RICARDO G . SANFELICE , and ANDREW R . TEEL ROBUST STABILITY AND CONTROL FOR SYSTEMS THAT COMBINE CONTINUOUS - TIME AND DISCRETE - TIME DYNAMICS

1066-033X/09/$25.00©2009IEEE Digital Object Identifier 10.1109/MCS.2008.931718 M any dynamical systems combine behaviors that are typical of continuous-time dynamical systems with behaviors that are typical of discrete-time dynamical systems. For example, in a switched electrical circuit, voltages and currents that change continuously according to classical electrical network laws also change discontinuously due to switches opening or closing. Some biological systems behave similarly, with continuous change during normal operation and discontinuous change due to an impulsive stimulus. Similarly, velocities in a multibody system change continuously according to Newton’s second law but undergo instantaneous changes in velocity and momentum due to collisions. Embedded systems and, more generally, systems involving both digital and analog components form another class of examples. Finally, modern control algorithms often lead to both kinds of behavior, due to either digital components used in implementation or logic and decision making encoded in the control algorithm. These examples fi t into the class of hybrid dynamical systems, or simply hybrid systems. This article is a tutorial on modeling the dynamics of hybrid systems, on the elements of stability theory for hybrid systems, and on the basics of hybrid control. The presentation and selection of material is oriented toward the analysis of asymptotic stability in hybrid systems and the design of stabilizing hybrid controllers. Our emphasis on the robustness of asymptotic stability to data perturbation, external disturbances, and measurement error distinguishes the approach taken here from other RAFAL GOEBEL, RICARDO G. SANFELICE, and ANDREW R. TEEL