## By using a multiple discontinuous Lyapunov function approach and exploring the properties of mode-dependent average dwell time(MDADT) switching signal, new sufficient conditions of E-exponential stability for linear switched singular systems are presented.

New Stability Conditions of Linear Switched Singular Systems by Using Multiple Discontinuous Lyapunov Function Approach

## By using a multiple discontinuous Lyapunov function approach and adopting the mode-dependent average dwell time (MDADT) switching signals, new sufficient conditions of E-exponential stability and l 2 − gain analysis for linear switched singular systems are presented.

Stability and L2–Gain analysis of linear switched singular systems by using multiple discontinuous Lyapunov function approach

## To solve the problem, a general multiple discontinuous Lyapunov functions (MDLFs) analysi.

Stability and ℒ2-gain analysis based on multiple discontinuous Lyapunov function approaches for switched systems with unstable modes

## Moreover, multiple discontinuous Lyapunov function (MDLF) approach, which is less conservative than the traditional multiple Lyapunov function (MLF) method, is used to analyse the closed-loop stability and performance by incorporating the idea of AED–ADT.

Finite-time H ∞ control for discrete-time switched systems with admissible edge-dependent average dwell time

## By constructing discontinuous Lyapunov functions, it is proved that the proposed ET controllers guarantee the stability and <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance of the closed-loop systems.

Event-Triggered H∞ Control for T–S Fuzzy Systems via New Asynchronous Premise Reconstruction Approach

## By constructing discontinuous Lyapunov functions, it is proved that the proposed ET controllers guarantee the stability and H∞ performance of the closed-loop systems.

Event-Triggered H∞ Control for T-S Fuzzy Systems via New Asynchronous Premise Reconstruction Approach.

## To reflect more realistic the information on both the intervals e(t) to $$e(t_{k})$$ and e(t) to $$e(t_{k+1})$$ , a novel two-side sampling-interval-dependent discontinuous Lyapunov functional (DLF) is constructed, which can fully utilizes the available characteristics of actual sampling information.

Further Results on Sampled-Data Synchronization Control for Chaotic Lur’e Systems with Time Delay

## By taking advantage of characteristic information on the whole sampling interval, a new two-sided sampling-interval-dependent discontinuous Lyapunov functional is first constructed, which depends on the available information of both the intervals from tk to t and from t to t k + 1.

Further results on sampled-data synchronization control for chaotic neural networks with actuator saturation

## This paper is devoted to proposing improved discontinuous Lyapunov functionals for the stability analysis of sampled-data systems.

Improved Discontinuous Lyapunov Functionals for Stability Analysis of Sampled-Data Systems

## Firstly, constructing an improved discontinuous Lyapunov-Krasovskii function (LKF), which is fully considered the characteristics of sampled-data to reduce the conservativeness.

Improved results on synchronisation of Markovian jump complex dynamical networks via sampled-data controller and convex combination

## By designing discontinuous Lyapunov function with time-varying Lyapunov matrix, sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained to ensure the stability of the closed-loop system.

Event-Triggered Controller Design With Varying Gains for T–S Fuzzy Systems

## By designing discontinuous Lyapunov function with time-varying Lyapunov matrix, sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained to ensure the stability of the closed-loop system.

Event-Triggered Controller Design With Varying Gains for T-S Fuzzy Systems.

## The estimation error is analyzed via a discontinuous Lyapunov function, and an e -independent observer gain is designed.

Impulsive observer-based design for state estimation of a class of nonlinear singularly perturbed systems with discrete measurements

## By constructing discontinuous Lyapunov functions, it is proved that the proposed ET controllers guarantee the stability and <inline-formula> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance of the closed-loop systems.

Event-Triggered H∞ Control for T–S Fuzzy Systems via New Asynchronous Premise Reconstruction Approach

## To reflect more realistic the information on both the intervals e(t) to $$e(t_{k})$$ and e(t) to $$e(t_{k+1})$$ , a novel two-side sampling-interval-dependent discontinuous Lyapunov functional (DLF) is constructed, which can fully utilizes the available characteristics of actual sampling information.

Further Results on Sampled-Data Synchronization Control for Chaotic Lur’e Systems with Time Delay

## This paper is devoted to proposing improved discontinuous Lyapunov functionals for the stability analysis of sampled-data systems.

Improved Discontinuous Lyapunov Functionals for Stability Analysis of Sampled-Data Systems

10.1016/J.MATCOM.2021.03.021

## Technically, the work integrates with the new type of discontinuous Lyapunov-Krasovskii functional candidate with integral terms, several delay-dependent stability conditions, and Wirtinger-based integral inequality.

Memory sampled data control for switched-type neural networks and its application in image secure communications

10.1016/J.AUTOMATICA.2019.06.017

## The closed-loop system is formulated through a hybrid systems framework, within which stability is proven using a discontinuous Lyapunov-like function and a meagre-limsup invariance argument.

Reset integral control for improved settling of PID-based motion systems with friction

## Using the discontinuous Lyapunov-Krasoskii functional (LKF) approach and the free-matrix-based integral inequality bounds processing technique, a stability condition with less conservativeness has been obtained, and the controller of the sampled-data T-S fuzzy system with the quantized state has been designed.

Quantized Sampled-Data Control for T-S Fuzzy System Using Discontinuous LKF Approach

## In this paper, the discontinuous Lyapunov-based method is proposed to reject time variant and bounded disturbances.

Multirate control of nonlinear robotic manipulators with network structure under bounded disturbances