on the structure of generalized plant convexifying static h control problems abstract this paper shows that under specific structures of generalized plants the set of static controllers satisfying internal stability and a certain level of h performance becomes convex more precisely we characterize such static h controllers by an lmi with controller variables being kept directly as decision variables the structural conditions on the generalized plant are not too strict and we show that generalized plants corresponding to a sort of mixed sensitivity problems indeed satisfy these conditions for the generalized plants of interest we further prove that full order dynamical h controllers can be characterized by an lmi with a simple change of variables in stark contrast to the known lmi based h controller synthesis the change of variables is free from the coefficient matrices of the generalized plant and this property is promising when dealing with a variety of robust control problems related issues such as robust controller synthesis against real parametric uncertainties are also discussed

brief paper output feedback variable structure control design with an h2 performance bound constraint in this paper we give an lmi based method for designing an output feedback variable structure control vsc system with an h 2 constraint the uncertain system model under consideration may have nonmatching disturbance input signals nonmatching disturbance input signal reduction is performed via h 2 norm minimization in terms of a constrained riccati inequality we give a sufficient condition for the existence of a linear sliding surface and a compensator guaranteeing an h 2 constraint and we show that the control parameters can be characterized by using the solution to the given inequality condition we also give a simple lmi based design algorithm of an output feedback vsc law guaranteeing an h 2 constraint finally by using a design example we show that our method can supplement the existing results

load updating for finite element models a method for reducing the differences between experimental testing or real world events and their finite element counterparts is presented in this method system identification or finite element model updating are not performed instead the loads on the finite element model that would create equivaient displacements or strains are identified by various means thus saving a large amount of computational effort this method of finding an applied load is also extremely useful in the analysis of testing data for vehicles and other structures using methods based on classical least squares methods we present the basis for finite element load updating and sample application through the use of a computer program for a beam under static loads we examine the conditioning number of the resulting system of equations and provide a least squares solution that is more robust through the use of singular value decomposition this allows an easier analysis of structural models for example of a prototype vehicle by determining the loads that the prototype is subjected to in testing these loads can then be used on other models of that vehicle during the design process to decrease the time spent in testing while increasing design s reliability by reducing uncertainties in the applied load

simultaneous stabilization via static output feedback and state feedback in this paper the simultaneous stabilization problem is considered using the matrix inequality approach some necessary and sufficient conditions for simultaneous stabilizability of strictly proper multi input multi output mimo plants via static output feedback and state feedback are obtained in the form of coupled algebraic riccati inequalities it is shown that any such stabilizing feedback gain is the solution of some coupled linear quadratic control problems where every cost functional has a suitable cross term a heuristic iterative algorithm based on the linear matrix inequality technique is presented to solve the coupled matrix inequalities the effectiveness of the approach is illustrated by numerical examples

trust region methods for solving the optimal output feedback design problem we consider the problem of designing feedback control laws when a complete set of state variables is not available for linear autonomous control systems with quadratic performance criterion the design problem consists of choosing an appropriate static output feedback sof gain matrix according to a certain objective function the corresponding non linear matrix optimization problem can be interpreted as an equality constrained minimization problem for solving this problem we propose a constrained trust region ctr algorithm which presents a new and efficient numerical approach for this problem class on the other hand based on the formulation used in the past the sof problem can be also interpreted as an unconstrained programming problem thus based on this interpretation we also develop an unconstrained trust region utr method finally several numerical examples for optimal sof problems demonstrate the applicability of the considered algorithm

a novel event triggered transmission scheme and cal l _ 2 control co design for sampled data control systems this note is concerned with the event triggered l2 control for a sampled data control system a novel event triggered transmission scheme is first proposed to determine whether or not the sampled data should be transmitted under this scheme the sampled data transmission should be executed only when a threshold is violated which means that less sampled data is transmitted this scheme does not require any special hardware for continuous measurement then the sampled data control system is modeled as a sampled data error dependent system a stability criterion is derived by constructing a novel lyapunov krasovskii functional which fully utilizes the sawtooth structure characteristic of an artificial delay based on this stability criterion a sufficient condition on the existence of a state feedback controller is given a co design algorithm is provided to obtain the parameters of the event triggered transmission scheme and the controller gain simultaneously finally an inverted pendulum example is given to show the effectiveness of the event triggered transmission scheme and the co design algorithm

