zbMATH — the first resource for mathematics

Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Static output feedback stabilisation with $H_{\infty}$ performance for a class of plants. (English) Zbl 0974.93054
Summary: The problem of static output feedback control of a linear system is considered. The existence of a static output feedback control law is given in terms of the solvability of two coupled Lyapunov inequalities which result in a nonlinear optimisation problem. However, using state-coordinate and congruence transformations and by imposing a block-diagonal structure on the Lyapunov matrix, we will see that the determination of a static output feedback gain reduces, for a specific class of plants, to finding the solution of a system of linear matrix inequalities. The class of plants considered is those which are minimum phase with a full row rank Markov parameter. The method is extended to incorporate $H_{\infty}$ performance objectives. This results in a sub-optimal static $H_{\infty}$ control law found by non-iterative means. The simplicity of the method is demonstrated by a numerical example.

MSC:
 93D15 Stabilization of systems by feedback 93B36 $H^\infty$-control 15A39 Linear inequalities of matrices 93B17 System transformation
LMI toolbox
Full Text:
References:
 [1] Benton, R. E.; Smith, D.: Static output feedback stabilization with prescribed degree of stability. IEEE trans. Automat. control 43, No. 10, 1493-1496 (1998) · Zbl 0956.93022 [2] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, SIAM studies in applied mathematics. (1994) · Zbl 0816.93004 [3] Cao, Y. Y.; Sun, Y. X.: Static output feedback simultaneous stabilization: ilmi approach. Int. J. Control 70, No. 5, 803-814 (1998) · Zbl 0930.93066 [4] Davis, C.; Kahan, W. M.; Weinberger, H. F.: Norm-preserving dilations and their applications to optimal error bounds. SIAM J. Numer. anal. 19, No. 3, 445-469 (1982) · Zbl 0491.47003 [5] P. Gahinet, A. Nemirovski, A.J. Laub, M. Chilali, LMI Control Toolbox, The Math Works, May 1995. [6] J.C. Geromel, P.L.D. Perez, R. Souza, Output feedback stabilisation of uncertain systems through a min/max problem, IFAC World Congress, 1993. [7] Geromel, J. C.; Souza, R.; Skelton, R. E.: Static output feedback controllers: stability and convexity. IEEE trans. Automat. control 43, No. 1, 120-125 (1998) · Zbl 0952.93106 [8] Iwasaki, T.; Skelton, R. E.: All controllers for the general H$\infty$control problem: LMI existence conditions and state space formulas. Automatica 30, No. 8, 1307-1317 (1994) · Zbl 0806.93017 [9] Iwasaki, T.; Skelton, R. E.; Geromel, J. C.: Linear quadratic suboptimal control with static output feedback. System control lett. 23, 421-430 (1994) · Zbl 0873.49021 [10] Kar, I. N.: Design of static output feedback controller for uncertain systems. Automatica 35, No. 1, 169-175 (1999) · Zbl 0945.93603 [11] Packard, A.; Doyle, J. C.: The complex structured singular value. Automatica 29, No. 1, 71-109 (1993) · Zbl 0772.93023 [12] Scherer, C.; Gahinet, P.; Chilali, M.: Multi-objective output-feedback control via lmi optimization. IEEE trans. Automat. control 30, No. 8, 1307-1317 (1997) · Zbl 0883.93024 [13] Syrmos, V. L.; Abdallah, C. T.; Dorato, P.; Grigoriadis, K.: Static output feedback -- a survey. Automatica 33, No. 2, 125-137 (1997) · Zbl 0872.93036