Abstract
In many engineering problems the plant is known only approximately. It is important to know therefore that the system will perform adequately if the true plant is only approximately equal to the model or nominal plant around which the system is designed. This is particularly crucial with regard to the issue of stability. In this chapter we show how one particular form of this robust stability issue reduces to an interpolation problem which in turn can be solved explicitly via the formalism developed in Chapter 18.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Notes for Part VI
J. Doyle and G. Stein [ 1981 ], Multivariable feedback design: concepts for a classical/modern synthesis, IEEE Trans. Auto. Control AC26, 4–16.
M.T. Chen and C.A. Desoer [ 1982 ], Necessary and safficient conditions for robust stability of linear distributed feedback systems, Int. J. Control 35, 255–267.
M. Vidyasagar [ 1985 ], Control System Synthesis: a Factorization Approach, The MIT Press, Cambridge, MA.
A. Bhaya and C.A. Desoer [ 1986 ], Necessary and sufficient conditions on Q (= C(I + PC) -1 ) for stabilization of the linear feedback system S(P, C), Systems and Control Letters 7, 35–38.
H. Kimura [ 1984 ], Robust stabilizability for a class of transfer functions, IEEE Trans. Auto. Control AC-29, 788–793.
M. Vidyasagar and H. Kimura [ 1986 ], Robust controllers for uncertain linear multivariable systems, Automatica 22, 85–94.
K. Glover [ 1986 ], Robust stabilization of linear multivariable systems: relations to approximation, Int. J. Control 43, 741–766.
R. Curtain and K. Glover [ 1986 ], Robust stabilization of infinite dimensional systems by finite dimensional controllers, Systems and Control Letters 7, 41–47.
M.S. Verma [ 1989 ], Robust stabilization of linear time-invariant systems, IEEE Trans. Auto. Control 34, 870–875.
K. Glover and D. McFarlane [ 1989 ], Robust stabilization of normalized coprirne factor plant descriptions with H∞-bounded uncertainty, IEEE Trans. Auto. Control 34, 821–830.
J. Doyle [ 1981 ], Analysis of feedback systems with structured uncertainty, IEEE Proc. 129D, 242–250.
B.A. Francis [ 1987 ], A Course in H >∞ Control Theory, Springer-Verlag, BerlinHeidelberg-New York.
J.C. Doyle, K. Glover, P.P. Khargonekar and B.A. Francis [ 1989 ], State space solutions to standard H2 and H∞, control problems, IEEE Trans. Auto. Control AC-34, 831–847.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer Basel AG
About this chapter
Cite this chapter
Ball, J.A., Gohberg, I., Rodman, L. (1990). Robust Stabilization. In: Interpolation of Rational Matrix Functions. Operator Theory: Advances and Applications, vol 45. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7709-1_26
Download citation
DOI: https://doi.org/10.1007/978-3-0348-7709-1_26
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-7711-4
Online ISBN: 978-3-0348-7709-1
eBook Packages: Springer Book Archive