# Lyapunov-Based Sufficient Conditions for Stability of Hybrid Systems With Memory

@article{Liu2015LyapunovBasedSC, title={Lyapunov-Based Sufficient Conditions for Stability of Hybrid Systems With Memory}, author={Jun Liu and Andrew R. Teel}, journal={IEEE Transactions on Automatic Control}, year={2015}, volume={61}, pages={1057-1062} }

Hybrid systems with memory are dynamical systems exhibiting both hybrid and delay phenomena. In this note, we study the asymptotic stability of hybrid systems with memory using generalized concepts of solutions. These generalized solutions, motivated by studying robustness and well-posedness of such systems, are defined on hybrid time domains and parameterized by both continuous and discrete time. We establish Lyapunov-based sufficient conditions for asymptotic stability using both Lyapunov…

## 35 Citations

### Lyapunov Conditions for Input-to-State Stability of Hybrid Systems With Memory

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This paper studies input-to-state stability for hybrid systems with memory, which models hybrid dynamics affected by time delays. Using both Lyapunov–Razumikhin functions and Lyapunov–Krasovskii…

### Stability Analysis for Homogeneous Hybrid Systems With Delays

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A novel theorem is presented for hybrid systems with the characteristic of homogeneity so that the system is globally preasymptotically stable and under the homogeneous assumption, some rather weak conditions are obtained.

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This chapter outlines a framework that allows studying hybrid systems with delays through generalized solutions and summarizes some recent results on basic existence and well-posedness of solutions and stability analysis using Lyapunov-based methods.

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Finite-time stability can be guaranteed if the finite-time convergent mode is active long enough and the value of the generalized Lyapunov functions increase between consecutive switches.

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Hybrid systems subject to delayed jumps form a class of dynamical systems with broad applications. This article develops sufficient conditions for robust asymptotic stability of hybrid systems in the…

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This paper studies the problem of the input-to-state stability for homogeneous hybrid systems with bounded time-varying delays by using Lyapunov-Razumikhin approach and finds that with the homogeneous assumption, some special results can be obtained.

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It is shown that even if the value of the generalized Lyapunov function increases between consecutive switches, finite- time stability can still be guaranteed if the finite-time convergent mode is active long enough.

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