Discrete‐time output feedback for Markov jump systems with uncertain transition probabilities

This article addresses the output feedback control for discrete‐time Markov jump linear systems. With fully known transition probability, sufficient conditions for an internal model based controller design are obtained. For the case where the transition probabilities are uncertain and belong to a convex polytope with known vertices, we provide a sufficient LMI condition that guarantees the norm of the closed‐loop system is below a prescribed level. That condition can be improved through an iterative procedure. Additionally, we are able to deal with the case of cluster availability of the Markov mode, provided that some system matrices do not vary within a given cluster, an assumption that is suitable to deal with packet dropout models for networked control systems. A numerical example shows the applicability of the design and compares it with previous results. Copyright © 2012 John Wiley & Sons, Ltd.     

Design of dynamic output feedback decentralized controllers via a separation procedure

This paper investigates the well-known separation properties that hold in the design of unconstrained output feedback controllers and tries to generalize them to cope with the design of structurally constrained decentralized controls. This problem, which until now has been open, presents additional constraints which destroy the useful properties that lead to separation. Necessary and sufficient conditions for decentralized stability and H₂ norm minimization are given, providing a framework in which a suitable ad hoc separation procedure is developed. A numerical algorithm based on crossdecomposition is presented and applied in two situations: first, when separation fails to provide a feasible solution; and then, to improve the obtained controller. An example and a comprehensive benchmark illustrate and validate the method.     

Robust stability of time varying polytopic systems

This paper provides global asymptotic stability conditions for time-varying continuous-time polytopic systems, using a parameter dependent Lyapunov function. The time varying parameter uncertainty as well as its time derivative are modelled as belonging to polytopic convex sets and their dependence is made explicit to get less conservative results. A particular case, characterized by the parameter uncertainty satisfying a linear differential equation is analyzed and a simpler version of the aforementioned stability conditions is presented. The results are expressed in terms of linear matrix inequalities being thus numerically solvable with no big difficulty. The theory is illustrated by the determination of the asymptotic stability region of a Mathieu's type equation with an uncertain time varying parameter.     

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 objectives (also gain-scheduled controllers) can be addressed without employing a unique Lyapunov matrix to test all objectives (scheduled operation points). The theory is illustrated by several numerical examples.     

Convex analysis and global optimization of joint actuator locationand control problems

It is shown that the optimal value of the continuous-time linear-quadratic problem regarded as a function of the system model and index parameters exhibits properties (convexity, concavity, and monoticity) specially suitable for optimization purposes. Based on this fact, a procedure for the global solution determination of eventually nonconvex problems, involving the above-mentioned function, is proposed. Such problems embody some known designs, such as filtering under noise uncertainty or precision constraints and optimal actuator/sensor location. The last problem is deeply analyzed, and two practical applications, namely satellite attitude control and large flexible system control, are included     

H2-norm optimization with constrained dynamic outputfeedback controllers: decentralized and reliable control

This paper addresses some open problems in the area of dynamic output feedback control design. The first one is the structurally constrained decentralized control problem, and the second is related to robust and reliable control. A necessary and sufficient condition for decentralized and quadratic stabilizability is given and used to provide a solution to the H₂-norm optimization problem. A numerical cross decomposition algorithm is developed and satisfactorily applied to find the solution of some illustrative examples. A comprehensive benchmark validates the results     

Experimental and analytical assessment of the behavior of stainless steel reinforced concrete beams

This paper reports the results of a comprehensive experimental test program on high performance and standard AISI 316L stainless, steel reinforced concrete beams. Experimental results were compared with theoretical analysis data using current reinforcement mechanical feature standards and experimental testing-based ones, to identify any resistance, ductility and membrane collapse mode difference. It is also proved the importance of establishing a specific standard on the use of stainless steel reinforcement, in order to enable its more widespread, structural use, and not only for its corrosion resistance.

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Résumé Dans ce travail sont présentés les résultats d'un vaste programme d'essais expérimentaux réalisés, sur des poutres en béton armé normal et à haute résistance; toutes les poutres sont renforcées de barres d'acier inoxydable. Les résultats obtenus à partir de l'analyse expérimentale ont étés comparés avec ceux obtenus par une analyse théorique dans laquelle on a utilisé les valeurs des caractéristiques mécaniques de l'acier, soit standardisées, soit obtenues à partir de l'expérimentation, afin de mettre en évidence pour les poutres, les différences en termes de résistance, de ductilité et de mode de rupture.

     

2 guaranteed cost control for uncertain continuous-time linear systems

This paper proposes a solution to the ₂ guaranteed cost control problem for uncertain, continuous-time linear systems. It consists of the determination of a constant state feedback stabilizing matrix gain and a ₂-norm upper bound, valid for all feasible models. The uncertainties are only assumed to be convex-bounded, a concept which generalizes the important case of interval matrices uncertainties. The results follow from a new parameterization of all stabilizing gains over a convex set. As an additional property, the above mentioned ₂-norm upper bound reduces to the minimum ₂ cost in case of precisely known linear systems.     

Model reduction of discrete time systems through linear matrix inequalities*

In this paper, model reduction of discrete time linear systems is revisited. The main objective is to define a convex programming problem expressed in terms of linear matrix inequalities which provides a good suboptimal solution to the model reduction problem. The quality of the proposed suboptimal solution is assessed through comparisons, performed via simulation, with the already classical balanced truncation method. The results lead to the conclusion that the proposed method performs equivalently when the H ₂ norm of the reduction error is considered and significantly better when the H _∞ norm is considered instead.     

H2 and H∞ robust filtering for convexbounded uncertain systems

Investigates robust filtering design problems in H₂ and H_∞ spaces for continuous-time systems subjected to parameter uncertainty belonging to a convex bounded-polyhedral domain. It is shown that, by a suitable change of variables, both designs can be converted into convex programming problems written in terms of linear matrix inequalities. The results generalize the ones available in the literature to date in several directions. First, all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured. Then, assuming the order of the uncertain system is known, the optimal guaranteed performance H₂ and H_∞ filters are proven to be of the same order as the order of the system. A numerical example illustrate the theoretical results