Exponential stability and non-weighted <i>L</i> ₂ -gain analysis for switched neutral systems with unstable subsystems

Exponential stability and non-weighted $ L_2 $ L2-gain are studied for switched neutral systems with unstable subsystems. Initially, a time scheduling strategy is introduced to formulate switching-signal-based multiple discontinuous Lyapunov functions. Multiple discontinuous Lyapunov functions can be applied to each subsystem, thereby relaxing the limitations of traditional Lyapunov functions. Meanwhile, mode-dependent average dwell times are utilised to design fast and slow switching signals, ensuring stability in switched neutral systems where the switching between unstable and stable subsystems is arbitrary. Moreover, in the presence of external disturbances, the non-weighted $ L_2 $ L2-gain performance is discussed. Sufficient conditions are proposed to achieve the stability of switched neutral systems and non-weighted $ L_2 $ L2-gain performance using the linear matrix inequality method. The validity of this study is ultimately demonstrated through simulation examples.