A Multiaffine Approach for Extended Dissipativity Synthesis for Periodic Time-Varying Systems With Constrained Input
提出一种基于多仿射特性的参数化分段控制器设计方法，用于分析周期时变系统在输入约束和外部扰动下的扩展耗散性，并通过直升机模型仿真验证了稳定性和性能指标。
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.