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\(H_{\infty }\) and bibo stabilization of delay systems of neutral type. (English) Zbl 1157.93367
Summary: Frequency-domain tests for the \(H_{\infty }\) and BIBO stability of large classes of delay systems of neutral type are derived. The results are applied to discuss the stabilizability of such systems by finite-dimensional controllers.

93B36 \(H^\infty\)-control
93C23 Control/observation systems governed by functional-differential equations
93D25 Input-output approaches in control theory
Full Text: DOI
[1] Bellman, R; Cooke, K.L, Differential-difference equations, (1963), Academic Press New York · Zbl 0118.08201
[2] V. Blondel, Simultaneous Stabilization of Linear Systems, Lecture Notes in Control and Information Sciences, Vol. 191, Springer, London, 1994. · Zbl 0795.93083
[3] Bonnet, C; Partington, J.R, Bézout factors and L1-optimal controllers for delay systems using a two-parameter compensator scheme, IEEE trans. automat. control, 44, 1512-1521, (1999) · Zbl 0959.93052
[4] Bonnet, C; Partington, J.R, Analysis of fractional delay systems of retarded and neutral type, Automatica, 38, 1133-1138, (2002) · Zbl 1007.93065
[5] Curtain, R.F; Glover, K, Robust stabilization of infinite-dimensional systems by finite-dimensional controllers, Systems control lett., 7, 1, 41-47, (1986) · Zbl 0601.93044
[6] R.F. Curtain, H. Zwart, An Introduction to Infinite-dimensional Linear Systems Theory, Texts in Applied Mathematics, Vol. 21, Springer, New York, 1995. · Zbl 0839.93001
[7] Desoer, C.A; Vidyasagar, M, Feedback systems: input – output properties, (1975), Academic Press New York · Zbl 0327.93009
[8] Georgiou, T.T; Smith, M.C, Graphs, causality, and stabilizability: linear, shift-invariant systems on \(L2[0,∞)\), Math. control signals systems, 6, 195-223, (1993) · Zbl 0796.93004
[9] Loiseau, J.-J; Cardelli, M; Dusser, X, Neutral-type time-delay systems that are not formally stable are not BIBO stabilizable, IMA J. math. control inform., 19, 217-227, (2002) · Zbl 1001.93072
[10] Marshall, J.E; Górecki, H; Walton, K; Korytowski, A, Time-delay systems: stability and performance criteria with applications, (1992), Ellis Horwood London · Zbl 0769.93001
[11] O’Connor, D.A; Tarn, T.J, On stabilization by state feedback for neutral differential-difference equations, IEEE trans. automat. control, 28, 5, 615-618, (1983) · Zbl 0527.93049
[12] Partington, J.R; Glover, K, Robust stabilization of delay systems by approximation of coprime factors, Systems control lett., 14, 4, 325-331, (1990) · Zbl 0699.93078
[13] Partington, J.R; Mäkilä, P.M, Worst-case analysis of identification—BIBO robustness for closed-loop data, IEEE trans. automat. control, 39, 10, 2171-2176, (1994) · Zbl 0925.93149
[14] A. Quadrat, Une approche de la stabilisation par l’analyse algébrique: III. Sur une structure générale des contrôleurs stabilisants basée sur le rang stable, Conférence Internationale Francophone d’Automatique (CIFA), Nantes, France, 2002.
[15] Treil, S, The stable rank of the algebra H∞ equals 1, J. funct. anal., 109, 1, 130-154, (1992) · Zbl 0784.46037
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