Robust Stability and Stabilization of Continuous-Time Parameter-Varying Persidskii Systems

This article investigates analysis and design problems for a class of parameter-varying generalized Persidskii systems. A model within this class is simultaneously linear in time-varying parameters as in the linear parameter-varying (LPV) framework, and contains sector nonlinearities of the state, as in Persidskii systems. The conditions for (integral) input-to-state stability and input–output-to-state stability are established. These results are developed using both, parameter-dependent and independent, Lyapunov functions. To formulate these conditions, parameterized matrix inequalities are used, which are reduced to linear ones under additional assumptions concerning the model's dependence on the time-varying parameters. Finally, a new robust nonlinear control design method is also developed. The efficacy of these results is illustrated through a numerical academic example and a more complex model describing the nonlinear dynamics of aircraft longitudinal motion.