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Robust finite‐time stability of impulsive dynamical linear systems subject to norm‐bounded uncertainties

Robust finite‐time stability (FTS) for a class of uncertain hybrid systems is tackled for the first time in this paper. In particular, uncertain impulsive dynamical linear systems (U‐IDLS) are considered. U‐IDLS exhibit jumps in the state trajectory that can be either time‐driven (time‐dependent IDLS) or driven by specific state values (state‐dependent IDLS). Furthermore, U‐IDLS may exhibit uncertainties both in the linear dynamic and in the jump equation. In this paper, sufficient conditions for FTS of IDLS are provided. These results require the solution of feasibility problems involving differential‐difference linear matrix inequalities (D/DLMIs), which can be numerically solved in an efficient way, as illustrated in the proposed examples. Copyright © 2010 John Wiley & Sons, Ltd.