The Kalman–Yakubovich–Popov lemma is a result in system analysis and control theory which states: Given a number >, two n-vectors B, C and an n x n Hurwitz matrix A, if the pair (,) is completely controllable, then a symmetric matrix P and a vector Q satisfying

Kalman–Yakubovich–Popov引理 （Kalman–Yakubovich–Popov lemma）是 系統分析 及 控制理论 的結果，其中提到：給定一數 ，二個n維向量B, C，及n x n的 赫維茲穩定矩陣 A（所有特徵值的實部都為負值），若 具有完全 可控制性，則滿足下式的對稱矩陣P和向量Q. 存在的充份必要條件是. 而且，集合 是 的不可觀測子空間。 此引理可以視為是穩定性理論 李亞普諾夫方程 的推廣。 建構了由 狀態空間 A, B, C建構的 线性矩阵不等式 以及其 頻域 條件的關係。

KY引理给出了至关重要的 频域条件 与 状态空间条件 之间的等价关系，基于这种等价关系，可以直接对某一个渐近稳定且可控的线性系统运用控制理论中的多种重要定理，比如直接判断状态空间给出的系统是否positive real，有界实引理和H无穷控制设计等。 Meyer-Kalman-Yakubovich. 如果上述线性时不变可控的系统的输出也有控制项 (误差)的输入，比如 \bold y=\bold c^T\bold x+\frac {\gamma} {2}u 呢？ 给定一数 {\displaystyle \gamma >0} ，向量b和c，以及 赫维兹稳定矩阵 …

Kalman-Yakubovich-Popov (KYP) Lemma (also frequently called “positive real lemma”) is a major result of the modern linear system theory. It is a collection of statements related to existence and properties of quadratic storage functions for LTI state space models and quadratic supply rates.

We use the term Kalman-Yakubovich-Popov(KYP)Lemma, also known as the Positive Real Lemma, to refer to a collection of eminently important theoretical statements of modern control theory, providing valuable insight into the connection between frequency domain, time domain, and quadratic dissipativity properties of LTI systems.

Kalman-Yakubovich-Popov Lemma 1 A simplified version of KYP lemma was used earlier in the derivation of optimal H2 controller, where it states existence of a stabilizing solution of a Riccati equation associated with a non-singular abstract H2 optimization problem. This lecture presents the …

2021年4月30日 · The Kalman–Popov–Yakubovich (KYP) Lemma is a widely used lemma in control theory. It is sometimes also referred to as the Bounded Real Lemma. The KYP lemma can be used to determine the H ∞ {\displaystyle H_{\infty }} norm of a system and is also useful for proving many LMI results.

The positive-real version originally appeared in [Yak62], and both are instances of what is now called the Kalman–Yakubovich–Popov (KYP) lemma. Let A ∈ Rn×n, B ∈ Rn×p, C ∈ Rp×n and D ∈ Rp×p be given matrices corresponding to a system with the same number p of inputs as outputs, and. internal states.

The Kalman-Yakubovich-Popov (KYP) lemma has been a cornerstone in system theory and network analysis and synthesis. It relates an analytic property of a square transfer matrix in the frequency domain to a set of algebraic equations involving parameters of …

Kalman–Popov–Yakubovich (KYP) 引理是控制理论中广泛使用的引理。 它有时也被称为有界实引理。 KYP 引理可用于确定 H ∞ {\displaystyle H_{\infty }} 系统的范数，也适用于证明许多LMI结果。