related problems are also discussed

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

fault estimation observer design for discrete time takagi sugeno fuzzy systems based on piecewise lyapunov functions this paper studies the problem of robust fault estimation fe observer design for discrete time takagi sugeno t s fuzzy systems via piecewise lyapunov functions both the full order fe observer ffeo and the reduced order fe observer rfeo are presented the objective of this paper is to establish a novel framework of the fe observer with less conservatism first under the multiconstrained design an ffeo is proposed to achieve fe for discrete time t s fuzzy models then using a specific coordinate transformation an rfeo is constructed which results in a new fault estimator to realize fe using current output information furthermore by the piecewise lyapunov function approach less conservative results on both ffeo and rfeo are derived by introducing slack variables simulation results are presented to illustrate the advantages of the theoretic results that are obtained in this paper

dense output for extrapolation methods this paper is concerned with dense output formulas for extrapolation methods for ordinary differential equations in particular the extrapolated explicit euler method the gbs method for non stiff equations and the extrapolated linearly implicit euler method for stiff and differential algebraic equations are considered existence and uniqueness questions for dense output formulas are discussed and an algorithmic description for their construction is given several numerical experiments illustrate the theoretical results

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

a method of optimal scaling for multivariate ordinal data and its extensions this paper develops a method of optimal scaling for multivariate ordinal data in the framework of a generalized principal component analysis this method yields a multidimensional configuration of items a unidimensional scale of category weights for each item and optionally a multidimensional configuration of subjects the computation is performed by alternately solving an eigenvalue problem and executing a quasi newton projection method the algorithm is extended for analysis of data with mixed measurement levels or for analysis with a combined weighting of items numerical examples and simulations are provided the algorithm is discussed and compared with some related methods

quadratic stability and stabilization of uncertain linear discrete time systems with state delay abstract this paper deals with the problem of quadratic stability analysis and quadratic stabilization for uncertain linear discrete time systems with state delay the system under consideration involves state time delay and time varying norm bounded parameter uncertainties appearing in all the matrices of the state space model necessary and sufficient conditions for quadratic stability and quadratic stabilization are presented in terms of certain matrix inequalities respectively a robustly stabilizing state feedback controller can be constructed by using the corresponding feasible solution of the matrix inequalities two examples are presented to demonstrate the effectiveness of the proposed approach

robustness of pole assignment in a specified region an analysis of pole assignment is given for systems under linear time invariant perturbations based upon the lyapunov approach new techniques to calculate allowable element bounds for highly structured perturbations are presented under these allowable perturbations both stability robustness and a certain performance robustness are thus ensured examples are given to illustrate the proposed methods

h sub infinity control and quadratic stabilization of systems with parameter uncertainty via output feedback the article concerns linear systems which are subject to both time varying norm bounded parameter uncertainty and exogenous disturbance it addresses the robust h sub infinity control problem of designing a linear dynamic output feedback controller such that the closed loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties it is shown that such a problem is equivalent to a scaled h sub infinity control problem

digital idle speed control of automotive engines a safety problem for hybrid systems abstract we address the idle speed control problem in automotive electronics using hybrid methods to derive a digital control law with guaranteed properties associating a switching system with the hybrid system that describes the engine operation is crucial to developing a computationally feasible approach for switching systems with minimum and maximum dwell times and controlled resets we are able to derive digital control strategies with guaranteed properties that ensure safety the proposed methodology while motivated by the idle control problem is of general interest for hybrid systems for which minimum and maximum dwell times can be established in our modeling approach we do not assume synchronization between sampling time and switching time this is an important technical aspect in general and in particular for our application where there is no reason why sampling and switching should be synchronized some simulation results are included to demonstrate the effectiveness of the approach

pole assignment of linear uncertain systems in a sector via a lyapunov type approach the problem of designing robust control laws in performance and in stability for uncertain linear systems is considered performances are taken into account using root clustering of the closed loop dynamic matrix in a sector of the complex plane a synthesis procedure based on a sufficient condition for quadratic stabilization and root clustering such as stabilizability is given using an auxiliary convex problem the results are illustrated by a significant example from the literature

