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Stability analysis and synthesis of systems subject to norm bounded, bounded rate uncertainties. (English) Zbl 1249.93137
Summary: In this paper we consider a linear system subject to norm bounded, bounded rate time-varying uncertainties. Necessary and sufficient conditions for quadratic stability and stabilizability of such class of uncertain systems are well known in the literature. Quadratic stability guarantees exponential stability in presence of arbitrary time-varying uncertainties; therefore it becomes a conservative approach when, as it is the case considered in this paper, the uncertainties are slowly-varying in time. The first contribution of this paper is a sufficient condition for the exponential stability of the zero input system; such condition, which takes into account the bound on the rate of variation of the uncertainties, results to be a less conservative analysis tool than the quadratic stability approach. Then the analysis result is used to provide an algorithm for the synthesis of a controller guaranteeing closed loop stability of the uncertain forced system.

93D09 Robust stability
93C05 Linear systems in control theory
93B50 Synthesis problems
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[1] Amato F.: Stability analysis of systems subject to norm bounded, bounded rate uncertainties. Proc. of the 6th IEEE Mediterranean Conference on Control and Automation, Alghero 1998 · Zbl 1249.93137 · www.kybernetika.cz · eudml:33466
[2] Amato F., Corless M., Mattei M., Setola R.: A robust stability margin in the presence of time varying, bounded rate gains. Internat. J. Robust and Nonlinear Control 7 (1997), 127-143 <a href=”http://dx.doi.org/10.1002/(SICI)1099-1239(199702)7:23.0.CO;2-G” target=”_blank”>DOI 10.1002/(SICI)1099-1239(199702)7:23.0.CO;2-G | · Zbl 0866.93074
[3] Barmish B. R.: Stabilization of uncertain systems via linear control. IEEE Trans. Automat. Control AC-28 (1983), 848-850 · Zbl 0554.93054 · doi:10.1109/TAC.1983.1103324
[4] Boyd S., Ghaoui L. El, Feron E., Balakrishnan V.: Linear Matrix Inequalities in System and Control Theory. SIAM Press, 1994 · Zbl 0816.93004
[5] Corless M.: Robust stability analysis and controller design with quadratic Lyapunov functions. Variable Structure and Lyapunov Control (A. S. I. Zinober, Springer-Verlag, Berlin 1993 · Zbl 0803.93032
[6] Ghaoui L. El, Balakrishnan V.: Synthesis of fixed-structure controllers via numerical optimization. Proc. of the 33rd IEEE Conference on Decision and Control, Lake Buena Vista 1994, pp. 2678-2683
[7] Geromel J. C., Peres P. L. D., Bernussou J.: On a convex parameter space method for linear control design of uncertain systems. SIAM J. Control Optim. 29 (1991), 381-402 · Zbl 0741.93020 · doi:10.1137/0329021
[8] Hinrichsen D., Pritchard A. J.: Stability radii of linear systems. Systems Control Lett. 7 (1986), 1-10 · Zbl 0631.93064 · doi:10.1016/0167-6911(86)90094-0
[9] Narendra K. S., Taylor J. H.: Frequency Domain Criteria for Absolute Stability. Academic Press, New York 1973 · Zbl 0266.93037
[10] Safonov M. G., Goh K. C., Ly J. H.: Control System synthesis via bilinear matrix inequalities. Proc. of the American Control Conference, Baltimore 1994, pp. 45-49
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