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Alexander Lanzon

Publications and source records attributed to Alexander Lanzon.

7 recordsLinked to original sources
arXiv2025

Instance-Based Transfer Learning with Similarity-Aware Subject Selection for Cross-Subject SSVEP-Based BCIs

Steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs) can achieve high recognition accuracy with sufficient training data. Transfer learning presents a promising solution to alleviate data requirements for the target subject by leveraging data from source subjects; however, effectively addressing individual variability among both target and source subjects remains a challenge. This paper proposes a novel transfer learning framework, termed instance-based task-related component analysis (iTRCA), which leverages knowledge from source subjects while considering their individual contributions. iTRCA extracts two types of features: (1) the subject-general feature, capturing shared information between source and target subjects in a common latent space, and (2) the subject-specific feature, preserving the unique characteristics of the target subject. To mitigate negative transfer, we further design an enhanced framework, subject selection-based iTRCA (SS-iTRCA), which integrates a similarity-based subject selection strategy to identify appropriate source subjects for transfer based on their task-related components (TRCs). Comparative evaluations on the Benchmark, BETA, and a self-collected dataset demonstrate the effectiveness of the proposed iTRCA and SS-iTRCA frameworks. This study provides a potential solution for developing high-performance SSVEP-based BCIs with reduced target subject data.

cs.HC↗
arXiv2025

On phase in scaled graphs

The scaled graph has been introduced recently as a nonlinear extension of the classical Nyquist plot for linear time-invariant systems. In this paper, we introduce a modified definition for the scaled graph, termed the signed scaled graph (SSG), in which the phase component is characterized by making use of the Hilbert transform. Whereas the original definition of the scaled graph uses unsigned phase angles, the new definition has signed phase angles which ensures the possibility to differentiate between phase-lead and phase-lag properties in a system. Making such distinction is important from both an analysis and a synthesis perspective, and helps in providing tighter stability estimates of feedback interconnections. We show how the proposed SSG leads to intuitive characterizations of positive real and negative imaginary nonlinear systems, and present various interconnection results. We showcase the effectiveness of our results through several motivating examples.

eess.SY↗
arXiv2023

Converse negative imaginary theorems

Converse negative imaginary theorems for linear time-invariant systems are derived. In particular, we provide necessary and sufficient conditions for a feedback system to be robustly stable against various types of negative imaginary (NI) uncertainty. Uncertainty classes of marginally stable NI systems and stable strictly NI systems with restrictions on their static or instantaneous gains are considered. It is shown that robust stability against the former class entails the strictly NI property, whereas the latter class entails the NI property. We also establish a non-existence result that no stable system can robustly stabilise all marginally stable NI uncertainty, thereby showing that the uncertainty class of NI systems is too large as far as robust feedback stability is concerned, thus justifying the consideration of subclasses of NI systems with constrained static or instantaneous gains.

eess.SY↗
arXiv2022

Feedback Stability Analysis via Dissipativity with Dynamic Supply Rates

We propose a general notion of dissipativity with dynamic supply rates for nonlinear systems. This extends classical dissipativity with static supply rates and dynamic supply rates of miscellaneous quadratic forms. The main results of this paper concern Lyapunov and asymptotic stability analysis for nonlinear feedback dissipative systems that are characterised by dissipation inequalities with respect to compatible dynamic supply rates but involving possibly different and independent auxiliary systems. Importantly, dissipativity conditions guaranteeing stability of the state of the feedback systems, without concerns on the stability of the state of the auxiliary systems, are provided. The key results also specialise to a simple coupling test for the interconnection of two nonlinear systems described by dynamic (Psi, Pi, Upsilon, Omega)-dissipativity, and are shown to recover several existing results in the literature, including small-gain, passivity indices, static (Q, S, R)-dissipativity, dissipativity with terminal costs, etc. Comparison with the input-output approach to feedback stability analysis based on integral quadratic constraints is also made.

eess.SY↗
arXiv2016

Foundations of negative imaginary systems theory and relations with positive real systems

In this paper we lay the foundations of a not necessarily rational negative imaginary systems theory and its relations with positive real systems theory and, hence, with passivity. In analogy with the theory of positive real functions, in our general framework, negative imaginary systems are defined in terms of a domain of analyticity of the transfer function and of a sign condition that must be satisfied in such domain. In this way, on the one hand, our theory does not require to restrict the attention to systems with rational transfer function and, on the other hand | just by suitably selecting the domain of analyticity to be either the right half complex plane or the complement of the unit disc in the complex plane | we particularize our theory to both continuous-time and to discrete-time systems. Indeed, to the best of our knowledge, this is first time that discrete-time negative imaginary systems are studied in the literature. In this work, we also aim to provide a unitary view of the different notions that have appeared so far in the literature within the framework of positive real and in the more recent theory of negative imaginary systems, and to show how these notions are characterized and linked to each other. A stability analysis result for the interconnection of discrete-time systems is also derived.

math.DS↗
arXiv2011

A New Stability Result for the Feedback Interconnection of Negative Imaginary Systems with a Pole at the Origin

This paper is concerned with stability conditions for the positive feedback interconnection of negative imaginary systems. A generalization of the negative imaginary lemma is derived, which remains true even if the transfer function has poles on the imaginary axis including the origin. A sufficient condition for the internal stability of a feedback interconnection for NI systems including a pole at the origin is given and an illustrative example is presented to support the result.

math.OC↗