Stabilization and second-order optimization for multimodule impulsive switched linear systems

In this work, we investigate stabilization and optimization issues for a class of multimodule impulsive switched linear systems. First, we establish a necessary and sufficient criterion on asymptotic stabilizability via a pathwise state-feedback scheme, which achieves the merits of both time-driven and state-feedback mechanisms. Then, we present an impulse/switching instant optimization problem that usually arises in finite-horizon optimal control. To reduce the computational burden, we propose a novel method via developing efficiently computable expressions for the cost function, the gradient vector, and the Hessian matrix. Next, we design a second-order optimization algorithm searching for the optimal impulse/switching instants. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.