A numerical sufficiency test for the asymptotic stability of linear time-varying systems

Stability of linear nonautonomous multivariable systems with differentiable matrices

“…It is still one of the most burning problems of control theory, because of the absence of its complete solution. One of the main methods for the stability analysis of systems with slowly varying matrices is the freezing method [1][2][3][4][5][6][7][8][9]. In particular, in the interesting recent paper [4] in the framework of the freezing approach, a numerical method is suggested.…”

New stability conditions for a class of linear time-varying systems

“…Comparing with the existing results (Amato et al, 1993;Desoer, 1969;Garcia et al, 2010;Guo & Rugh, 1995;Ilchmann et al, 1987;Jetto & Orsini, 2009;Kamen et al, 1989;Krause & Kumar, 1986;Mullhaupt et al, 2007;Rosenbrock, 1963;Solo, 1994;Tan & Duan, 2009), here, the system matrix function A(t) and its derivativeȦ(t) (provided ∥Ȧ(t)∥ exists) are allowed to be unbounded at t = +∞.…”

“…Numerous important results, including but not limited to Amato, Celentano, and Garofalo (1993), Desoer (1969), Garcia, Peres, and Tarbouriech (2010), Guo and Rugh (1995), Ilchmann, Owens, and Prätzel-Wolters (1987), Jetto and Orsini (2009), Kamen, Khargonekar, and Tannembaum (1989), Krause and Kumar (1986), Mullhaupt, Buccieri, and Bonvin (2007), Solo (1994) and Tan and Duan (2009), have been obtained through the efforts…”

Necessary and sufficient numerical conditions for asymptotic stability of linear time-varying systems

“…Although from a theoretical point of view there exist necessary and sufficient conditions in the literature [8][9][10], a lot of effort has been dedicated to the search for numerically tractable necessary and sufficient conditions (see [11] and references therein). In many cases, only sufficient conditions are obtained, as for instance in the methods based on the analysis of the eigenvalues of a time-invariant system [12,13].…”