%0 Journal Article
%@ 0018-9286
%A Di Cairano, Stefano
%A Heemels, W.P.M.H.
%A Lazar, Mircea
%A Bemporad, Alberto
%D 2014
%F eprints:2260
%I IEEE 
%J IEEE Transactions on Automatic Control 
%K Asymptotic stability; Closed loop systems; Lyapunov methods; Optimal control; Optimization; Systematics
%N 10
%P 2629 -2643
%T Stabilizing dynamic controllers for hybrid systems: a hybrid control Lyapunov function approach  
%U http://eprints.imtlucca.it/2260/
%V 59
%X This paper proposes a dynamic controller structure and a systematic design procedure for stabilizing discrete-time hybrid systems. The proposed approach is based on the concept of control Lyapunov functions (CLFs), which, when available, can be used to design a stabilizing state-feedback control law. In general, the construction of a CLF for hybrid dynamical systems involving both continuous and discrete states is extremely complicated, especially in the presence of non-trivial discrete dynamics. Therefore, we introduce the novel concept of a hybrid control Lyapunov function, which allows the compositional design of a discrete and a continuous part of the CLF, and we formally prove that the existence of a hybrid CLF guarantees the existence of a classical CLF. A constructive procedure is provided to synthesize a hybrid CLF, by expanding the dynamics of the hybrid system with a specific controller dynamics. We show that this synthesis procedure leads to a dynamic controller that can be implemented by a receding horizon control strategy, and that the associated optimization problem is numerically tractable for a fairly general class of hybrid systems, useful in real world applications. Compared to classical hybrid receding horizon control algorithms, the proposed approach typically requires a shorter prediction horizon to guarantee asymptotic stability of the closed-loop system, which yields a reduction of the computational burden, as illustrated through two examples.