Practical \(\mu\)-stability of nonlinear integro-differential systems with delay (Q2714597)

Here, the integro-differential system NEWLINE\[CARRIAGE_RETURNNEWLINE \frac{dx}{dt} = A(t)x+ \int_0^t C(t,s)x(s) ds + \mu R(t,x,x_t),\tag{1} CARRIAGE_RETURNNEWLINE\]NEWLINE is considered with \(x\in \mathbb{R}^n\), \(A(t)\) and \(C(t,s)\) are continuous \(n\times n\)-matrix-valued functions, \(R: \mathbb{R}_+\times \mathbb{R}^n\times C\to \mathbb{R}^n\), \(\mu\) is a small parameter. In terms of a constructed comparison system for system (1) sufficient conditions for the practical \(\mu\)-stability are established.