On characterizations of the input-to-state stability property
Systems & Control Letters
A Smooth Converse Lyapunov Theorem for Robust Stability
SIAM Journal on Control and Optimization
A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems
Automatica (Journal of IFAC)
Brief paper: Input-to-state stability of switched systems and switching adaptive control
Automatica (Journal of IFAC)
HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Stability analysis of hybrid systems via small-gain theorems
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Automatica (Journal of IFAC)
The analysis of global input-to-state stability for piecewise affine systems with time-delay
International Journal of Automation and Computing
Distributed formation control of nonholonomic mobile robots without global position measurements
Automatica (Journal of IFAC)
Pre-orders for reasoning about stability properties with respect to input of hybrid systems
Proceedings of the Eleventh ACM International Conference on Embedded Software
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In this paper we will extend the input-to-state stability (ISS) framework to continuous-time discontinuous dynamical systems (DDS) adopting piecewise smooth ISS Lyapunov functions. The main motivation for investigating piecewise smooth ISS Lyapunov functions is the success of piecewise smooth Lyapunov functions in the stability analysis of hybrid systems. This paper proposes an extension of the well-known Filippov's solution concept, that is appropriate for 'open' systems so as to allow interconnections of DDS. It is proven that the existence of a piecewise smooth ISS Lyapunov function for a DDS implies ISS. In addition, a (small gain) ISS interconnection theorem is derived for two DDS that both admit a piecewise smooth ISS Lyapunov function. This result is constructive in the sense that an explicit ISS Lyapunov function for the interconnected system is given. It is shown how these results can be applied to construct piecewise quadratic ISS Lyapunov functions for piecewise linear systems (including sliding motions) via linear matrix inequalities.