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Analysis and design for robust performance with structured uncertainty. (English) Zbl 0768.93065
Summary: Necessary and sufficient conditions for stability and performance robustness of discrete-time systems are provided in terms of the spectral radius of a certain nonnegative matrix. The conditions are easily computable and provide a simple and efficient method for computation of the robustness conditions for SISO as well MIMO perturbations. The problem of robust controller synthesis is explored, and an iteration scheme for controller synthesis is introduced.

93D09 Robust stability
93B36 \(H^\infty\)-control
93B50 Synthesis problems
93C55 Discrete-time control/observation systems
Full Text: DOI
[1] Dahleh, M.A.; Ohta, Y., A necessary and sufficient condition for robust BIBO stability, (), 271-275 · Zbl 0654.93057
[2] Dahleh, M.A.; Pearson, J.B., \(λ\^{}\{1\}\) optimal feedback controllers for mino discrete time systems, IEEE trans. automat. control., 32, 4, 314-322, (April 1987)
[3] Doyle, J.C., Analysis of feedback systems with structured uncertainty, (), 242-250, 6
[4] Doyle, J.C.; Wall, J.E.; Stein, G., Performance and robustness analysis for structured uncertainty, (), 629-636
[5] Horn, R.; Johnson, C., Matrix analysis, (1985), Cambridge University Press · Zbl 0576.15001
[6] Khammash, M.; Pearson, J.B., Robust disturbance rejection in \(λ\^{}\{1\}- optimal\) control systems, Systems control lett., 14, 93-101, (1990) · Zbl 0692.93029
[7] Khammash, M., Stability and performance robustness of discrete-time systems with structured uncertainty, () · Zbl 0800.93994
[8] Khammash, M.; Pearson, J.B., Performance robustness of discrete-time systems with structured uncertainty, IEEE trans. automat. control, 36, 398-412, (April 1991)
[9] Khammash, M.; Pearson, J.B., Robustness in the presence of structured uncertainty, (), 337-342
[10] Khammash, M.; Pearson, J.B., Robustness synthesis for discrete-time systems with structured uncertainty, (), 2720-2724
[11] McDonald, J.S.; Pearson, J.B., \(λ\^{}\{1\}\) optimal control of multivariable systems with output norm constraints, Automatica, 27, 2, 317-329, (1991) · Zbl 0735.49029
[12] Mendlovitz, M., A simple solution to the \(λ\^{}\{1\}\) optimization problem, Systems control lett., 12, 5, 461-463, (June 1989)
[13] Safonov, M.G., Robustness and stability aspects of stochastic multivariable feedback system design, ()
[14] Safonov, M.G.; Athans, M., A multiloop generalization of the circle criterion for stability margin analysis, IEEE trans. automat. control, 26, 415-422, (April 1981)
[15] Safonov, M., Stability margins of diagonally perturbed multivariable feedback systems, (), 251-256, 6
[16] Staffans, O.J., Mixed sensitivity minimizatwion problems with rational \(λ1- optimal\) solutions, J. optim. theory appl., 70, 173-189, (1991) · Zbl 0743.90105
[17] Staffans, O.J., On the four-black model matching problem in \(λ1\), ()
[18] Varga, R., Matrix iterative analysis, (1963), Prentice-Hall Englewood Cliffs, NJ
[19] Vidyasagar, M., Input-output analysis of large-scale interconnected systems, () · Zbl 0454.93002
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