Results 21 to 30 of about 1,177,096 (136)

A note on the formulas for the Drazin inverse of the sum of two matrices

Open Mathematics, 2019
In this paper we derive the formula of (P + Q)D under the conditions Q(P + Q)P(P + Q) = 0, P(P + Q)P(P + Q) = 0 and QPQ2 = 0. Then, a corollary is given which satisfies the conditions (P + Q)P(P + Q) = 0 and QPQ2 = 0. Meanwhile, we show that the additive
Liu Xin, Yang Xiaoying, Wang Yaqiang
doaj   +1 more source

The Schur Complements of Generalized Doubly Diagonally Dominant Matrices

, 2003
As is known, the Schur complements of diagonally dominant matrices are diagonally dominant; the same is true of doubly diagonally dominant matrices. The purpose of this paper is to extend the results to the generalized doubly diagonally dominant matrices
Huang, Yunqing, Liu, Jianzhou, Zhang, Fuzhen, Fuzhen Zhang, Yunqing Huang, Jianzhou Liu   +5 more
core   +1 more source

Linear Mechatronic Modeling of Rectangular Tank Sloshing Dynamics

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT Sloshing dynamics in partially filled tanks can strongly influence system‐level behavior when fluid motion couples with rigid‐body dynamics. This paper presents a linear and acausal two‐dimensional sloshing model for rectangular tanks, based on the reformulation of established sloshing theory within a modular, multi‐domain modeling framework ...
Magnus Steinstø, Eilif Pedersen
wiley   +1 more source

Generalized Schur functions and augmented Schur parameters [PDF]

, 2005
Every Schur function s(z) is the uniform limit of a sequence of finite Blaschke products on compact subsets of the open unit disk. The Blaschke products in the sequence are defined inductively via the Schur parameters of s(z).
Wanjala, Gerald, Dijksma, Aad
core   +4 more sources

Friction‐Aware Force‐Realizable Safety Control for Four‐Wheel Independently Steered and Driven Mobile Robots

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT Safety‐critical control remains a major challenge for four‐wheel independently steered and driven (4ISD) mobile robots, where high‐accuracy path tracking and obstacle avoidance must be achieved under over‐actuated steering–driving coordination, tire–ground friction limits, and wheel‐torque constraints.
Ruitong Liu, Kenji Hashimoto
wiley   +1 more source

Marginally Strictly Negative Imaginary Systems

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT This article revisits a fundamental question in negative imaginary (NI) systems theory: what is the weakest viable notion of strictness that still preserves the classical feedback stability picture? To address this question, we introduce the notion of marginally strictly negative imaginary (MSNI) systems to accommodate simple nonzero imaginary‐
Tianzhe Zhang, Chao Chen, Alexander Lanzon, Sei Zhen Khong   +3 more
wiley   +1 more source

Optimization Problems of Hermitian Quadratic Matrix-Valued Functions and Applications

Axioms
In this paper, we investigate optimization problems for a Hermitian quadratic matrix-valued function involving two variable matrices. We derive algebraic formulas for the maximal and minimal ranks and partial inertias of this function based on a ...
Sihem Guerarra
doaj   +1 more source

Spectral Submanifolds of Delay Systems: Control in Continuous and Discrete Time

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT This paper presents both continuous‐time and discretization‐based approaches for constructing spectral submanifolds (SSMs) for time delay systems. The continuous‐time approach built upon sun–star calculus, reformulates the governing delay differential equation (DDE) as an operator differential equation (OpDE).
Bence Szaksz, Gábor Orosz, Gábor Stépán   +2 more
wiley   +1 more source

Initial State Privacy of Nonlinear Systems on Riemannian Manifolds

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT In this paper, we investigate initial state privacy protection for discrete‐time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances.
Le Liu, Yu Kawano, Antai Xie, Ming Cao
wiley   +1 more source

A Matrix Identity on the Schur Complement

, 2004
This article presents a matrix identity on the Schur complement along with various applications. In particular, it gives a simple and transparent proof for the Crabtree–Haynsworth quotient formula for the Schur complement.
Zhang, Fuzhen
core   +1 more source