Related papers: Multilinear Time Invariant System Theory
In this paper, a necessary and sufficient condition for the controllability of networked systems with heterogeneous dynamics is established where the nodes are higher dimensional linear time invariant systems and the network topology is…
The purpose of this paper is to initiate a phase theory for tensors under the Einstein product, and explore its applications in multilinear control systems. Firstly, the sectorial tensor decomposition for sectorial tensors is derived, which…
This paper studies a class of complex-valued linear systems whose state evolution dependents on both the state vector and its conjugate. The complex-valued linear system comes from linear dynamical quantum control theory and is also…
A novel lattice Boltzmann (LB) model for multiphase flows is developed that complies with the thermodynamic foundations of kinetic theory. By directly devising the collision term for LB equation at the discrete level, a self-tuning equation…
This paper investigates the relationship between subsystems and time in a closed nonrelativistic system of interacting bosons and fermions. It is possible to write any state vector in such a system as an unentangled tensor product of…
For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…
The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Many complex scenarios require the coordination of agents possessing unique points of view and distinct semantic commitments. In response, standpoint logic (SL) was introduced in the context of knowledge integration, allowing one to reason…
Real-world time series often exhibit strong non-stationarity, complex nonlinear dynamics, and behavior expressed across multiple temporal scales, from rapid local fluctuations to slow-evolving long-range trends. However, many contemporary…
Comparing with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. This paper studies the…
Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential…
We propose a novel approach in the study of transport phenomena in dense systems or systems with long range interactions where multiple particle interactions must be taken into consideration. Within Boltzmann's kinetic formalism, we study…
State-space models effectively model multivariate time series by updating over time a representation of the system state from which predictions are made. The state representation is usually a vector without any explicit structure.…
This paper considers a strongly connected network of agents, each capable of partially observing and controlling a discrete-time linear time-invariant (LTI) system that is jointly observable and controllable. Additionally, agents…
Performance analysis for linear time-invariant (LTI) systems has been closely tied to quadratic Lyapunov functions ever since it was shown that LTI system stability is equivalent to the existence of such a Lyapunov function. Some metrics…
Many physical systems are inherently time-varying in nature. When these systems are linearized around a trajectory, generally, the resulting system is Linear Time-Varying (LTV). LTV systems describe an important class of linear systems and…
The theory of linear time invariant systems is well established and allows, among other things, to formulate and solve control problems in finite time. In this context the control laws are typically taken in a space of the form L^p(0,T;U).…
This paper considers a leader-following problem for a group of heterogeneous linear time invariant (LTI) followers that are interacting over a directed acyclic graph. Only a subset of the followers has access to the state of the leader in…
We introduce a new class of time-continuous recurrent neural network models. Instead of declaring a learning system's dynamics by implicit nonlinearities, we construct networks of linear first-order dynamical systems modulated via nonlinear…