high order accuracy nonpolynomial spline solutions for 2μth order two point boundary value problems sixth order accurate method based on quintic nonpolynomial spline function for the numerical solution of 2 th order two point bvps where is a positive integer is presented by transforming the problem into a system of second order two point bvps the nonpolynomial spline function is used to drive some consistency relations for computing approximation to the solution of this problem the proposed approach gives better approximations than existing polynomial spline and finite difference methods and has a lower computational cost convergence analysis of the proposed method is discussed numerical examples are included to illustrate the practical usefulness of our method

h guaranteed cost control for uncertain continuous time linear systems abstract this paper deals with the h guaranteed cost control problems for continuous time uncertain systems it consist of the determination of a stabilizing state feedback gain which imposes on all possible closed loop models an h norm upper bound 0 assuming that the uncertain domain is convex bounded and the uncertain system is quadratic stabilizable with disturbance attenuation it is shown how to determine by means of a convex programming problem the global minimum of as a particular and important case for precisely known linear systems the last problem reduces to the classical h optimal control problem the results follow from the definition of a special parameter space on which the above mentioned problems are convex

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

robust control with structure perturbations the problem of making a given stabilizing controller robust so that the closed loop system remains stable for prescribed ranges of variations of a set of physical parameters in the plant the problem is treated in the state space and transfer function domains in the state space domain a stability hypersphere is determined in the parameter space using lyapunov theory the radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere in the transfer function domain a corresponding stability margin is defined and optimized on the basis of the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed loop characteristic polynomial the design algorithms are illustrated by examples

static output feedback controllers stability and convexity the main objective of this paper is to solve the following stabilizing output feedback control problem given matrices a b sub 2 c sub 2 with appropriate dimensions find if one exists a static output feedback gain l such that the closed loop matrix a b sub 2 lc sub 2 is asymptotically stable it is known that the existence of l is equivalent to the existence of a positive definite matrix belonging to a convex set such that its inverse belongs to another convex set conditions are provided for the convergence of an algorithm which decomposes the determination of the aforementioned matrix in a sequence of convex programs hence this paper provides a new sufficient but not necessary condition for the solvability of the above stabilizing output feedback control problem as a natural extension we also discuss a simple procedure for the determination of a stabilizing output feedback gain assuring good suboptimal performance with respect to a given quadratic index some examples borrowed from the literature are solved to illustrate the theoretical results

an alternate numerical solution to the linear quadratic problem this note proposes a new method based on convex programming for solving the linear quadratic problem lqp directly on the parameter space generated by the feedback control gain all stabilizing controllers are mapped into a convex set the problem is then formulated as a minimization of a linear function over this convex set its optimal solution furnishes under certain conditions the same feedback control gain obtained from the classical riccati equation generalizations to decentralized control and output feedback control design are included the theory is illustrated by some numerical examples

design of affine controllers via convex optimization we consider a discrete time time varying linear dynamical system perturbed by process noise with linear noise corrupted measurements over a finite horizon we address the problem of designing a general affine causal controller in which the control input is an affine function of all previous measurements in order to minimize a convex objective in either a stochastic or worst case setting this controller design problem is not convex in its natural form but can be transformed to an equivalent convex optimization problem by a nonlinear change of variables which allows us to efficiently solve the problem our method is related to the classical design procedure for time invariant infinite horizon linear controller design and the more recent purified output control method we illustrate the method with applications to supply chain optimization and dynamic portfolio optimization and show the method can be combined with model predictive control techniques when perfect state information is available

damping parameter design optimization in structural systems using an explicit h norm bound abstract this paper examines the damping parameter design optimization problem for structural systems with collocated measurements and inputs so that h norm bound constraints are satisfied we utilize a particular solution of the bounded real lemma that provides an explicit upper bound on the h norm of a collocated structural system using this upper bound result the damping design is formulated as a linear matrix inequality lmi optimization problem with respect to the damping coefficients of the structural system the formulation is particularly useful for large scale structural systems where existing methods are computationally prohibitive numerical examples demonstrate the benefits and computational advantages of the proposed damping parameter design method

