New strategy for robust stability analysis of discrete-time uncertain systems. (English) Zbl 1118.93043

Summary: A new robust stability analysis approach is developed for uncertain discrete-time linear time-invariant systems with polytopic or affine parameter-dependent uncertainty models. The proposed approach is based on a combination of a branch-and-bound like strategy with linear matrix inequality (LMI) based analysis formulations. Two sufficient conditions are considered, one for the robust stability of the uncertain system and other one for the contrary situation. If both sufficient conditions fail to characterize the polytope, then it is iteratively subdivided into subpolytopes until some one proves to be unstable or all ones are verified to be robustly stable. The polytope subdivision is implemented by means of a specially developed simplex subdivision algorithm. Exhaustive numerical tests prove the efficiency of the proposed approach when compared with the most recent LMI-based formulations.


93D09 Robust stability
93C55 Discrete-time control/observation systems
93C41 Control/observation systems with incomplete information
Full Text: DOI


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