Control Problems on Time Scales
In this chapter, two types of control problems of impulsive systems on time scales are discussed. Section 10.1 formulates the controllability and observability of impulsive time-varying linear systems, and presents the controllability and observability results. In Section 10.2, pinning synchronization of linear dynamical networks (DNs) on time scales is studied. A pinning impulsive control scheme that takes into account time-delay effects is presented to achieve synchronization of DNs on time scales with the state of an isolated node. Based on the theory of time scales and the direct Lyapunov method, a synchronization criterion is established for linear DNs on general time scales. Numerical simulations are given to illustrate the effectiveness of the theoretical analysis.