Prescribed-time predictor control of LTI systems with input delay

Abstract

This paper deals with the problem of prescribedtime stabilization of controllable linear systems with input delay. The problem is reformulated under a cascade PDE-ODE setting from which a prescribed-time predictor feedback is designed based on the backstepping approach, and whose transformation makes use of time-varying kernels. The bounded invertibility of the transformation is guaranteed. It is proved that the solution converges to the equilibrium in a prescribed-time. A simulation example is presented to illustrate the results.

Prescribed-time predictor control of LTI systems with distributed input delay

“…cascade linear hyperbolic PDE with an LTI system) introduced in [3], [34], and that employed a Backstepping-forwarding transformation, and a reductionbased change of variable. As in [12], the main idea of our approach is to transform the original system into a target system that is UPrTS (in an appropriate sense) and that we choose to satisfy the property of convergence in a prescribed time T + h + t 0 . Here, T is fixed a priori, h is the known input delay and for simplicity of notations, we take the initialization time t 0 = 0.…”

“…(50) 1) Stability result: Theorem 2: Let c be given by (12) and let r min = min i=1,...,n {r i } with r i > 0 involved in (41)-(42). Let h > 0, c 0 > 0, T > 0 fixed .…”

“…Nevertheless, results for finite-, fixed-and prescribed-time concepts for time-delay systems remain sparse. Some pioneering contributions on finite/fixed-time stability of time-delay systems are [11], [18], [25]; more recent results are [10], [33], [24] and [12], [13], where the latter deals with prescribed-time predictor control for LTI systems with input delay. Although, to best of our knowledge, prescribed-time stabilization for LTI systems with distributed input delay has not been studied yet in the literature.…”

Predictor-Feedback Prescribed-Time Stabilization of LTI Systems With Input Delay

“…We call it prescribed-time predictor control. A conference paper [15] contains some preliminary results on prescribed-time predictor control for a scalar linear equation with input delay and includes also a brief overview of some results for the n-dimensional case that are fully covered in this paper. Indeed, in contrast to the conference version, this paper deals with n-dimensional linear systems with single delayed input and provides the complete results and details for all proofs as well as a detailed analysis and discussions on the novel prescribed-time predictor control and the bounded invertibility of the the backstepping transformation with timevarying kernels.…”