despite providing robustness, high-gain observers impose a peaking phenomenon, which may cause instability, on the system states. in this paper, an adaptive saturation is proposed to attenuate the undesirable mentioned phenomenon in high-gain observers. a real-valued and differentiable sigmoid function is considered as the saturating element whose parameters (height and slope) are adaptively tu...

This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily ...

This paper studies stability and hybrid synchronization of a time-delay financial hyperchaotic system. Based on Lyapunov stability theorem and differential inequalities, stability is obtained by intermittent linear state feedback control. Furthermore, hybrid synchronization method is firstly proposed to synchronize a financial hyperchaotic system and globally synchronization is obtained by prop...

We show how piecewise quadratic Lyapunov functions can be used to estimate regions of attraction for linear systems with saturation. The central issues of how to restrict the analysis region and how to optimize the size of the domain of attraction are addressed, and the approach is demonstrated on several examples. We observe that the piecewise quadratic Lyapunov functions yield significant imp...

We propose a general approach to safe reinforcement learning control based on Lyapunov design methods. In our approach, a Lyapunov function—a special form of domain knowledge—is used to formulate the action choices available to a reinforcement learning agent. A learning agent choosing among these actions provably enjoys performance guarantees, and satisfies safety constraints of various kinds. ...

We consider a switching system with time delay composed of a finite number of linear delay differential equations (DDEs). Each DDE consists of a sum of a linear ODE part and a linear DDE part. We study two particular cases: (a) all the ODE parts are stable and (b) all the ODE parts are unstable and determine conditions for delay independent stability. For case (a), we extend a standard result o...