Finite-time L1 and L∞ boundedness for nonlinear singular switched positive systems with D-perturbations. (August 2022) - Li, Shuo
Abstract: 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. Highlights: The definitions of finite-time L 1 and L ∞ boundedness are firstly proposed for NSSPSs. The nonlinear constraints and D-perturbations are firstly considered for SSPSs. A necessary and sufficient condition of positivity is firstly provided for NSSPSs. Disturbance in norm bounded integrable and uniformly bounded signal are considered. Sufficient conditions of finite-time boundedness are derived for NSSPSs. Sufficient criteria of finite-time L 1 and L ∞ boundedness are proposed for NSSPSs.