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

stabilizability conditions of multivariable uncertain systems via output feedback control a stabilizability condition is established for stabilizing multivariable uncertain dynamical systems with matched uncertainties by linear static output feedback control it is shown that under the assumptions of minimum phase and nonsingular high frequency gain for the nominal plant stabilization with linear static output feedback control is achievable a necessary and sufficient condition is also obtained for the existence of constant output feedback which makes the closed loop system strictly positive real

convex analysis of output feedback control problems robust stability and performance this paper addresses the problem of optimal h sub 2 control by output feedback necessary and sufficient conditions on the existence of a linear stabilizing output feedback gain are provided in terms of the intersection of a convex set and a set defined by a nonlinear real valued function the results can be easily extended to deal with linear uncertain systems where uncertainties are supposed to belong to convex bounded domains providing an h sub 2 guaranteed cost output feedback control thanks to the properties of the above mentioned function we show that under certain conditions convex programming tools can be used for numerical purposes examples illustrate the theoretical results

the constrained lyapunov problem and its application to robust output feedback stabilization given a dynamical system whose description includes time varying uncertain parameters it is often desirable to design an output feedback controller leading to asymptotic stability of a given equilibrium point when designing such a controller one may consider static i e memoryless or dynamic compensation in this paper we show that solvability of various output feedback design problems is implied by existence of a solution to a certain constrained lyapunov problem clp the clp can be stated in purely algebraic terms once the clp is described we provide necessary and sufficient conditions for its solution to exist subsequently we consider application of the clp to a number of robust stabilization problems involving static output feedback and observer based feedback

brief paper optimal reduced order compensation of time varying discrete time systems with deterministic and white parameters the finite horizon optimal compensation problem is considered in the case of linear time varying discrete time systems with deterministic and white stochastic parameters and quadratic criteria the dimensions of the compensator are a priori fixed and may be time varying also the dimensions of the system may be time varying strengthened discrete time optimal projection equations sdope are developed which within the class of minimal compensators are equivalent to the first order necessary optimality conditions based on the sdope and their associated boundary conditions two numerical algorithms are presented to solve the two point boundary value problem one is a homotopy algorithm while the second iterates the sdope repeatedly forward and backward in time the latter algorithm is much more efficient and constitutes a generalization of the single iteration of the control and estimation riccati equations associated with the full order problem for systems with deterministic parameters the algorithms are illustrated with a numerical example the case of systems with deterministic parameters will be treated as a special case of systems with white parameters

lmi relaxations for reduced order robust cal h _ infty control of continuous time uncertain linear systems this technical note is concerned with the problem of reduced order robust h dynamic output feedback control design for uncertain continuous time linear systems the uncertain time invariant parameters belong to a polytopic domain and affect all the system matrices the search for a reduced order controller is converted in a problem of static output feedback control design for an augmented system to solve the problem a two stage linear matrix inequality lmi procedure is proposed at the first step a stabilizing state feedback scheduled controller with polynomial or rational dependence on the parameters is determined this parameter dependent state feedback controller is used at the second stage which synthesizes the robust parameter independent output feedback h dynamic controller a homogeneous polynomially parameter dependent lyapunov function of arbitrary degree is used to assess closed loop stability with a prescribed h attenuation level as illustrated by numerical examples the proposed method provides better results than other lmi based conditions from the literature

stabilizing static output feedback receding horizon controls for linear discrete time invariant systems in this paper a stabilizing static output feedback receding horizon control rhc is proposed for linear discrete time invariant systems an inequality condition on the terminal weighting matrices is presented under which the closed loop stability of static output feedback receding horizon controls is guaranteed it is shown that the stabilizing static output feedback receding horizon control problem can be represented as a non linear minimization problem based on linear matrix inequalities lmis an algorithm for solving the presented non linear minimization problem is proposed in addition this result is extended to an arbitrary reference tracking problem that is one of the main features of receding horizon control finally the efficiency of the proposed algorithm is illustrated by numerical examples

