PhD defence | Taghreed Sugati, On Stability and Stabilization of Hybrid Systems

On Stability and Stabilization of Hybrid Systems

The thesis addresses the stability, input-to-state stability (ISS), and stabilization problems for hybrid systems with and without time delay.

Firstly, a class of uncertain switched systems with an external bounded input is addressed. The problems of ISS and stabilization by a robust reliable control are established by using multiple Lyapunov function technique along with the average dwell-time approach. Then, these results are further extended to include time delay in the system states, and delay systems subject to impulsive effects.

Secondly, the problem of designing a decentralized, robust reliable control for deterministic impulsive large-scale systems with admissible to guarantee exponential stability is investigated. Then, reliable observers are also considered to estimate the states of the same system. Furthermore, a time-delayed large-scale impulsive system undergoing stochastic noise is addressed and the problems of stability and stabilization are investigated.

Thirdly, a class of switched singularly perturbed systems is also considered.  Due to the dominant behavior of the slow subsystem, the stabilization of the full system is achieved through the slow subsystem. Moreover, switched singularly perturbed systems with time-delay in the slow system are considered.