Abstract: It is concerned with L₁-control of continuous affine nonlinear systems with prescribed exponentially convergent rate and performance by using set-valued analysis method. The concept of controlled λ-exponentially contractive set for the systems is introduced, and relation between the set and that for its Euler approximation discrete-time system is also established. For affine nonlinear continuous-time systems, a sufficient condition for the existence of static-state continuous nonlinear feedback for the L₁-control problem is presented. The result extends to the one in reference in stability sense.

Key words: Nonlinear continuous-time systems, L₁-control, ρ-performance, contractive set, Nonlinear feedback

摘要： 用集值分析方法研究了仿射非线性连续时间系统具λ-指数收敛率和ρ-性能的L₁控制问题。首先，引入连续时间系统的受控λ-收缩集概念，并建立了与其Euler逼近的离散系统的受控收缩集之间的关系。然后，结合此概念，得到了这个问题有静态连续非线性解的充分条件。这推广了在稳定性意义下文献中的结果。

关键词: 非线性连续时间系统, L₁控制, ρ-性能, 收缩集, 非线性反馈