Integrated fault estimation and fault tolerant control for systems with generalized sector input nonlinearity (Q2207235)

Consider a time-invariant linear system defined by the state equation \(\dot{x}=Ax+B\psi+E\omega+Ff, t \geq 0\), where the initial state \(x_0\) belongs to a given set \(\Omega_0\), and \(\omega,f\), resp., are time-dependent disturbance, fault terms fulfilling some \(L_2[0,+\infty)\)-conditions. With a time-dependent piece-wise continuous nonlinear function \(\psi(\cdot,t)\), the system input \(\psi =\psi(v,t)\) depends on the output \(v=\Gamma(\hat{x},\hat{f})\) of a linear feedback controller involving a state estimator \(\hat{x}\) and an adaptation law \(\hat{f}\) to estimate the fault term \(f\). Moreover, there is a linear system output \(y=Cx\). The aim is then to derive sufficient stability conditions for the closed-loop system and for minimum \(L_2\)-gain performance. Finally, a case study is given.