Marieke Heidema | Searcharxiv

arXiv2026

Robust stabilization of discrete-time linear systems requires nonlinear dynamic feedback

This paper studies the problem of robust stabilization of linear input-state systems in discrete time. We prove that for any compact set of stabilizable systems, there exists a dynamic state-feedback controller that globally asymptotically stabilizes all systems in the set. In addition, we show that for some compact sets of stabilizable systems, no nonlinear static or linear dynamic state-feedback law can achieve this task. This proves that, in general, robust stabilization requires a feedback law that is both nonlinear and dynamic. We extend our study to robust exponential stabilization with a given rate of decay. Finally, for polytopic sets of systems, we introduce an algorithm for the design of robust feedback laws.

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arXiv2024

Learning in memristive electrical circuits

Memristors are nonlinear two-terminal circuit elements whose resistance at a given time depends on past electrical stimuli. Recently, networks of memristors have received attention in neuromorphic computing since they can be used as a tool to perform linear algebraic operations, like matrix-vector multiplication, directly in hardware. In this paper, the aim is to resolve two fundamental questions pertaining to a specific, but relevant, class of memristive circuits called crossbar arrays. In particular, we show (1) how the resistance values of the memristors at a given time can be determined from external (voltage and current) measurements, and (2) how the resistances can be steered to desired values by applying suitable external voltages to the network. The results will be applied to solve a prototypical learning problem, namely linear least squares, by applying and measuring voltages and currents in a suitable memristive circuit.

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