On stability of systems with periodic structure alterations (Q1842473)

Unlike previous works, the author investigates the stability of systems with structure alternation, in which the dimension of the unknown variable \(x(t)\) changes in different subintervals of its domain. The discussed system is of the form \(\dot x= f(t, x, i)\), \(x\in n_ i\), \(t\in (\tau_{i+ \mu k}(x), \tau_{i+ 1+\mu k}(x))\) and \(x(t)= \phi_{i+ 1,i}(t, x(t- 0))\), \(t= \tau_{i+ 1+ \mu k}(x)\). Using a Lyapunov function, four theorems giving criteria for stability of the zero solution \(x= 0\) are presented.