Abstract
We extend earlier results on the Dynamic Disturbance Decoupling Problem via regular feedback to nonsquare, noninvertible systems. Instrumental in the solution of the problem is the so called Singh’s algorithm and what we like to call a Singh compensator. The theory developed is illustrated by means of two examples. Moreover, we make some remarks about the solution of the Dynamic Disturbance Decoupling Problem via nonregular feedback.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
G. Basile and G. Marro, Controlled and conditioned invariant subspaces in linear system theory, J. Optimiz. Theory Appl, 3, (1969), pp. 306–315.
S.P. Bhattacharyya, Disturbance rejection in linear systems, Int. J. Control, 5, (1974), pp. 633–637.
M.D. di Benedetto, J.W. Grizzle and C.H. Moog, Rank invariants of nonlinear systems, SIAM J. Control Optimiz., 27, (1989), pp. 658–672.
R.M. Hirschorn, Invertibility of Multivariable Nonlinear Control Systems, IEEE Trans. Automat. Control, AC-24, (1979), pp. 855–865.
H.J.C. Huijberts, H. Nijmeijer and L.L.M. van der Wegen, Dynamic disturbance decoupling for nonlinear systems, Memo.no. 835, Department of Applied Mathematics, University of Twente, (1989). Submitted for publication.
H.J.C. Huijberts, A nonregular solution of the nonlinear dynamic disturbance decoupling problem with an application to a complete solution of the nonlinear model matching problem, Memo.no. 862, Department of Applied Mathematics, University of Twente. Submitted for publication.
A. Isidori and C.H. Moog, On the nonlinear equivalent of the notion of transmission zeros, in Modelling and Adaptive Control, C.I. Byrnes and A. Kurzhanski, eds., Lecture Notes in Control and Information Sciences, 105, Springer, Berlin, 1988, pp. 146–158.
A. Isidori, Nonlinear Control Systems (Second Edition), Springer, Berlin, (1989).
C.H. Moog, Nonlinear Decoupling and Structure at Infinity, Math. Control Signals Systems, 1, (1988), pp. 257–268.
H. Nijmeijer and A.J. van der Schaft, Nonlinear Dynamical Control Systems. Springer, New York, (1990).
A.J. van der Schaft, On clamped dynamics of nonlinear systems, in Analysis and Control of Nonlinear Systems, C.I. Byrnes, C.F. Martin and R.E. Saeks, eds., Elsevier, Amsterdam, (1988), pp. 499–506.
S.N. Singh, A Modified Algorithm for Invertibility in Nonlinear Systems, IEEE Trans. Automat. Control, AC-26, (1981), pp. 595–598.
W.M. Wonham, Linear Multivariable Control: a Geometric Approach (Third Edition), Springer, New York, (1985).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Birkhäuser Boston
About this chapter
Cite this chapter
Huijberts, H.J.C., Nijmeijer, H., van der Wegen, L.L.M. (1991). Dynamic disturbance decoupling for nonlinear systems: The nonsquare and noninvertible case. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_21
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3214-8_21
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7835-1
Online ISBN: 978-1-4612-3214-8
eBook Packages: Springer Book Archive