How to determine the stability of a system?

How to determine the stability of the system The four nature of the system is linear, and when the invariance, causality and stability are important. Last Wang Yingji asked the judgment of system stability, further introduction. For the determination of the continuous system and discrete system, the description in the textbook is as follows: If the pole of the continuous system H (S) is in the left half-open plane of the S plane, the extreme point of the discrete system h (z) is in the unit circle of the z plane. The system is a stable causal system. If the system function is known, according to the above method, first seek the pole of the system function, then according to the position of the pole point, it can determine the stability of the system, so, the problem finally comes down to solve the root of a plurality of equations, according to the problem. Solutions. Wu Dazheng's textbook mention some simple example, explaining how to determine the stability of the system, and some system parameters should satisfy what conditions when satisfying the stability of the system. However, when the equation is high, such as 3 times, 4 times, etc., if you can't find the root of the equation, what should I do? The textbook has not been explained. Another textbook, is also the textbook used by my first self-study, that is, the "Signal and System" (Second Edition, Xi'an Electronic Science and Technology Press, which is edited by Xi'an Chen Shengtan, etc., 2001). Two important guidelines, Ruth-Hurwitz Guidelines and July guidelines. Russe - Holwitz guidelines should be teach in traditional control theory, it is a method of discriminating the real characteristics of algebraic equation roots, and you can know how many loaded roots containing how many loads are included without solving equations. Due to the development of computer technology, it is now very mature with a computer to solve the high equation. Therefore, Rose-Holviz guidelines and the importance of Juli criteria gradually decrease, and many textbooks have not told these two guidelines. However, these two guidelines have had an indelible achievement in history, and it is difficult to understand, and students should know about these two guidelines. Search for keyword "Ross - Holvis Guidelines" in Baidu Library or "Juli Code", it is easy to find these two guidelines. EDTOR: JQ, read full article, original title: How to determine the stability of the system Article Source: [Micro Signal: DIGITAL_SIGNALS, WeChat public number: International IEEE Signal Processing Magazine] Welcome to add attention! Please indicate the source of the article.

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