Bounded input—bounded output stability of systems†

International Journal of Control (Impact Factor: 1.65). 07/1970; 12(1):65-72. DOI: 10.1080/00207177008931821


The bounded input-bounded output stability of nth-order systems is discussed in this work. In essence, one can demonstrate such stability when it is possible to construct a Liapunov function V whose total time derivative under the forcing function can be given by [Vdot] ≤ rV + sV where r and s are positive constants. This differential inequality implies a bounded response, and bounded input—bounded output stability is demonstrated via this method for an asymptotically stable constant coefficient system, an asymptotically stable linear periodic system, a forced non-linear system of the Lurie type that satisfies a Popov-type condition,, and a linear time-varying system satisfying a circle criterion. While similar results have been obtained (Kalman and Bertram 1960, Sandberg 1964 a, 1965 a, b. Zames 1965), the approach used in this work following that of Goldwyn et, al. (1966) has been extended to distributed parameter networks and systems (de Figueiredo and Chao 1969) and has been used in the study of global properties of non-Hurwitzian control systems (de Figueiredo and Dutertre 1970).

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    ABSTRACT: A general method is developed for constructing regions of practical stability for nonlinear lumped-parameter systems. The region of practical stability serves as a bound on the system response for a general class of magnitude-constrained disturbances. The construction method is based on a modified Liapunov approach but is not restricted to a particular type of Liapunov function. The method is applicable to higher order systems in which several disturbance variables are present. Numerical results are presented for a CSTR with magnitude-constrained disturbances in feed composition and feed temperature. On a mis au point une méthode générale pour ériger des zones de stabilité pratique dans le cas de systèmes non-linéaires de paramètres mis en block. La zone de stabilité pratique sert de limite à la réaction du système pour une catégorie générale de perturbations d'ampleur restreinte. La méthode utilisée pour l'établissement des dites zones est basée sur la technique de Liapunov modifiée et ne se limite pas à un genre particulier de fonction de Liapunov; elle s'applique à des systèmes d'ordre plus élevé où l'on rencontre plusieurs variables de perturbation. On présente des résultats numériques dans le cas d'un réacteur à réservoir agité constamment où il se produit des perturbations d'ampleur restreinte dans la composition et la température d'alimentation.
    No preview · Article · Aug 1971 · The Canadian Journal of Chemical Engineering