Stabilization of linear systems with indeterminate parameters (Q2714562)

Following \textit{I. R. Peterson} and \textit{C. V. Hollot} [Automatica 22, No. 4, 397-411 (1986; Zbl 0602.93055)] the author considers a linear system with indefinite parameters NEWLINE\[NEWLINE \begin{gathered} \dot x = \bigg[A_0 + \sum\limits_{i=1}^k A_ir_i(t)\bigg] x+ \bigg[B_0 + \sum\limits_{i=1}^l B_is_i(t)\bigg] u,\\ |r_i(t)|\leq\overline r,\quad i=1,2,\dots,k;\quad \overline r\geq 0,\\ |s_i(t)|\leq\overline s,\quad i=1,2,\dots,l;\quad \overline s\geq 0. \end{gathered}\tag{1} NEWLINE\]NEWLINE Under some assumptions on system (1) the stabilization of its solutions in terms of algebraic Riccati equation is discussed. The expediency of asymptotic approximation applications is shown by the example of an airplane longitudinal motion stabilization.