This paper presents necessary and sufficient conditions for the existence of a Lyapunov function in the Lur’e form that guarantees the absolute stability of a Lur’e control system with multiple nonlinearities. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If these inequalities are feasible, the free parameters in the Lyapunov function, such as...

For delay Lur’e control systems with multiple non-linearities and time-varying uncertainties, necessary and sufficient conditions for the existence of Lyapunov functional in the extended Lur’e form with negative definite derivative to guarantee robust absolute stability are derived by solving a set of linear matrix inequalities(LMIs). Moreover, some new delay-dependent absolute stability criter...

Abstract. In this paper we study the absolute stability of Lurie control systems with multiple time-delays and nonlinearities, based on the Lyapunov stability theory via the approach of decomposing matrices, by using extended Lyapunov functional, we avoid the use of the stability assumption on the main operator and derive to improve stability criteria, which are strictly less conservative than ...

Improving the clock stability is of fundamental importance for development quantum-enhanced metrology. One main limitations arises from randomly fluctuating local oscillator (LO) frequency, which introduces ``phase slips'' long interrogation times and hence failure frequency-feedback loop. Here we propose a strategy to improve atomic clocks by interrogating two ensembles sharing same LO. The ar...

We present stability analyses for the boundary-layer flow over broad cones (half-angle ψ > 40◦) rotating in imposed axial flows. Preliminary convective instability analyses are presented that are based on the Orr–Sommerfeld equation for a variety of axial-flow speeds. The results are discussed in terms of the limited existing experimental data and previous stability analyses on related bodies. ...