a complex projection scheme and applications in this paper an extended projection method in the complex number field is presented we consider two classes of complex linear matrix inequalities and then derive the corresponding projection operators applications to the control system with pole assignment problem and the robust stability of linear descriptor systems which are described in complex linear matrix inequalities are given based on the numerical algorithms some examples are illustrated for the merits of the proposed method

pole assignment for uncertain systems in a specified disk by state feedback this paper presents a method for assigning the poles in a specified disk by state feedback for a linear discrete or continuous time uncertain system the uncertainty being norm bounded for this the quadratic d stabilizability concept which is the counterpart of quadratic stabilizability in the context of pole placement is defined and a necessary and sufficient condition for quadratic d stabilizability derived this condition expressed as a parameter dependent discrete riccati equation enables one to design the control gain matrix by solving iteratively a discrete riccati equation

controller design with regional pole constraints a design procedure is developed that combines linear quadratic optimal control with regional pole placement specifically a static and dynamic output feedback control problem is addressed in which the poles of the closed loop system are constrained to lie in specified regions of the complex plane these regional pole constraints are embedded within the optimization process by replacing the covariance lyapunov equation by a modified lyapunov equation whose solution in certain cases leads to an upper bound on the quadratic cost functional the results include necessary and sufficient conditions for characterizing static output feedback controllers with bounded performance and regional pole constraints sufficient conditions are also presented for the fixed order i e full and reduced order dynamic output feedback problem with regional pole constraints circular elliptical vertical strip parabolic and section regions are considered

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

effective solution of discontinuous ivps using a runge kutta formula pair with interpolants an automatic technique for solving discontinuous initial value problems is developed and justified the technique is based on the use of local interpolants such as those that have been developed for use with runge kutta formula pairs numerical examples are presented to illustrate the significant improvement in efficiency and reliability that results when this technique is used with standard methods

multi constrained fault estimation observer design with finite frequency specifications for continuous time systems the design of a multi constrained full order fault estimation observer ffeo with finite frequency specifications is studied for continuous time systems by constructing an augmented system a multi constrained ffeo in finite frequency domain is proposed to achieve fault estimation meanwhile the presented ffeo can avoid the overdesign problem generated by the entire frequency domain by the generalised kalman yakubovich popov lemma furthermore by introducing slack variables improved results on ffeo design in different frequency domains are obtained such that different lyapunov matrices can be separately designed for each constraint simulation results are presented to demonstrate the effectiveness and potentials of the proposed techniques

numerical solution of differential algebraic equations in mechanical systems simulation abstract the numerical solution of the differential algebraic equations of motion of mechanical systems offers many computational challenges in this paper we describe progress which has been made in understanding the formulation of the equations of motion from the viewpoint of numerical stability and outline some of the difficulties which must be resolved for efficient and reliable numerical methods in real time simulation of mechanical systems

output feedback fault tolerant control by a set theoretic description of ts fuzzy systems this paper is concerned with the observer based output feedback fault tolerant control problem for ts fuzzy systems by constructing a set theoretic description of fuzzy systems the equivalence class theory in set theory is applied for designing observer and controller for less conservative results firstly we designed the observer to get the information of the actuator faults in the system then we use this information to design the fault tolerant controller to compensate for the effect of faults and guarantee stability of the system finally a simple nonlinear massspringdamper system is presented to illustrate the effectiveness of the proposed approach

non fragile robust h control for uncertain spacecraft rendezvous system with pole and input constraints this article investigates the robust h control problem for a class of spacecraft rendezvous systems with parameter uncertainties and subject to input constraint pole constraint and external and controller perturbations based on the lyapunov theory a sufficient condition for the existence of the non fragile robust state feedback controller is given in terms of linear matrix inequalities lmis then proper non fragile controller design can be cast as a convex optimisation problem subject to lmi constraints with the obtained controller the spacecraft rendezvous mission can be accomplished an illustrative example is provided to show the effectiveness of the proposed control design method

event location for ordinary differential equations abstract an initial value problem for y f t y may have an associated event function g t y an event is said to occur at t when g t y t 0 we consider problems for which the definition of f t y changes at the time of an event a number of solvers locate events and restart the integration there so as to deal with the changes in f but there is little theoretical support for what is done here we prove that with reasonable assumptions about the problem and the solver the error of the numerical solution is qualitatively the same whether or not events occur numerical results obtained with a wide range of solvers confirm the theory developed here

