zbMATH — the first resource for mathematics

Controller design for plants with structured uncertainty. (English) Zbl 0772.93028
Summary: This paper addresses the problem of designing feedback controllers to achieve good performance in the presence of structures plant uncertainty and bounded but unknown disturbances. A general formulation for the performance robustness problem is presented and exact computable conditions are furnished. These conditions are then utilized for synthesizing robust controllers which involves solving \(\ell_ 1\) optimization problems. These solutions are computed using the duality theory of Lagrange multipliers. Approximations and computational issues are discussed.

93B51 Design techniques (robust design, computer-aided design, etc.)
93B05 Controllability
93B50 Synthesis problems
Full Text: DOI
[1] Bamieh, B.A.; Dahleh, M., On robust stability with structured time-invariant perturbations, Syst. contr. lett., (1993), (Submitted.) · Zbl 0785.93071
[2] Bamieh, B.A.; Dahleh, M.A.; Pearson, J.B., Minimization of the L∞-induced norm for sampled-data systems, IEEE trans. aut. control, (1992), (To appear.)
[3] Boyd, S.P.; Barratt, C.H., ()
[4] Boyd, S.P.; Doyle, J.C., Comparison of peak and RMS gains for discrete-time systems, Syst. contr. lett., 9, 1-6, (1987) · Zbl 0644.93050
[5] Dahleh, M.A., BIBO stability robustness for coprime factor perturbations, IEEE trans. aut. control, 37, 352-355, (1992)
[6] Dahleh, M.; Dahleh, M.A., Optimal rejection of persistent and bounded disturbances: continuity properties and adaptation, IEEE trans. aut. control, 35, 687-696, (1990) · Zbl 0800.93655
[7] Dahleh, M.A.; Pearson, J.B., ℓ^{1} optimal feedback controllers for MIMO discrete-time systems, IEEE trans. aut. control, 32, 314-322, (1987) · Zbl 0622.93041
[8] Dahleh, M.A.; Pearson, J.B., Optimal rejection of persistent disturbances, robust stability and mixed sensitivity minimization, IEEE trans. aut. control, 33, 722-731, (1988) · Zbl 0657.93019
[9] Dahleh, M.A.; Pearson, J.B., Minimization of a regulated response to a fixed input, IEEE trans. aut. control, 33, 924-930, (1988) · Zbl 0675.93005
[10] Dahleh, M.A.; Ohta, Y., A necessary and sufficient condition for robust BIBO stability, Syst. contr. lett., 11, 271-275, (1988) · Zbl 0654.93057
[11] Dahleh, M.A.; Richards, D., Application of modern control theory on a model of the X-29 aircraft, ()
[12] Dahleh, M.A.; Voulgaris, P.; Valavani, L., Optimal and robust controllers for periodic and multi-rate systems, IEEE trans. aut. control, 37, 90-99, (1992) · Zbl 0747.93028
[13] Dahleh, M.A.; Elia, N.; Diaz-Bobillo, I., Controller design via linear programming, (1993), (In preparation.)
