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Robust finite-time stability of impulsive dynamical linear systems subject to norm-bounded uncertainties. (English) Zbl 1225.93087
Summary: 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.
MSC:
93D09Robust stability of control systems
93C05Linear control systems
93C41Control problems with incomplete information
34H05ODE in connection with control problems