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This paper proposes a hybrid observer for state estimation over a network. The network provides delayed measurements of the output of the plant at time instants that are not necessarily periodic and are accompanied by timestamps provided by a clock that synchronizes with the clock of the observer in finite time. The proposed observer, along with the plant and communication network, are modeled by a hybrid dynamical system that has two timers, a logic variable, and two memory states to capture the mechanisms involved in the events associated with sampling and arrival of information, as well as the logic in the estimation algorithm. The hybrid model also includes a generic clock synchronization scheme to cope with a mismatch between the clocks at the plant and the observer. Convergence properties of the estimation error of the system are shown analytically and supported by numerical examples.more » « less
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Cost evaluation problems for hybrid inclusions are studied. Sufficient conditions, in the form of Lyapunov-like inequalities, are provided to derive an upper bound on the cost associated with the solution to a hybrid inclusion with respect to a hybrid cost functional. Under additional sufficient conditions, we determine the cost exactly without computing solutions. Constructive results are proposed to solve cost evaluation problems in some relevant applications. Numerical examples are presented.more » « less
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Regional stability analysis of linear systems with multi-rate samplers and actuator saturation is studied. A hybrid controller is used to perform a fusion of measurements sampled at different times. In between sampling events, the controller behaves as a copy of the plant. When a new measurement is available, the controller state undergoes a jump. The resulting system is analyzed in a hybrid system framework. Sufficient conditions in the form of matrix inequalities are given to determine estimates of the basin of attraction of the closed-loop system. Finally, the effectiveness of the proposed methodology is shown in an example.more » « less
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This paper deals with robust minimum-time control of a class of asymptotically null-controllable with bounded input planar systems. A hybrid controller is proposed to robustly achieve global finite time stability of a set of points wherein the plant state is zero. The resulting controller provides time optimal response from initial conditions in a certain subset of the state space, and finite time convergence elsewhere. Finally, the effectiveness of the proposed methods is demonstrated in a numerical example.more » « less
