caa a22 4500 463203100 CHVBK 20180405153117.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s00200-006-0027-4 doi (NATIONALLICENCE)springer-10.1007/s00200-006-0027-4 Root neighborhoods, generalized lemniscates, and robust stability of dynamic systems [Elektronische Daten] [Rida Farouki, Chang Han] A root neighborhood (or pseudozero set) of a degree-n polynomial p(z) is the set of all complex numbers that are the roots of polynomials whose coefficients differ from those of p(z), under a specified norm in $${\mathbb{C}^{n+1}}$$ , by no more than a fixed amount $${\epsilon}$$ . Root neighborhoods corresponding to commonly used norms are bounded by higher-order algebraic curves called generalized lemniscates. Although it may be neither convenient nor useful to derive their implicit equations, such curves are amenable to graphical analysis by means of simple contouring algorithms. Root neighborhood methods offer advantages over alternative approaches (the Kharitonov theorems and their generalizations) for investigating the robust stability of dynamic systems with uncertain parameters, since they offer valuable insight concerning which roots of the characteristic polynomial will become unstable first, and the relative importance of parameter variations on the root locations—and hence speed and damping of the system response. We derive a generalization of root neighborhoods to the case of polynomial coefficients having an affine linear dependence on a set of complex uncertainty parameters, bounded under a general weighted norm, and we discuss their applications to robust stability problems. The methods are illustrated by several computed examples. Springer-Verlag, 2007 Polynomial roots nationallicence Root neighborhoods nationallicence Pseudozero sets nationallicence Spectral sets nationallicence Generalized lemniscate nationallicence Kharitonov theorem nationallicence Robust stability nationallicence Farouki Rida Department of Mechanical and Aeronautical Engineering, University of California, 95616, Davis, CA, USA aut Han Chang Department of Mechanical and Aeronautical Engineering, University of California, 95616, Davis, CA, USA aut Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/1-2(2007-02-01), 169-189 0938-1279 18:1-2<169 2007 18 200 https://doi.org/10.1007/s00200-006-0027-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00200-006-0027-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Farouki Rida Department of Mechanical and Aeronautical Engineering, University of California, 95616, Davis, CA, USA aut NATIONALLICENCE 700 1- Han Chang Department of Mechanical and Aeronautical Engineering, University of California, 95616, Davis, CA, USA aut NATIONALLICENCE 773 0- Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/1-2(2007-02-01), 169-189 0938-1279 18:1-2<169 2007 18 200 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer