相关论文: New geometric results in eigenstructure assignment

In this paper, we consider the computational complexity of bounding the reachable set of a Linear Time-Invariant (LTI) system controlled by a Rectified Linear Unit (ReLU) Two-Level Lattice (TLL) Neural Network (NN) controller. In…

In this paper, we address a general eigenstructure assignment problem where the objective is to distribute the closed-loop modes over the components of the system outputs in such a way that, if a certain mode appears in a given output, it…

We here characterize the minimality of realization of arbitrary linear time-invariant dynamical systems through (i) intersection of the spectra of the realization matrix and of the corresponding state submatrix and (ii) moving the poles by…

Block full rank pencils introduced in [Dopico et al., Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems, Linear Algebra Appl., 2020] allow us to obtain local information…

In this paper, we provide novel characterizations of the weakly unobservable and the strongly reachable subspaces corresponding to a given state-space system. These characterizations provide closed-form representations for the said…

When computing the eigenstructure of matrix pencils associated with the passivity analysis of perturbed port-Hamiltonian descriptor system using a structured generalized eigenvalue method, one should make sure that the computed spectrum…

This paper presents a novel approach for solving the pole placement and eigenstructure assignment problems through data-driven methods. By using open-loop data alone, the paper shows that it is possible to characterize the allowable…

In this paper, we study the reachability of two closely related matrices appearing in the analysis of linear time-varying (LTV) systems over a finite time interval, namely, its closed-loop state transition matrix via a state feedback…

We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…

The main objective of this article is to develop a matrix pencil approach for the study of the controllability and reachability of a class of linear singular discrete time systems. The description equation of a practical system may be…

We consider the classic problem of pole placement by state feedback. We offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole-placing feedback matrix that can deliver any set of desired closed-loop…

Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear…

We propose a real-space approach explaining and controlling the occurrence of edge-localized gap states between the spectral quasibands of binary tight binding chains with deterministic aperiodic long-range order. The framework is applied…

In this article, a new notion of modal strong structural controllability is introduced and examined for a family of LTI networks. These networks include structured LTI subsystems, whose system matrices have the same zero/nonzero/arbitrary…

This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the solution of the classic infinite-horizon linear quadratic control problem. In particular, a geometric analysis…

The role of nonlinearity on topology has been investigated extensively in Hermitian systems, while nonlinearity has only been used as a tuning knob in a PT symmetric non-Hermitian system. Here, in our work, we show that nonlinearity plays a…

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz bound in neural…

Understanding relationships between attention heads is essential for interpreting the internal structure of Transformers, yet existing metrics do not capture this structure well. We focus on the subspaces spanned by attention-head weight…

By exploiting the connection between solving algebraic $\top$-Riccati equations and computing certain deflating subspaces of $\top$-palindromic matrix pencils, we obtain theoretical and computational results on both problems. Theoretically,…

In this study, we detail the procedures for designing gain scheduling controllers by Linear Quadratic $H_\infty$ robust optimization methods in Linear Matrix Inequalities (LMI) framework. The controllers are aimed at steering control of the…