[14] Deodhare, G.; Vidyasagar, M., Some results on ℓ_{1}-optimality of feedback control systems: the SISO discrete-time case, IEEE trans. aut. control, 35, 1082-1085, (1990) · Zbl 0724.93038
[15] Desoer, C.A.; Vidyasagar, M., ()
[16] Doyle, J.C., Analysis of feedback systems with structured uncertainty, (), 242-250
[17] Doyle, J.C.; Stein, G., Multivariable feedback design: concepts for a classical/modern synthesis, IEEE-trans. A-C, 26, 4-16, (1981) · Zbl 0462.93027
[18] Doyle, J.C.; Glover, K.; Khargonekar, P.P.; Francis, B.A., State space solutions to standard H2 and H∞ control problems, IEEE trans. aut. control, 34, 831-847, (1989) · Zbl 0698.93031
[19] Diaz-Bobillo, I.; Dahleh, M.A., State feedback ℓ_{1} optimal controllers can be dynamic, (), Report No. LIDS-P-2051. (To appear.) · Zbl 0767.93030
[20] Diaz-Bobillo, I.; Dahleh, M.A., Minimization of the maximum peak-to-peak gain: the general multiblock problem, IEEE trans. aut. control, (1992), (To appear) · Zbl 0810.49035
[21] Dullerud, G.; Francis, B.A., \(L\^{}\{1\}\) analysis and design of sampled-data systems, IEEE trans. aut. control, 37, 436-446, (1992) · Zbl 0756.93053
[22] Francis, B.A., ()
[23] Glover, K.; McFarlane, D., Robust stabilization of normalized coprime factor plant description with H∞ bounded uncertainty, IEEE trans. aut. control, 34, 830-831, (1989) · Zbl 0698.93063
[24] Horn, R.; Johnson, C., ()
[25] Khammash, M., Necessary and sufficient conditions for the robustness of time-varying systems with applications to sampled-data systems, IEEE trans. aut. control, (1992), (To appear.)
[26] Khammash, M.; Pearson, J.B., Robust disturbance rejection in ℓ^{1}-optimal control systems, Syst. contr. lett., 14, 93-101, (1990) · Zbl 0692.93029
[27] Khammash, M.; Dahleh, M., Time-varying control and the robust performance of systems with structured norm-bounded uncertainty, Automatica, (1993), (To appear.)
[28] Khammash, M.; Pearson, J.B., Performance robustness of discrete-time systems with structured uncertainty, IEEE trans. aut. control, 36, 398-412, (1991) · Zbl 0754.93063
[29] Khammash, M.; Pearson, J.B., Robustness synthesis for discrete-time systems with structured uncertainty, (), 2720-2724
[30] Khammash, M.; Pearson, J.B., Analysis and design of robust performance with structured uncertainty, Syst. contr. lett., (1992), (To appear.) · Zbl 0768.93065
[31] Luenberger, D.G., ()
[32] McDonald, J.S.; Pearson, J.B., ℓ_{1}-optimal control of multivariable systems with output norm constraints, Automatica, 27, 317-329, (1991) · Zbl 0735.49029
[33] Mendlovitz, M.A., A simple solution to the ℓ_{1} optimization problem, Syst. contr. lett., 12, 461-463, (1989) · Zbl 0678.90056
[34] Packard, A.; Doyle, J.C., The complex structured singular value, Automatica, (1992), (To appear.) · Zbl 0772.93023
[35] Shamma, J., Robust stability with time-varying structured uncertainty, IEEE trans. aut. control, (1992), (Submitted.)
[36] Sivashankar, N.; Khargonekar, P., \(L∞ -induced\) norm of sampled-data systems, () · Zbl 0802.93017
[37] Staffans, O.J., On the four-block model matching problem in ℓ_{1}, ()
[38] Staffans, O.J., Mixed sensitivity minimization problems with rational ℓ_{1}-optimal solutions, J. of optimization theory and applications, 70, 173-189, (1991) · Zbl 0743.90105
[39] Vidyasagar, M., Input-output analysis of large-scale interconnected systems, () · Zbl 0454.93002
[40] Vidyasagar, M., ()
[41] Vidyasagar, M., Optimal rejection of persistent bounded disturbances, IEEE trans. aut. control, 31, 527-534, (1986) · Zbl 0594.93050
[42] Voulgaris, P.; Dahleh, M.A.; Valavani, L., Slowly-varying systems: ℓ_{∞} to ℓ∞ performance implications to adaptive control, Automatica, (1993), (Submitted.)
[43] Willems, J.C., ()
[44] Youla, D.C.; Jabr, H.A.; Bongiorno, J.J., Modern Wiener-Hopf design of optimal controllers—part 2: the multivariable case, IEEE trans. aut. control, 21, 319-338, (1976) · Zbl 0339.93035
[45] Zames, G., Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses, IEEE trans. aut. control, 26, 301-320, (1981) · Zbl 0474.93025
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.