Showing papers on "Feedback linearization published in 1978"
TL;DR: In this paper, the problem of finding invariants under nonlinear feedback for systems of the form x ˙ = f ( x ) + ∑ u i g i (x ) ; f ( 0 ) = 0 is investigated and the invariants found here describe a degree of intrinsic nonlinearity of a control system.
385 citations
01 Jan 1978
TL;DR: In this paper, a general approach is developed for the nonlinear control of multivariable systems such that the transient responses exhibit the desired properties, and the closed loop systems are asymptotically stable.
Abstract: It is often desirable to have controllers which respond fast to large errors and which respond slowly to the small errors that are often due to sensor noise. Some nonlinear controllers having these properties are developed here by modifying optimal linear state feedback controllers so that they have state-dependent gains. A general approach is developed for the nonlinear control of multivariable systems such that the transient responses exhibit the desired properties, and the closed loop systems are asymptotically stable.
34 citations
TL;DR: In this paper, the authors compare statistical linearization, perturbation expansions, and projection operators for the approximate solution of nonlinear multimode stochastic equations, and show that the method of statistical linearisation is completely equivalent to the neglect of certain well-defined diagrams in the perturbations, resulting in the first Kraichnan-Wyld approximation.
Abstract: We compare the methods of statistical linearization, perturbation expansions, and projection operators for the approximate solution of nonlinear multimode stochastic equations. The model equations we choose for this comparison are coupled, nonlinear, first-order, one-dimensional complex mode rate equations. We show that the method of statistical linearization is completely equivalent to the neglect of certain well-defined diagrams in the perturbation expansion resulting in the first Kraichnan-Wyld approximation, and to the retention of only Markovian terms in the projection operator method, i.e., those terms that are local in time.
11 citations
01 Mar 1978
TL;DR: In this article, a synthesis theory for feedback systems with nonlinear uncertain plants to satisfy prescribed output tolerances is presented, where the essence of the theory is to convert the nonlinear plant set to a linear time-invariant one for which a design procedure exists.
Abstract: : A synthesis theory for feedback systems with nonlinear uncertain plants to satisfy prescribed output tolerances is presented. The essence of the theory is to convert the nonlinear plant set to a linear time-invariant one for which a design procedure exists. Schauder's fixed point theorem is applied to prove the equivalence of these two plant sets.
10 citations