Input-output finite-time stabilization of periodic piecewise systems with multiple disturbances

In this work, the problems of input-output finite-time stability and disturbance rejection for continuous-time periodic piecewise systems with linear fractional uncertainty, matched and mismatched disturbances are investigated. In detail, the matched disturbances that are ensuing from the exogenous systems can be tackled by modeling a periodic piecewise disturbance observer (PPDO), which effectively estimates the disturbance with high precision. The mismatched part can be sorted out by implementing H_∞ control protocol and meanwhile the state feedback is quantized in accordance with the logarithmic quantizer. On the whole, by combining the quantized state-feedback control law with the output of the PPDO, the anti-disturbance control protocol is developed. Moreover, by constructing a Lyapunov function with periodic piecewise positive definite matrices, a collection of adequate criteria affirming the system's input-output finite-time stability are procured in the context of linear matrix inequalities (LMIs). Subsequently, the time-varying periodic piecewise gain values of the crafted disturbance observer and developed controller are acquired by working on the LMIs. Conclusively, the simulation results are provided, including the 2-degree of freedom vibration system, to verify the potential of the developed control strategy.