Finite-Time Stability of Hybrid Systems With Unstable Modes

In this work, we study finite-time stability of hybrid systems with unstable modes. We present sufficient conditions in terms of multiple Lyapunov functions for the origin of a class of hybrid systems to be finite-time stable. More specifically, we show that even if the value of the Lyapunov function increases during continuous flow, i.e., if the unstable modes in the system are active for some time, finite-time stability can be guaranteed if the finite-time convergent mode is active for a sufficient amount of cumulative time. This is the first work on finite-time stability of hybrid systems using multiple Lyapunov functions. Prior work uses a common Lyapunov function approach, and requires the Lyapunov function to be decreasing during the continuous flows and non-increasing at the discrete jumps, thereby, restricting the hybrid system to only have stable modes, or to only evolve along the stable modes. In contrast, we allow Lyapunov functions to increase both during the continuous flows and the discrete jumps. As thus, the derived stability results are less conservative compared to the earlier results in the related literature, and in effect allow the hybrid system to have unstable modes.

Stability of delayed switched systems via Razumikhin technique and application to switched neural networks

This paper investigates the globally exponential stability of delayed switched systems via Razumikhin technique. According to mode-dependent dwell average time and multiple Lyapunov functions, new Razumikhin-type stability results are deduced. In contrast to the existing Rzumikhin-type results, the proposed ones are less conservative. In order to demonstrate the applicability, some stability and stabilization results for switched neural networks with time-varying delays are also derived. Several numerical examples are also employed to show the effectiveness and superiority of the obtained results.

A New Switched State Jump Observer for Traffic Density Estimation in Expressways Based on Hybrid-Dynamic-Traffic-Network-Model

When faced with problems such as traffic state estimation, state prediction, and congestion identification for the expressway network, a novel switched observer design strategy with jump states is required to reconstruct the traffic scene more realistically. In this study, the expressway network is firstly modeled as the special discrete switched system, which is called the piecewise affine system model, a partition of state subspace is introduced, and the convex polytopes are utilized to describe the combination modes of cells. Secondly, based on the hybrid dynamic traffic network model, the corresponding switched observer (including state jumps) is designed. Furthermore, by applying multiple Lyapunov functions and S-procedure theory, the observer design problem can be converted into the existence issue of the solutions to the linear matrix inequality. As a result, a set of gain matrices can be obtained. The estimated states start to jump when the mode changes occur, and the updated value of the estimated state mainly depends on the estimated and the measured values at the previous time. Lastly, the designed state jump observer is applied to the Beijing Jingkai expressway, and the superiority and the feasibility are demonstrated in the application results.