Input-Output Finite-Time Stability and State-Feedback Stabilization of Nonlinear Quadratic Systems

In this paper we extend the concept of Input- Output Finite-Time Stability (IO-FTS) to the class of nonlinear quadratic systems (NLQSs), which is particularly suited to study the dynamics of robotic systems, bio-systems and of a number of other processes of interest in the field of applied sciences. So far, the research on IO-FTS has mainly concerned linear systems; this point strongly motivates the investigation of NLQSs, due to the above-mentioned wide range of applications of this class of systems. To this regard, the main result of the paper consists of a sufficient condition guaranteeing the IO-FTS of NLQSs subject to L2 input disturbances; then the analysis result is exploited to design a state-feedback controller guaranteeing the IO finite-time stabilization of a given NLQS. Such sufficient conditions are given in terms of numerically-tractable optimization problems based on Linear Matrix Inequalities (LMIs). Some numerical examples illustrate the effectiveness of the proposed approach.