This work studies the problem of design of discrete-time nonlinear observers in the presence of exogenous disturbances. In particular, the present work proposes a systematic design method for discrete-time nonlinear state and disturbance observers in modular form, consisting of an observer for the disturbance-free part of the system, along with a disturbance observer and a stateestimate correct...

Min-max systems are timed discrete event dynamic systems containing min, max and plus operations. A min-max system is balanced if it admits a global cycle time (generalized eigenvalue) for every possible assignment of parameters. This paper proves that the testing of the balance property for min-max systems is co-NP hard by showing that the test of inseparability is co-NP hard. The latter resul...

For a given set of background interference signals, it is well known that the optimal sequence can be obtained by solving an eigenvalue problem. However, one usual practical constraint on the sequences in that the sequence elements should have a constant amplitude. We show that when the choice is limited to binary sequences, the sequence assignment problem is NP-hard. We propose a Local Search ...

We develop a parallel Jacobi-Davidson approach for finding a partial set of eigenpairs of large sparse polynomial eigenvalue problems with application in quantum dot simulation. A Jacobi-Davidson eigenvalue solver is implemented based on the Portable, Extensible Toolkit for Scientific Computation (PETSc). The eigensolver thus inherits PETSc’s efficient and various parallel operations, linear so...

Linear state constraints define a polyhedron in the state space of a dynamical system. If this polyhedron can be made positively invariant by state feedback, the constraints are satisfied all along the trajectory for any initial point in this polyhedron. In this paper, some algebraic invariance relations are established for continuous-time linear systems. The existence of a solution to the corr...

Let $D \subset \mathbb{R}^d$ be a bounded, connected domain with smooth boundary, and let $-\Delta u = \mu\_1 u$ the first nontrivial eigenfunction of Laplace operator Neumann boundary conditions. We prove that $$ \max\_{x \in D} \~u(x) \leq 60 \cdot \partial we emphasize this constant is uniform among all domains in dimensions. In particular, hot spots conjecture cannot fail by an arbitrarily ...

This paper is dedicated to the regularity of optimal sets for second eigenvalue Dirichlet Laplacian. Precisely, we prove that if set $\Omega$ minimizes functional \[ \mathcal F_\Lambda(\Omega)=\lambda_2(\Omega)+\Lambda |\Omega|, \] among all subsets a smooth bounded open $D\subset \mathbb{R}^d$, where $\lambda_2(\Omega)$ Laplacian on and $\Lambda>0$ fixed constant, then equivalent union two dis...

Since Maxwell’s theory is a gauge theory, it is quite important to evaluate the corresponding zero-point energy by a careful assignment of boundary conditions on the potential and on the ghost fields. Recent work by the authors has shown that, for a perfectly conducting spherical shell, it is precisely the contribution of longitudinal and normal modes of the potential which enables one to repro...