Regional stability of a class of nonlinear hybrid systems: an LMI approach

This paper presents sufficient conditions to the regional stability problem of a class of nonlinear hybrid systems in the piecewise nonlinear form. The nonlinear local models are defined by a differential equation of the type x˙=A_i(x)x+b_i(x), where A_i(x) and b_i(x) are affine functions of x. This class of systems is equivalently represented by x˙=A(x,δ)x+b(x,δ) with δ denoting a vector of logical variables that modifies the local model of the system in accordance with the continuous dynamics. Using a single polynomial Lyapunov function, v(x)=x´P(x)x, we present LMI conditions that assure the local stability of the nonlinear system with a guaranteed domain of attraction.