Input-output-to-state stability (Q2719146)

The authors study finite-dimensional, nonlinear systems of the form NEWLINE\[NEWLINE\dot x= f(x,u,w),\quad y= h(x),NEWLINE\]NEWLINE where \(u\) denotes a control input, and \(w\) denotes a disturbance which takes value on a compact convex set. The main result states that the following three facts are equivalent.NEWLINENEWLINENEWLINE1) Uniform input-output-to-state stability (UIOSS). It means that the norm of the state variable can be majorized at every instant \(t\) by suitable functions of the initial state, of the past control and of the past output. This is interpreted as a detectability property.NEWLINENEWLINENEWLINE2) Existence of a positive definite, proper function \(V\) solving an appropriate dissipation inequality (characterization in terms of Lyapunov functions).NEWLINENEWLINENEWLINE3) Existence of a state norm-estimator (observer).NEWLINENEWLINENEWLINEThe paper deals with other related properties such as integral-to-integral IOSS and global asymptotic stability modulo output.