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Clocks and Insensitivity to Small Measurement Errors

Eduardo D. Sontag (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with the problem of stabilizing a system in the presence of small measurement errors. It is known that, for general stabilizable systems, there may be no possible memoryless state feedback which is robust with respect to such errors. In contrast, a precise result is given here, showing that, if a (continuous-time, finite-dimensional) system is stabilizable in any way whatsoever (even by means of a dynamic, time varying, discontinuous, feedback) then it can also be semiglobally...

Closed-loop structure of decouplable linear multivariable systems

Javier Ruiz, Jorge Luis Orozco, Ofelia Begovich (2005)

Kybernetika

Considering a controllable, square, linear multivariable system, which is decouplable by static state feedback, we completely characterize in this paper the structure of the decoupled closed-loop system. The family of all attainable transfer function matrices for the decoupled closed-loop system is characterized, which also completely establishes all possible combinations of attainable finite pole and zero structures. The set of assignable poles as well as the set of fixed decoupling poles are determined,...

Complementary matrices in the inclusion principle for dynamic controllers

Lubomír Bakule, José Rodellar, Josep M. Rossell (2003)

Kybernetika

A generalized structure of complementary matrices involved in the input-state- output Inclusion Principle for linear time-invariant systems (LTI) including contractibility conditions for static state feedback controllers is well known. In this paper, it is shown how to further extend this structure in a systematic way when considering contractibility of dynamic controllers. Necessary and sufficient conditions for contractibility are proved in terms of both unstructured and block structured complementary...

Continuous-time input-output decoupling for sampled-data systems

Osvaldo Maria Grasselli, Laura Menini (1999)

Kybernetika

The problem of obtaining a continuous-time (i. e., ripple-free) input-output decoupled control system for a continuous-time linear time-invariant plant, by means of a purely discrete-time compensator, is stated and solved in the case of a unity feedback control system. Such a control system is hybrid, since the plant is continuous-time and the compensator is discrete-time. A necessary and sufficient condition for the existence of a solution of such a problem is given, which reduces the mentioned...

Continuous-time periodic systems in H 2 and H . Part II: State feedback problems

Patrizio Colaneri (2000)

Kybernetika

This paper deals with some state-feedback H 2 / H control problems for continuous time periodic systems. The derivation of the theoretical results underlying such problems has been presented in the first part of the paper. Here, the parametrization and optimization problems in H 2 , H and mixed H 2 / H are introduced and solved.

Control Lyapunov functions and stabilization by means of continuous time-varying feedback

Iasson Karafyllis, John Tsinias (2009)

ESAIM: Control, Optimisation and Calculus of Variations

For a general time-varying system, we prove that existence of an “Output Robust Control Lyapunov Function” implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the resulting closed-loop system. The main results of the present work constitute generalizations of a well known result due to Coron and Rosier [J. Math. Syst. Estim. Control 4 (1994) 67–84] concerning stabilization of autonomous systems by means of time-varying periodic...

Control Lyapunov functions and stabilization by means of continuous time-varying feedback

Iasson Karafyllis, John Tsinias (2008)

ESAIM: Control, Optimisation and Calculus of Variations

For a general time-varying system, we prove that existence of an “Output Robust Control Lyapunov Function” implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the resulting closed-loop system. The main results of the present work constitute generalizations of a well known result due to Coron and Rosier [J. Math. Syst. Estim. Control4 (1994) 67–84] concerning stabilization of autonomous systems by means of time-varying...

Control Systems on the Orthogonal Group SO(4)

Ross M. Adams, Rory Biggs, Claudiu C. Remsing (2013)

Communications in Mathematics

We classify the left-invariant control affine systems evolving on the orthogonal group S O ( 4 ) . The equivalence relation under consideration is detached feedback equivalence. Each possible number of inputs is considered; both the homogeneous and inhomogeneous systems are covered. A complete list of class representatives is identified and controllability of each representative system is determined.

Correcteurs proportionnels-intégraux généralisés

Michel Fliess, Richard Marquez, Emmanuel Delaleau, Hebertt Sira-Ramírez (2002)

ESAIM: Control, Optimisation and Calculus of Variations

Nous introduisons pour les systèmes linéaires constants les reconstructeurs intégraux et les correcteurs proportionnels-intégraux généralisés, qui permettent d’éviter le terme dérivé du PID classique et, plus généralement, les observateurs asymptotiques usuels. Notre approche, de nature essentiellement algébrique, fait appel à la théorie des modules et au calcul opérationnel de Mikusiński. Plusieurs exemples sont examinés.

Correcteurs proportionnels-intégraux généralisés

Michel Fliess, Richard Marquez, Emmanuel Delaleau, Hebertt Sira–Ramírez (2010)

ESAIM: Control, Optimisation and Calculus of Variations

For constant linear systems we are introducing integral reconstructors and generalized proportional-integral controllers, which permit to bypass the derivative term in the classic PID controllers and more generally the usual asymptotic observers. Our approach, which is mainly of algebraic flavour, is based on the module-theoretic framework for linear systems and on operational calculus in Mikusiński's setting. Several examples are discussed.

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