@article{eprints2260,
          volume = {59},
           month = {September},
          number = {10},
           pages = {2629 --2643},
           title = {Stabilizing dynamic controllers for hybrid systems: a hybrid control Lyapunov function approach
},
            year = {2014},
       publisher = {IEEE },
         journal = {IEEE Transactions on Automatic Control },
          author = {Stefano Di Cairano and W.P.M.H. Heemels and Mircea Lazar and Alberto Bemporad},
             url = {http://eprints.imtlucca.it/2260/},
        abstract = {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.},
        keywords = {Asymptotic stability; Closed loop systems; Lyapunov methods; Optimal control; Optimization; Systematics}
}