Input–Output Finite‐Time Stability and Stabilization of Nonautonomous Nonlinear Quadratic Systems via State and Output Feedback

ABSTRACT

This paper presents novel results regarding the input–output finite‐time stability (IO‐FTS) of nonlinear quadratic systems (NLQSs), a class of dynamical models particularly useful for the study of robotic systems, biochemical reaction networks, and other processes of interest to the applied sciences. After introducing the class of nonautonomous NLQSs, a sufficient condition ensuring the IO‐FTS of NLQSs, with time‐varying parameters and subject to input disturbances, represents the first main contribution. The analysis conditions are then exploited to develop state‐ and output‐feedback control laws that achieve IO finite‐time stabilization for an assigned NLQS. These sufficient conditions are expressed in terms of feasibility problems based on linear matrix inequalities (LMIs), which can be efficiently solved via off‐the‐shelf numerical tools. The applicability of the devised results is illustrated throughout the paper using examples of analysis and synthesis related to flight control systems described by NLQSs with time‐varying parameters.