Improved Stability Analysis and Gain-Scheduled Controller Synthesis for Parameter-Dependent Systems.

F. Wang and V. Balakrishnan

IEEE Trans. Automatic Control, vol. 47, no. 5, pages 720-734, May 2002

Abstract: We present new algorithms for robust stability analysis and gain-scheduled controller synthesis for linear systems affected by time-varying parametric uncertainties. These new techniques can also be applied to parameter-dependent nonlinear systems with real-rational nonlinearities. Sufficient conditions for robust stability as well as conditions for the existence of a robustly stabilizing gain-scheduled controller are given in terms of a finite number of Linear Matrix Inequalities (LMIs); explicit formulae for constructing robustly stabilizing gain-scheduled controllers are given in terms of the feasible set of these LMIs. The improvement offered by our approach over existing methods for stability analysis and gain-scheduled controller synthesis for parameter-dependent linear systems are analyzed in theory. Numerical examples demonstrate that our approach can offer significant improvement in practice.

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