Equilibrium stability of a nonlinear structural switching system with actuator delay (Q2181442)

The paper starts from the linear system with delay in control \[ \displaystyle{\dot{x} = Ax(t) + B_cu(t-h)} \] For this system there is applied the finite spectrum assignment leading to the closed loop switched system \[ \displaystyle{\dot{x} = A_ix(t) + A_{di}x(t-h) + B_cK_i\int_{-h}^0 e^{-A_is}B_cu_i(t-h+s)ds + F_i(x)\;,\;i=1,\ldots,m} \] where \(i\) denotes one of the linear systems resulting from the structural switches accompanying the system. Observe that the controller is synthesized for each system \(i\). The term \(F_i(x)\) accounts for the nonlinear terms. There is proved stability by the first approximation for each of the systems which commute, via a quadratic Lyapunov Krasovskii functional.