Abstract
The paper presents some connections between the solvability conditions expressed in terms of linear matrix inequalities and the ones using Riccati equations. It is shown that the methodology based on the Bounded Real Lemma, mainly used in the singular H∞ control theory, can be successfully employed in nonsingular problems, providing solvability conditions in terms of the stabilizing solutions to algebraic Riccati equations.
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References
Adamjan, V.M., D.Z. Arov and M.G. Krein (1978). Infinite block Hankel matrices and related extension problems. AMS Transi., Vol. 111, 133–156.
Anderson, B.D.O. and S. Vongpanitlerd (1973). Network Analysis. Prentice Hall, Englewood Cliffs.
Ball, J.A. and J.W. Helton (1983). A Beurling-Lax theorem for the Lie group U(m,n) which contains most classical interpolation theory. J. Op. Theory, Vol. 9,107–142.
Boyd, S., L. El-Ghaoui, E. Feron and V. Balakrishnan (1994). Linear matrix inequalities in systems and control theory. Studies in Applied Mathematics, SIAM, Philadelphia, PA, Vol. 15.
Doyle, J.C., K. Glover, P. Khargonekar and P. Francis (1989). State-space solutions to standard H 2 and H ∞ control problem. IEEE-Trans-Autom. Control, Vol. 34, 831–848.
Francis, B.A. (1986). A course in H ∞ control theory. Springer Verlag.
Gahinet, P. (1992). A New Representation of H ∞ Suboptimal Controllers. Rapport de Recherche, No. 1641, INRIA.
Gahinet, P. and P. Apkarian (1994). A linear matrix inequality approach to H ∞ control. International journal Robust and Nonlinear Control, No. 4,421–448.
Glover, K. and J.C. Doyle (1988). State-space formulae for all stabilizing controllers that satisfy an H ∞-norm bound and relations to risk sensitivity. Systems & Control Letters, Vol. 11,167–172.
Ionescu, V., C. Oara and M. Weiss (1999). Generalised Riccati Theory and Robust Control: A Popov Function Approach, John Wiley, 1999.
Ionescu, V. and A. Stoica (1999). Robust Stabilisation and H ∞ Problems. Kluwer Academic Publishers, 1999.
Iwasaki, T. and R.E. Skelton (1994). All controllers for the general H ∞ control problem: LMI existence conditions and state pace formulas. Automatica, Vol. 30,1307–1317.
Kwakernaak, H. (1986). A polynomial approach to minimax frequency domain optimization of multivariable feedback systems,Int. J. Contr., Vol. 44,117–156.
Sampei, M., T. Mita and M. Nakamichi (1990). An algebraic approach to H ∞ output feedback control problems. Systems & Control Letters, Vol. 14,13–24.
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Stoica, A. (2004). On The Connection Between Riccati Inequalities And Equations In H ∞ Control Problems. In: Voicu, M. (eds) Advances in Automatic Control. The Springer International Series in Engineering and Computer Science, vol 754. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-9184-3_24
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DOI: https://doi.org/10.1007/978-1-4419-9184-3_24
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-4827-6
Online ISBN: 978-1-4419-9184-3
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