Finite-time L ₁ and L _∞ boundedness for nonlinear singular switched positive systems with D-perturbations

The article studies the positivity, finite-time L ₁ boundedness and finite-time L _∞ boundedness for nonlinear singular switched positive systems(NSSPSs) with D-perturbations. Firstly, a necessary and sufficient positivity condition is presented for NSSPSs by singular value decomposition approach. Then, considering the disturbance signal in the form of norm bounded integrable signal, based on average dwell time and co-positive Lyapunov function approach, a sufficient condition of finite-time boundedness is derived for NSSPSs, and further considering the disturbance attenuation L ₁-gain performance, the result of finite-time L ₁ boundedness is presented for the considered system. In addition, considering the disturbance signal in the form of uniformly bounded signal, a sufficient condition of finite-time boundedness is derived for NSSPSs, and further considering the disturbance attenuation L _∞-gain performance, the result of finite-time L _∞ boundedness is presented for the considered system. Finally, the correctness and effectiveness of the results are verified with four given examples.