Exponential stability and L2 gain analysis of uncertain fractional reset control systems

Abstract

Abstract This paper considers the stability problem of a class of uncertain fractional reset control systems that undergo the ${L}_2$ gain performance improvement via the conformable fractional calculus. To remove the Zeno phenomenon in the system’s response, a new reset law based on the time regularization technique is designed. By developing a theory to design a new reset control, the stability of the proposed fractional order (FO) linear system with model uncertainties and bounded exogenous input is proved via an extended quadratic Lyapunov function and some efficient linear matrix inequalities. Likewise, the impulsive effect in the control input is removed by employing an appropriate low-pass filter (LPF). In the end, two numerical examples show that when the plant is modelled by the FO differential equations, by utilizing the constructive role of fractional reset controller, the robustness of FO reset system can also be attained.