State feedback stabilization of linear impulsive systems

Stabilizability of linear impulsive systems

“…As a consequence of [8, Lemma 2.7], strong reachability is equivalent to boundedness and positive definiteness of W (t, σ ℓ+2 (t)) uniformly in t and T satisfying Assumption 2.1 and is further shown in [8] to be sufficient to achieve exponential stabilization via state feedback. The development therein does not require the impulsive system to be reversible, i.e., A I invertible, at the expense of added complexity in the analysis.…”

“…The development therein does not require the impulsive system to be reversible, i.e., A I invertible, at the expense of added complexity in the analysis. On the other hand, the systems under consideration in [8] did not include the discrete-time input signal.…”

“…Here we provide alternate formulae for stabilizing feedback gains that incorporate the discrete-time input signal and for which the resulting closed-loop system is susceptible to a more direct stability analysis than that conducted in [8]. A straightforward adaptation of [8, Lemmas 2.7 and 2.9] indicates that a strongly reachable reversible impulsive state equation (1) (with associated integer ℓ) has a weighted controllability gramian…”

“…Here we present a stabilizability analysis for a class of impulsive linear systems that builds upon recent investigations D. A. Lawrence is with the School of Electrical Engineering and Computer Science, Ohio University, Athens, OH, USA dal@ohio.edu into reachability properties [7], [9] and feedback stabilization [8]. As with the development in [11], [12], a linear impulsive state system can be decomposed into, loosely speaking, reachable and unreachable subsystems defined in terms of an invariant subspace associated with the set of reachable states.…”

Novel LMI-based stability and stabilization analysis on impulsive switched system with time delays

“…For non-delay system, many investigations have been done. In [26], by using switched Lyapunov functions, the new general criteria of exponential stability and asymptotic stability with arbitrary and conditioned impulsive switching for a new class of hybrid impulsive and switching models have been established; in [27], the results on robust stability for this class of impulsive switched systems are obtained and sufficient conditions for the existence of a guaranteed cost control law are also given; in [28], the new fundamental properties are derived and several sufficient conditions are presented on the exponential stability and robust stabilization for singular impulsive closed-loop systems; in [29], through the receding horizon strategy, the problem on state feedback stabilization for a class of linear impulsive systems featuring arbitrarily-paced impulse times is investigated. However, for delay system, there are many problems need to be solved.…”