Robust Guaranteed Cost Composite Anti-bump $$L_2$$ -Gain Control for a Class of Switched Systems Under Mixed State-Dependent Switching

The robust guaranteed cost composite anti-bump \(L_2\)-gain control for switched systems is investigated in this paper. By constructing a convex combination of positive definite matrices and segmenting the switching interval, a novel multiple convex Lyapunov function suitable for composite anti-bump switching (ABS) control problem is proposed. A new definition of composite ABS performance is presented without reference signals, which restrains the control and rate bumps of the system caused by switchings only at switching instants. Then, imposing a dwell time on the state-dependent switching law, a mixed state-dependent switching scheme is presented based on the multiple convex Lyapunov function. Robust guaranteed cost composite anti-bump control strategy is established for a class of switched systems to overcome the conflicts among guaranteed cost performance, composite bumpless switching performance and \(L_2\)-gain performance. Eventually, an actual aircraft engine model is employed to demonstrate the validity of the proposed approach.