Impulsive Systems Haddad by Haddad, Wassim M., PDF

By Haddad, Wassim M.,

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Hence, 'ljJ(T, 0, xo) E as n S and inf{t E lR+ : 'ljJ(t,O,xo) E S} = rnin{t E lR+ : 'ljJ(t,O,xo) E V}, which implies that the first resetting time tl is well defined for all initial conditions Xo E V. Next, it follows from A2 that t2 is also well defined and t2 i= tl· Repeating the above arguments it follows that the resetting times tk are well defined and distinct. 2) also exists and is unique over a forward time interval. However, it is important to note that the analysis of impulsive dynamical systems can be quite involved.

6 Invariant Set Theorems for State-Dependent Impulsive Dynamical Systems In this section, we generalize the Krasovskii-LaSalle invariance prin- ciple to state-dependent impulsive dynamical systems. This result characterizes impulsive dynamical system limit sets in terms of continuously differentiable functions. In particular, we show that the sys~em trajectories converge to an invariant set contained in a union of level surfaces characterized by the continuous-time dynamics and the resetting system dynamics.

60) establish asymptotic stability for linear state-dependent impulsive systems. These conditions are implied by P > 0, AJ'P + PAc < 0, and AIPAd - P < 0, which can be solved using a Linear Matrix Inequality (LMI) feasibility problem [27]. 4 An Invariance Principle for State-Dependent Impulsive Dynamical Systems In this section, we develop an invariance principle for state-dependent impulsive dynamical systems. The following key assumption and several definitions are needed for the statement of the next fundamental result on positive limit sets for impulsive dynamical systems.

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Impulsive Systems Haddad by Haddad, Wassim M.,

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