Practical stability for linear systems with parametric uncertainty (Q2748343)

The authors discuss the robust stability of the following linear differential system with parametric uncertainty NEWLINE\[NEWLINE\dot x=\Bigl(A_0+ \sum_{i=1,\dots,s} \delta_iA_i\Bigr) x+\Bigl(B_0+ \sum_{i=1,\dots,s} \delta_iB_i\Bigr)^\mu,\;y=C_2x,\;x(0)=x_0, \tag{*}NEWLINE\]NEWLINE where \(A_0,B_0, A_i,B_i,C_2\) are real constant matrices of appropriate dimensions, \(\delta_i\) with \(|\delta_i |\leq \alpha\) denotes the parametric uncertainty, \(i=1,2, \dots,s\), where \(s\) is the number of uncertain parameters involved.NEWLINENEWLINENEWLINEUsing some known results on vector Lyapunov functions and a comparison principle given in the book of \textit{V. Lakshmikantham}, \textit{V. M. Matrosov} and \textit{S. Sivasundaram} [Vector Lyapunov functions and stability analysis of nonlinear systems, London, Kluwer (1991; Zbl 0721.34054)] and the paper by \textit{E. Feron}, \textit{P. Apkarian} and \textit{P. Gahinet} [IEEE Trans. Autom. Control 41, 1041-1046 (1996; Zbl 0857.93088)], some sufficient conditions are obtained for the strongly practical stability of the linear system (*). A simulation example using the Matlab LMI tool is also given.