Title :
Stability of cones of polynomials. An application to the design of high-gain controllers for saturated systems
Author :
Aguirre, Brandon ; Ibarra, C. ; Suárez, R.
Author_Institution :
Dept. de Matematicas, Univ. Autonoma Metropolitana-Iztapalapa, Mexico
Abstract :
Hinrichsen and Kharitonov (Math. Control Signal Systems, vol.8, p.97-117, (1995) gave necessary and sufficient conditions for a convex conic set of polynomials to be Hurwitz. However, that result is not simple to apply. In this paper, an easy-to-check sufficient condition is introduced. The obtained condition is a matrix inequality which is a simple algebraic test for the stability of rays of polynomials. As an application, for stable open-loop systems, a cone of gains c such that the function u=-kcTx is a stabilizing control feedback for all k>0, is shown to exist. Moreover, for the same cone of gains, it was established that there do not exist any first harmonic periodic orbits despite saturation
Keywords :
control system synthesis; feedback; matrix algebra; polynomials; stability; Hurwitz polynomials; convex conic polynomial set; first harmonic periodic orbits; high-gain controller design; matrix inequality; necessary and sufficient conditions; open-loop systems; polynomial cone stability; polynomial rays; saturated systems; saturation; stabilizing control feedback; Control systems; Eigenvalues and eigenfunctions; Feedback; Linear matrix inequalities; Open loop systems; Orbits; Polynomials; Stability; Sufficient conditions; Testing;
Conference_Titel :
Decision and Control, 2000. Proceedings of the 39th IEEE Conference on
Conference_Location :
Sydney, NSW
Print_ISBN :
0-7803-6638-7
DOI :
10.1109/CDC.2000.911996