fixed order controller design for polytopic systems using lmis convex parameterization of fixed order robust stabilizing controllers for systems with polytopic uncertainty is represented as a linear matrix inequality lmi using the kalman yakubovich popov kyp lemma this parameterization is a convex inner approximation of the whole nonconvex set of stabilizing controllers and depends on the choice of a central polynomial it is shown that with an appropriate choice of the central polynomial the set of all stabilizing fixed order controllers that place the closed loop poles of a polytopic system in a disk centered on the real axis can be outbounded with some lmis these lmis can be used for robust pole placement of polytopic systems

robust stability and robust pole assignment of linear systems with structured uncertainty sufficient conditions for the robust stability of linear time varying systems are presented the stability criteria are extended to the problem of the robust pole assignment of linear time invariant systems to a specified region these criteria both for robust stability and robust pole assignment improve some results in the literature examples are given to demonstrate the new criteria

robust pole placement in lmi regions discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality lmi regions a class of convex regions of the complex plane that embraces most practically useful stability regions the focus is on linear systems with static uncertainty on the state matrix for this class of uncertain systems the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary lmi regions the resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities lmis and cover both unstructured and parameter uncertainty these analysis results are then applied to the synthesis of dynamic output feedback controllers that robustly assign the closed loop poles in a prescribed lmi region with some conservatism this problem is again tractable via lmi optimization in addition robust pole placement can be combined with other control objectives such as h sub 2 or h sub spl infin performance to capture realistic sets of design specifications physically motivated examples demonstrate the effectiveness of this robust pole clustering technique

robust control with pole shifting via performance index modification robust controllers that ensure closed loop eigenvalue placement are designed for linear systems with parametric uncertainties by using an appropriate state weighting matrix choice and a relative stability degree an lmi based algorithm is proposed to provide guaranteed cost controllers that ensure i the closed loop nominal eigenvalues shifting by a pre specified amount ii a prescribed degree of stability for all system uncertainties of a given class a certain level of closed loop performance is also ensured by minimizing the associated guaranteed cost

orthonormal basis functions applied to optimal control design with closed loop pole location constraints this article proposes an optimal control design technique to ensure that the closed loop poles are assigned to prescribed locations in the complex plane a key element in this approach is the usage of orthonormal basis functions to parametrise the main design parameter this goal is achieved by using a quadratic cost based optimisation approach considering control effort penalisation as well as cheap control youla parametrisation is used subject to a set of constraints which guarantee stability zero steady error to constant references and disturbances and yielding the prescribed set of closed loop poles

open issues in devising software for the numerical solution of implicit delay differential equations we consider initial value problems for systems of implicit delay differential equations of the form my t f t y t y 1 t y t y m t y t where m is a constant square matrix with arbitrary rank and i t y t t for all t and i for a numerical treatment of this kind of problems a software tool has been recently developed 6 this code is called radar5 and is based on a suitable extension to delay equations of the 3 stage radau iia runge kutta method the aim of this work is that of illustrating some important topics which are being investigated in order to increase the efficiency of the code they are mainly relevant to i the error control strategies in relation to derivative discontinuities arising in the solutions of delay equations ii the integration of problems with unbounded delays like the pantograph equation iii the applications to problems with special structure as those arising from spatial discretization of evolutions pdes with delays several numerical examples will also be shown in order to illustrate some of the topics discussed in the paper

the problem of local optimality with osmod the possibility of obtaining locally optimal solutions with categorical data is pointed out for the original version of osmod development by saito and otsu a revision of the initialization strategy in osmod is suggested and its effectiveness in diminishing this possibility is demonstrated

optimal controller synthesis with d stability abstract in this paper we consider the problem of finding controllers which place the eigenvalues of the closed loop system matrix in a prespecified circular region in the left half plane and minimize an associated quadratic cost function we give solutions to both state feedback and output feedback synthesis problems

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

a survey of numerical methods for ivps of odes with discontinuous right hand side this work is dedicated to the memory of donato trigiante who has been the first teacher of numerical analysis of the second author the authors remember donato as a generous teacher always ready to discuss with his students able to give them profound and interesting suggestions here we present a survey of numerical methods for differential systems with discontinuous right hand side in particular we will review methods where the discontinuities are detected by using an event function so called event driven methods and methods where the discontinuities are located by controlling the local errors so called time stepping methods particular attention will be devoted to discontinuous systems of filippov s type where sliding behavior on the discontinuity surface is allowed

a general formula for eigenvalue assignment by static output feedback with application to robust design in this note generalizing an idea of a previous paper we derive a new expression of the characteristic polynomial of a linear system subject to static output feedback from this expression an explicit form of the assignment equations in the unknown elements of the feedback matrix is obtained the equations are completely general and seem much simpler than many others proposed until now in special cases a closed or almost a closed form solution is obtained the assignment equations are then used within an algorithm for global optimization to solve the problem of exactly assigning the eigenvalues of the nominal plant while maximizing the norm of perturbation matrices for which the perturbed eigenvalues remain in specified regions of the complex plane

continuous numerical methods for odes with defect control abstract over the last decade several general purpose numerical methods for ordinary differential equations odes have been developed which generate a continuous piecewise polynomial approximation that is defined for all values of the independent variable in the range of interest for such methods it is possible to introduce measures of the quality of the approximate solution based on how well the piecewise polynomial satisfies the ode this leads naturally to the notion of defect control numerical methods that adopt error estimation and stepsize selection strategies in order to control the magnitude of the associated defect can be very effective and such methods are now being widely used in this paper we will review the advantages of this class of numerical methods and present examples of how they can be effectively applied we will focus on numerical methods for initial value problems ivps and boundary value problems bvps where most of the developments have been introduced but we will also discuss the implications and related developments for other classes of odes such as delay differential equations ddes and differential algebraic equations daes

sliding motion in filippov differential systems theoretical results and a computational approach in this work we discuss some theoretical and numerical aspects of solving differential equations with discontinuous right hand sides of filippov type in particular i we propose second order corrections to the theory of filippov ii we provide a systematic and nonambiguous way to define the vector field on the intersection of several surfaces of discontinuity and iii we propose and implement a numerical method to approximate a trajectory of systems with discontinuous right hand sides and illustrate its performance on a few examples

robust h control for uncertain discrete singular systems with pole placement in a disk abstract this paper addresses the design of robust h controllers for uncertain discrete singular systems with time invariant uncertainty in both the state and measurement matrices the singular system to be controlled is not assumed to be regular a regular dynamic output feedback controller is designed such that a prescribed h performance condition is satisfied and the closed loop poles are placed in a specified disk while the regularity causality and stability of the closed loop system can be guaranteed for all admissible uncertainties the desired controller can be obtained by solving a set of matrix inequalities a numerical example is given to demonstrate the application of the proposed method

principals versus osmod a comment on saito and otsu saito and otsu 1988 compared their osmod method of nonmetric principal component analysis to an early and incorrect implementation of the principals algorithm of young takane and de leeuw 1978 in this comment we present results from the current correct implementations of the algorithm

pole assignment in a specified disk the problem of assigning all poles of a closed loop system in a specified disk by state feedback is considered for both continuous and discrete systems a state feedback control law is determined by using a discrete riccati equation this kind of pole assignment problem is named d pole assignment and its relation to the optimal control problem and its robustness properties are discussed the gain and phase margins for all closed loop poles to stay inside the specified disk d are determined for the proposed control

a general theory for matrix root clustering in subregions of the complex plane we consider the general problem of root clustering of a matrix in the complex plane let a in c n times n and s subset c find the largest class of s and an algebraic criterion which is necessary and sufficient for lambda i a in s i 1 2 n we introduce two types of regions which constitute the largest class of s known to date the criterion is presented both for open regions and closed ones the results are used to define a design methodology for control systems moreover all classical results are shown to be special cases of the present theory

