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New algebraic criteria for positive realness

✍ Scribed by D.D. Šiljak

Publisher
Elsevier Science
Year
1971
Tongue
English
Weight
821 KB
Volume
291
Category
Article
ISSN
0016-0032

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✦ Synopsis

We present new algebraic criteria for positive realness of real rational functions and matrices, which are formulated entirely in terms of the Routh-Hurwitz conditions. It is first shown how the Routh algorithm can be modijied to serve as a criterion for positive realness. Due to the outstanding algebraic simplicity of the Routh algorithm, this criterion yields an emient numerical procedure for testing positive realness. Once the Routh algorithm is successfully reformulated, the Hurwitz version of positive realness is almost automatic. Hurwitz-like determinants are obtained, which provide explicit conditions for positive realness often desired in the theory of networks atid systems. The matrix generaliation of the proposed Routh-Hurwitz criteria lead to numerical procedures for testing the positive real character of real rational matrices with desirable simplicity and suitability for machine calculations.

📜 SIMILAR VOLUMES

Algebraic criteria for positive realness
Algebraic criteria for positive realness relative to the unit circle
✍ D.D. Šiljak 📂 Article 📅 1973 🏛 Elsevier Science 🌐 English ⚖ 519 KB

A purely algebraic algorithm is developed for testing positive real character of real rational functions and matrices relative to the unit circle in the complex plane. Since the algorithm is entirely recursive and is performed in a$nite number of steps, it is suitable for machine computations.

Algebraic criteria for positive realness
Algebraic criteria for positive realness relative to the unit circle
✍ D.D. Šiljak 📂 Article 📅 1973 🏛 Elsevier Science 🌐 English ⚖ 516 KB

A purely algebraic algorithm is developed for testing positive real character of real rational functions and matrices relative to the unit circle in the complex plane. Since the algorithm is entirely recursive and is performed in finite xumber of steps, it is suitable for machine computations.