Stability robustness of linear output feedback systems with both time-varying structured and unstructured parameter uncertainties as well as delayed perturbations

Global exponential robust stability of Cohen–Grossberg neural network with time-varying delays and reaction–diffusion terms

“…Thus, it is almost impossible to get an exact model for the system due to the existence of various parameter uncertainties. So it is essential to introduce the robust technique to design a system with such uncertainty [15][16][17]. If the uncertainty of a system is only due to the deviations and perturbations of its parameters, and if those deviations and perturbations are all bounded, then the system is called an interval system.…”

The error loop and robust closed-loop stability

“…The main result is that structured and unstructured uncertainties may be accommodated by the state predictor sensitivity m S and the complement m V as shown in Figure 2. The result seems departing from literature [1], [2], [6], [7], [8], [9], [10], where either control law is dedicated to the purpose or no distinction between control and state predictor is made. On the contrary, structured uncertainties must be real-time estimated so as to update the embedded model.…”

“…The structured (or parametric) uncertainty h , denoted by a cloudy 2D box, either refers to discrepancies in the form of parameter uncertainty or to neglected (nonlinear) relations between model variables [6], [7], [8], [9]. Only state-tocommand relations are treated here.…”

“…Since they may be partly neglected, they must be included in u d and cancelled. Unstructured uncertainty, denoted by a cloudy 3D box, refers to model-class discrepancies and uncertainties [6], [7], [8], [9]. They take several forms [1], [2]; the output fractional form (multiplicative form in [2]) is adopted here as in [4] …”

Stability robustness of perturbed structured systems

“…The idea to construct Lyapunov functions to study robust stability has attracted considerable attention. In this way, some results on robust stability are given in [5] and in [6] robust stability bounds can be derived and it has been shown that these bounds are less conservative in most cases that the existing ones. The robust Schur and Hurwitz stability of the interval systems are considered in [7] and output feedback stabilization conditions and robust stability with respect to the delay time uncertainty are given in [8].…”