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

robust h control for uncertain discrete time systems with circular pole constraints this paper investigates the problem of robust h control for uncertain discrete time systems with circular pole constraints the system under consideration is subject to norm bounded time invariant uncertainties in both the state and input matrices the problem we address is to design state feedback controllers such that the closed poles are located within a prespecified circular region and the h norm of the closed loop transfer function is strictly less than a given positive scalar for all admissible uncertainties by introducing the notion of quadratic d stabilizability with an h norm bound the problem is solved necessary and sufficient conditions for quadratic d stabilizability with an h norm bound are derived our results can be regarded as extensions of existing results on robust h control and robust pole assignment of uncertain systems

robust state derivative pole placement lmi based designs for linear systems in some practical problems for instance in the control systems for the suppression of vibration in mechanical systems the state derivative signals are easier to obtain than the state signals necessary and sufficient lmi based conditions for pole placement of linear systems using state derivative feedback are proposed sufficient conditions for pole placement for a class of uncertain systems or systems subject to structural failures are also presented the simulation of practical applications illustrates the efficiency of the proposed methods

strong practical stability and stabilization of differential linear repetitive processes abstract differential linear repetitive processes evolve over a subset of the upper right quadrant of the 2d plane where the unique feature is a series of sweeps or passes through a set of dynamics governed by the solution of a linear matrix differential equation over a finite duration t 0 where is termed the pass length or duration on each pass an output termed the pass profile is produced which acts as a forcing function on and hence contributes to the dynamics of the next pass profile the result can be oscillations in the pass to pass direction that cannot be controlled by direct application of standard or 1d linear systems theory the existing stability theory demands a bounded input bounded output property uniformly which in the case of the along the pass dynamics means for t 0 and for k t 0 0 0 0 where the integer k 0 denotes the pass number or index the pass length is always finite however and hence this stability theory could well be too strong in many cases and in particular impose very strong conditions in terms of control law design this paper develops an alternative in such cases by relaxing the requirement for the bounded input bounded output property to hold when k and t simultaneously provides an explanation of the implications of this in the frequency domain and then develops control law design algorithms

generalized guaranteed cost control with d stability and multiple output constraints abstract this paper is concerned with the problem of robust generalized guaranteed cost control with d stability and multiple output constraints for a class of linear uncertain systems being a combination of output performance indices a generalized cost function is considered to the linear polytopic uncertain systems described in a unified framework the aim is to design a state feedback controller such that the closed loop system is robust d stable and the upper bound of the generalized cost function is as small as possible subject to multiple output constraints based on parameter dependent lyapunov functions convex conditions for the existence of such controllers are presented in terms of linear matrix inequality the proposed approach shows a unified treatment of the linear systems in the differential shift and delta domains numerical examples are provided to illustrate the effectiveness of the design method

convergence analysis of the solution of retarded and neutral delay differential equations by continuous numerical methods we have recently developed a generic approach to solving retarded and neutral delay differential equations ddes the approach is based on the use of an explicit continuous runge kutta formula and employs defect control the approach can be applied to problems with state dependent delays and vanishing delays in this paper we determine convergence properties for the numerical solution associated with methods that implement this approach we first analyze such properties for retarded ddes and then the analysis is extended to the case of neutral ddes ndes such an extension is particularly important since ndes have received little attention in the literature the main result we establish is that the global error of the numerical solution can be efficiently and reliably controlled by directly monitoring the magnitude of the associated defect our analysis can also be applied directly to other numerical methods which use defect error control based on runge kutta formulas for ddes

an efficient model predictive controller with pole placement for model predictive control mpc of constrained systems enlarging the feasible region is usually in conflict with improving the dynamic performance to resolve the conflict we proposed an efficient model predictive controller with pole placement for a class of discrete time linear systems by specifying a group of circular regions that contain the desired closed loop poles appropriate terminal weighting matrices and local controllers are calculated to construct a time varying terminal convex set which is a significant constraint for the online optimization problem during the online optimization the size of the terminal convex set can adjust itself according to the actual state at each sampling time in this way a large initial feasible region can be achieved while maintaining the good dynamic performance an illustrative example is used to show the effectiveness of the proposed approach

generalized riccati equations associated with guaranteed cost control an overview of solutions and features robust control of dynamic linear systems with parametric uncertainties is based on the solution of generalized riccati equations i e riccati equations with additional terms depending on the uncertainties in particular guaranteed cost controller design requires the existence and computation of positive definite solutions of such equations in the present paper an overview of the riccati equations arising in guaranteed cost control approaches is presented it is shown that different uncertainty descriptions and the corresponding upper bounding functions lead to various forms of generalized riccati equations that may admit either analytical or computational positive definite solutions the associated closed loop systems robustness features are also discussed