ISS for nonlinear systems in Takagi-Sugeno´s form using quadratic and non-quadratic Lyapunov functions

This paper studies the input-to-state stability (ISS) of nonlinear systems in Takagi-Sugeno´s form. Following the definitions and ISS properties proposed by Sontag and Wang [1], a condition in terms of Linear Matrix Inequalities (LMIs) and predefined norm-bounded inputs is derived. Due to the convex property of the weighted sum of input matrices, the input field is bounded and the ISS property holds for systems that are global asymptotic stable (GAS) in the absence of exogenous inputs. First, a existing ISS condition for Takagi-Sugeno (TS) systems that fulfill standard quadratic Lyapunov function is revisited. Then, a ISS condition using a non-quadratic Lyapunov function candidate is derived. To illustrate the applicability of both conditions two numerical examples are studied.