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

output feedback decentralized stabilization ilmi approach in this paper the static output feedback decentralized stabilization problem is addressed using a linear matrix inequality approach a necessary and sufficient condition for static output feedback decentralized stabilizability is derived for linear time invariant large scale systems it is proven that the existence of a stabilizing decentralized gain is equivalent to that of the solution of a quadratic matrix inequality the extension of the result to h control is studied an iterative lmi algorithm based on the linear matrix inequality technique is proposed to obtain the decentralized feedback gain examples show the effectiveness of the algorithm

quadratic characterization and use of output stabilizable subspaces this note treats the problem of stabilization of linear systems by static output feedback using the concept of c a b invariant subspaces the work provides a new characterization of output stabilizable c a b invariant subspaces through two coupled quadratic stabilization conditions an equivalence is shown between the existence of a solution to this set of conditions and the possibility to stabilize the system by static output feedback an algorithm is provided and numerical examples are reported to illustrate the approach

exponentially fitted methods applied to fourth order boundary value problems fourth order boundary value problems are solved by means of exponentially fitted methods of different orders these methods which depend on a parameter can be constructed following a six step flow chart of ixaru and vanden berghe special attention is paid to the expression for the error term and to the choice of the parameter in order to make the error as small as possible some numerical examples are given to illustrate the practical implementation issues of these methods

static output feedback stabilization with prescribed degree of stability the problem of finding a static output feedback matrix is restated the new formulation replaces the solution of a set of inversely coupled lyapunov inequalities with the simultaneous solution to an algebraic riccati inequality and a lyapunov inequality an algorithm is developed based on the restated problem unlike previous algorithms the algorithm is noniterative in linear matrix inequality lmi solutions the algorithm may be used to prescribe a given degree of stability while keeping the static output feedback gain small use of the algorithm is demonstrated via an example

ellipsoidal sets for resilient and robust static output feedback the implementation of a controller if not exact may lead to the so called fragility problem i e the loss of expected closed loop properties in the present note this difficult problem is dealt with considering robust static output feedback sof control for uncertain linear time invariant systems by analogy with robust analysis theory based on quadratic separation a new formulation for the sof design is shown to be a valuable way to tackle fragility issues indeed the use of a quadratic separator for design purpose allows to define a whole resilient nonfragile set of sof control laws results are formulated as matrix inequalities one of which is nonlinear a numerical algorithm based on nonconvex optimization is provided ant its running is illustrated on classical examples from literature

a smooth approximation based on exponential spline solutions for nonlinear fourth order two point boundary value problems methods of order two four and six based on exponential spline functions consisting of a polynomial part of degree three and an exponential part is developed to find approximation of linear and nonlinear fourth order two point boundary value problems it is shown that the free parameter k of the exponential part can be used to raise the order of accuracy of the new scheme convergence analysis of these methods is shown along with numerical examples each for linear and nonlinear are included to illustrate the practical usefulness of our methods

static output feedback stabilization with h sub spl infin performance for linear discrete time systems this note presents a new sufficient condition for the static output feedback stabilization of linear discrete time systems this new condition is expressed as a linear matrix inequality feasibility problem and hence easily tractable numerically an extension of this condition is given in order to incorporate h sub spl infin performance objectives the applicability of the proposed approach is shown through numerical examples and compared to some recent methods

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

convergence of numerical solution of a fourth order boundary value problem quintic spline procedure for the solution of a fourth order boundary value problem is developed spline relations are derived boundary condition formula of orders o h 6 and o h 8 are formulated the convergence of prescribed method is proved the matrix associated with the system of linear equations that arises is not required to be monotone the only requirement is that f x be positive numerical illustration are given

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

computational complexity of a problem arising in fixed order output feedback design this paper is concerned with a matrix inequality problem which arises in fixed order output feedback control design this problem involves finding two symmetric and positive definitive matrices x and y such that each satisfies a linear matrix inequality and that xy i it is well known that many control problems such as fixed order output feedback stabilization h control guaranteed h2 control and mixed h2 h control can all be converted into the matrix inequality problem above including static output feedback problems as a special case we show however that this matrix inequality problem is np hard

stabilization and h control of symmetric systems an explicit solution abstract in this paper we address the h control analysis the output feedback stabilization and the output feedback h control synthesis problems for state space symmetric systems using a particular solution of the bounded real lemma for an open loop symmetric system we obtain an explicit expression to compute the h norm of the system for the output feedback stabilization problem we obtain an explicit parametrization of all asymptotically stabilizing control gains of state space symmetric systems for the h control synthesis problem we derive an explicit expression for the optimally achievable closed loop h norm and the optimal control gains extension to robust and positive real control of such systems are also examined these results are obtained from the linear matrix inequality formulations of the stabilization and the h control synthesis problems using simple matrix algebraic tools