Cascade/feedback interconnections of prescribed-time input-to-state stable systems

• Published in: Systems & control letters Vol. 190; p. 105857
• Main Authors: Krishnamurthy, Prashanth, Khorrami, Farshad, Tzes, Anthony
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2024
• Subjects: Interconnected systems; Nonlinear systems; Prescribed time; Robust control; Stability of nonlinear systems; Robust control; Nonlinear systems; Stability of nonlinear systems; Prescribed time; Interconnected systems
• ISSN: 0167-6911
• DOI: 10.1016/j.sysconle.2024.105857

Achieving control objectives (e.g., stabilization or convergence of tracking error to zero, input-to-state stabilization) in “prescribed time” has attracted significant research interest in recent years. In this paper, we consider cascade and feedback interconnections of prescribed-time input-to-state stable (ISS) systems and study conditions under which the overall states of such interconnected systems also converge to the origin in the prescribed time interval. We show that these conditions are intrinsically related to properties of the time-varying “blow-up” functions that are central to prescribed-time control designs. We also generalize the results to interconnections of an arbitrary number of systems. As an illustrative example, we consider an interconnection of two uncertain systems that are prescribed-time stabilized using two different control design methods and show that the two separate controllers can be put together to achieve prescribed-time stability of the interconnected system. •Analysis of interconnections of prescribed-time (PT) input-to-state stable systems.•New notions of polynomially bounded blow-up functions and PT exponential convergence.•Cascade and feedback interconnections of two and arbitrary number of systems.•Simulation studies of cascade and feedback interconnections of systems.