采用李雅普诺夫第二方法直接证明了有限时域广义预测控制器 (GPC)可使系统闭环稳定 ,从而大大简化了该有限时域GPC控制器稳定性的证明 ;指出了当λ→ 0时 ,有限时域GPC控制器逼近实现零终点状态约束的最小能量控制器 ,进一步揭示出了该控制器实现闭环稳定的本质原因 .最后 ,给出了在极限条件下有限时域GPC控制器与Kleinman控制器等价性的更加简洁的证明 The Lyapunov second method is used to directly prove that a finite time domain GPC (Generalized Predictive Controller) can make the system closed-loop stable, which greatly simplifies the proof of the stability of the finite-time GPC controller. It is pointed out that when λ → 0, Finite time-domain GPC controller approaches the minimum energy controller which realizes the zero-end state constraint, further reveals the essential reason of the closed-loop stability of the controller.Finally, the finite-domain GPC controller with Kleinman control Equivalence of the more concise proof