A Multiaffine Approach for Extended Dissipativity Synthesis for Periodic Time-Varying Systems With Constrained Input

In this article, a multiaffine approach is utilized to study the extended dissipativity performance for a class of periodic time-varying systems with constrained input and exogenous disturbances, while providing a control law to stabilize the open-loop unstable system. Specifically, a parameterized piecewise controller design based on the multiaffine property is proposed to facilitate an extended dissipativity analysis and to achieve stabilizing control for periodic time-varying systems with norm-bounded uncertainties, ensuring the closed-loop system states remain asymptotically stable under bounded energy disturbances. Moreover, the analysis of extended dissipativity can yield time-varying matrix constraints for five sets of performance indices, respectively. These constraints can also be transformed into linear matrix inequalities using the properties of multiaffine functions. The effectiveness of this approach is demonstrated through simulations of stabilization and performance indices for a helicopter model, where first-order trigonometric functions are employed to characterize bounded periodic uncertainties.