A Note on the Controllability and Observability for Piecewise Linear Time‐varying Impulsive Systems

Abstract

This note studies the controllability and observability for piecewise time-varying impulsive systems. Necessary and sufficient criteria for complete controllability and observability are established. Two numerical examples are given to illustrate the utility and advantages of our criteria.

Controllability of linear impulsive matrix Lyapunov differential systems with delays in the control function

“…The matrix V given above is called the controllability Grammian of the system (1) having no impulses and no delays. Further the steering controller defined in (15) reduces to…”

“…Roughly speaking, a dynamical system is said to be state-controllable over some space V on some finite time interval, if it is possible to steer that system from every initial state in V to every desired final state in V by using the set of admissible control functions. The controllability of impulsive systems was first studied by Leela et al [26] and from then onwards many other mathematicians have contributed in the development of controllability of different types of impulsive systems, for example, refer [4,11,13,14,15,29,32,33,34] etc.…”

Controllability of linear impulsive systems -- an eigenvalue approach

“…Later the research on these systems took a rapid growth when many other control theorists started investigating the controllability of different types of impulsive systems. Some of the remarkable contributions were made by Benzaid and Sznaier [1], George et al [2], Guan et al ( [3], [4]), Xie and Wang [10], Zhao and Sun ([11], [12]), Han et al [5] and others. In [1], a homogeneous linear impulsive system is considered and its global null controllability is established.…”

State Estimation of Stochastic Impulsive System Via Stochastic Adaptive Impulsive Observer

“…Although, the stability problems of impulsive systems have been extensively studied in the literature [6][7][8][9][10][11][12] and many references therein, the observer design problem for impulsive systems has attracted less attention and not as many works are available in this area [13][14][15][16]. Observers which give an estimation for the state of the impulsive systems are very useful in analysis of natural impulsive systems.…”