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A simulation technique for checking the circle criterion
Systems & Control Letters, 1984 The paper deals with checking the \(L_ 2\)-stability of single-input single-output systems, which consists of a linear forward path and a nonlinear element in the feedback satisfying a sector constraint. For these systems, the circle criterion is well established for checking the stability.
Owens, D. H., Chotai, A.
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A Circle Criterion Generalization for Relative Stability
IEEE Transactions on Automatic Control, 1968It is shown that the circle criterion for linear systems containing a single time-varying element corresponds to a specialization of the Popov stability theory. The circle criteria are generalized using the Popov theory to give some measure of the degree of the system stability.
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Conservatism of the circle criterion-solution of a problem posed by A. Megretski
IEEE Transactions on Automatic Control, 2001 In the collection of open problems in mathematical systems and control theory [1], Megretski poses a problem related to the degree of conservativism of the well-known circle criterion follows. We solve this problem.
Rump, Siegfried M.
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2007 46th IEEE Conference on Decision and Control, 2007
The paper deals with the classical problem of the absolute stability in a SISO Lur'e system. The circle criterion is applied to different overlapping sectors and then, for all the functions in the 'union sector', a set of constraints is defined, so that they make globally asymptotically stable the closed loop system.
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The paper deals with the classical problem of the absolute stability in a SISO Lur'e system. The circle criterion is applied to different overlapping sectors and then, for all the functions in the 'union sector', a set of constraints is defined, so that they make globally asymptotically stable the closed loop system.
D. Materassi +3 more
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From the Nyquist Criterion to the Circle Criterion
IFAC Proceedings Volumes, 1996Abstract The Circle Criterion is a well-known sufficient condition for the exponential stability of a particular class of time varying systems. J.L. Willems proposed a criterion which in some sense links the Circle Criterion with the Nyquist Criterion. The proof invoh'es a time varying Liapunov function with semi-definite time derivative. In order to
R. Sepulchre, D. Aeyels, J.L. Willems
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Circle criterion in linear control design
2008 American Control Conference, 2008This paper presents a method for higher-order controller design with improved low-frequent disturbance rejection properties. Given a default PID-based controller, the circle criterion is used to construct an extra controller part that deals with resonances resulting from closing the loop. The advantage is twofold. First, a closed-loop shaping method is
Marcel Heertjes, Maarten Steinbuch
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International Journal of Control, 1973
Abstract This paper considers a criterion for the stability of multivariable control systems consisting of a linear sub-system with an arbitrary finite number of time-varying, non-linear feedback elements. The criterion established in this paper is such that, it makes use of the ‘ circle criterion ’ to some extent and shows, through a further theorem ...
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Abstract This paper considers a criterion for the stability of multivariable control systems consisting of a linear sub-system with an arbitrary finite number of time-varying, non-linear feedback elements. The criterion established in this paper is such that, it makes use of the ‘ circle criterion ’ to some extent and shows, through a further theorem ...
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The multivariable circle criterion for switched continuous systems
42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2004Traditional developments of the multivariable circle criterion have assumed continuity of the nonlinearity. This paper shows that the stability results of the multivariable circle criterion are valid for systems described by differential inclusions. This result is motivated by examining the control of a one-dimensional actuator array system in which ...
Mark Bedillion, William C. Messner
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Uniform approximation and the circle criterion
IEEE Transactions on Automatic Control, 1993Summary: We consider the input-output maps \(G\) of causal time-invariant systems, and give a complete characterization of those \(G\)'s that can be uniformly approximated by the maps of certain simple structures. The criterion is that \(G\) must satisfy certain continuity and approximately-finite-memory conditions. It is proved that the conditions are
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