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An infinite-dimensional bilinear optimal control problem with infinite-time horizon is considered. The associated value function can be expanded in a Taylor series around the equilibrium, the Taylor series involving multilinear forms which…
This paper proposes a robust learning methodology to place the closed-loop poles in desired convex regions in the complex plane. We considered the system state and input matrices to be unknown and can only use the measurements of the system…
In this paper explicit necessary and sufficient conditions for the constrained Sylvester-observer equation are established, in order to have a solution over the field of real numbers. Furthermore, a procedure is given for the computation of…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
In this study, we explore multiple higher-order pole solutions in spinor Bose--Einstein condensates. These solutions are associated with different pairs of higher-order poles of the transmission coefficient in the inverse scattering…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
In this paper, we show that for discrete time-varying linear control systems uniform complete controllability implies arbitrary assignability of dichotomy spectrum of closed-loop systems. This result significantly strengthens the result in…
Pole-swapping algorithms are generalizations of bulge-chasing algorithms for the generalized eigenvalue problem. Structure-preserving pole-swapping algorithms for the palindromic and alternating eigenvalue problems, which arise in control…
This work is to provide a comprehensive treatment of the relationship between the theory of the generalized (palindromic) eigenvalue problem and the theory of the Sylvester-type equations. Under a regularity assumption for a specific matrix…
In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic…
Conventionally, the concept of moment has been primarily employed in model order reduction to approximate system by matching the moment, which is merely the specific set of steady-state responses. In this paper, we propose a novel design…
In this paper we consider a class of systems of two coupled real scalar fields in bidimensional spacetime, with the main motivation of studying classical or linear stability of soliton solutions. Firstly, we present the class of systems and…
Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…
In this note, we establish a new closed formula for the solution of homogeneous second-order linear difference equations with constant coefficients by using matrix theory. This, in turn, gives new closed formulas concerning all sequences of…
We are interested in the feedback stabilization of general linear multi-dimensional first order hyperbolic systems in $\mathbb{R}^d$. Using a Lyapunov function with a suited weight function depending on the system under consideration we…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
We consider bilevel linear problems, where some parameters are stochastic, and the leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader's outcome can be modeled by a random…