An Extension of the Argument Principle and Nyquist Criterion to Systems with Unbounded Generators
نویسندگان
چکیده
The Nyquist Stability Criterion is generalized to systems where the (open-loop) system has infinite-dimensional input/output spaces and a (possibly) unbounded infinitesimal generator. This is done through use of the perturbation determinant and an extension of the Argument Principle to infinitesimal generators with trace-class resolvent.
منابع مشابه
Nyquist Stability Criterion
A stability test for time invariant linear systems can also be derived in the frequency domain. It is known as Nyquist stability criterion. It is based on the complex analysis result known as Cauchy's principle of argument. Note that the system transfer function is a complex function. By applying Cauchy's principle of argument to the open-loop system transfer function, we will get information a...
متن کاملA Stability Test for Control Systems with Delays Based on the Nyquist Criterion
The aim of this contribution is to revise and extend results about stability and stabilization of a retarded quasipolynomial and systems obtained using the Mikhaylov criterion in our papers earlier. Not only retarded linear time-invariant time-delay systems (LTI-TDS) are considered in this paper; neutral as well as distributeddelay systems are the matter of the research. A LTI-TDS system of ret...
متن کاملAN ALGORITHM FOR FINDING THE STABILITY OF LINEAR TIME-INVARIANT SYSTEMS
The purpose of this paper is to show that the ideas and techniques of the classical methods of finding stability, such as the criteria of Leonhard and Nyquist, can be used to derive simple algorithm to verify stability. This is enhanced by evaluating the argument of the characteristic equation of a linear system in the neighbourhood of the origin of the complex plane along the imaginary axis
متن کاملThe Nyquist criterion for LTI Time-Delay Systems
This paper extends results about stability and stabilization of a retarded quasipolynomial obtained using the Mikhaylov criterion earlier. Retarded quasipolynomials appear as numerators and denominators of linear time-invariant time-delay systems (LTI-TDS). A LTI-TDS system of retarded type (destitute of distributed delays) is said to be stable if all roots of its characteristic quasipolynomial...
متن کاملSTABILITY ANALYSIS OF A PLANKTON SYSTEM WITH DELAY
This paper is evolved to have insight of Plankton-Nutrients interactions in the presence of delay in the growth term of phytoplankton species .The conditions for asymptotic stability about endemic equilibrium are derived in the absence of delay.The Nyquist criteria is used to estimate the length of delay to preserve stability .Analytic criterion for the existence of hopf-bifurcation is also dis...
متن کامل