Robust finite‐time stability and stabilisation for switched linear parameter‐varying systems and its application to bank‐to‐turn missiles

Abstract

Finite-time stability analysis and controller synthesis for switched linear parameter-varying (LPV) systems are discussed in this paper. A new finite-time stability condition and robust finite-time controller design method are presented for switched LPV systems with two different structured uncertainty modelling assumptions (i.e. affine linear structured uncertainty or polytopic structured uncertainty). On the one hand, by using the piecewise parameter-dependent Lyapunov-like function, a less conservativeness finite-time stability condition is established. On the other hand, the new condition based on linear matrix inequalities relieves the controller design burden of dealing with specific applications. Finally, the provided design method is highly desirable to treat the problem of attitude control of bank-to-turn missiles with different channels coupling, and computer simulations demonstrate the effectiveness and superiority of the theoretical results.