• Media type: E-Article
  • Title: Robust Stability of Time-Varying Markov Jump Linear Systems with Respect to a Class of Structured, Stochastic, Nonlinear Parametric Uncertainties
  • Contributor: Dragan, Vasile; Aberkane, Samir
  • Published: MDPI AG, 2021
  • Published in: Axioms, 10 (2021) 3, Seite 148
  • Language: English
  • DOI: 10.3390/axioms10030148
  • ISSN: 2075-1680
  • Origination:
  • Footnote:
  • Description: This note is devoted to a robust stability analysis, as well as to the problem of the robust stabilization of a class of continuous-time Markovian jump linear systems subject to block-diagonal stochastic parameter perturbations. The considered parametric uncertainties are of multiplicative white noise type with unknown intensity. In order to effectively address the multi-perturbations case, we use scaling techniques. These techniques allow us to obtain an estimation of the lower bound of the stability radius. A first characterization of a lower bound of the stability radius is obtained in terms of the unique bounded and positive semidefinite solutions of adequately defined parameterized backward Lyapunov differential equations. A second characterization is given in terms of the existence of positive solutions of adequately defined parameterized backward Lyapunov differential inequalities. This second result is then exploited in order to solve a robust control synthesis problem.
  • Access State: Open Access