This paper introduces operators, semantics, characterizations, and
solution-independent conditions to guarantee temporal logic specifications for
hybrid dynamical systems. Hybrid dynamical systems are given in terms of
differential inclusions -- capturing the continuous dynamics -- and difference
inclusions -- capturing the discrete dynamics or events -- with constraints.
State trajectories (or solutions) to such systems are parameterized by a hybrid
notion of time. For such broad class of solutions, the operators and semantics
needed to reason about temporal logic are introduced. Characterizations of
temporal logic formulas in terms of dynamical properties of hybrid systems are
presented -- in particular, forward invariance and finite time attractivity.
These characterizations are exploited to formulate sufficient conditions
assuring the satisfaction of temporal logic formulas -- when possible, these
conditions do not involve solution information. Combining the results for
formulas with a single operator, ways to certify more complex formulas are
pointed out, in particular, via a decomposition using a finite state automaton.
Academic examples illustrate the results throughout the paper.Comment: 35 pages. The technical report accompanying "Linear Temporal Logic
for Hybrid Dynamical Systems: Characterizations and Sufficient Conditions"
submitted to Nonlinear Analysis: Hybrid Systems, 201
