Sufficient Conditions For Construction Research Articles

Limit Theorems for the Solutions of Multipoint Boundary-Value Problems in Sobolev Spaces

We consider the most general class of multipoint boundary-value problems for systems of linear ordinary differential equations of the first order whose solutions belong to a given Sobolev space $$ {W}_p^n $$n ϵ ℕ, 1 ≤ p ≤ ∞: Sufficient constructive conditions under which the solutions of these problems are continuous with respect to the parameter e for e = 0 in the space $$ {W}_p^n $$ are established.

State Estimation of MEMs Capacitor Using Taylor Expansion

This paper deals with state estimation of micro tunable capacitor subjected to nonlinear electrostatic force. For this end a nonlinear observer has been designed for state estimation of the structure. Necessary and sufficient conditions for construction of the observer are presented. Stability of the observer is checked using Lyapunov theorem. Observer design is based on converting of differential equation of dynamic error from heterogeneous to homogenous. For this process non-linear electrostatic term is presented as coefficient of error and it is done using decomposition of Taylor expansion of non-linear term. By stabilizing of homogenous differential equation gains of observer can be obtained. Ability of the observer in state estimation of micro tunable capacitor is checked and related results are presented.

Design of Direct Exponential Observers for Fault Detection of Nonlinear MEMS Tunable Capacitor

In this paper a novel method is proposed for construction of an exponential observer for nonlinear system. The presented method is based on direct solution of dynamic error without any linearzing of nonlinear terms. Necessary and sufficient conditions for construction of direct observer are presented. Stability of the observer is checked using Lyapunov theorem. Also the ability of this observer is checked with implementing of observer for fault detection of micro tunable capacitor subjected to nonlinear electrostatic force.

A unified setting for decoupling with preview and fixed-lag smoothing in the geometric context

Exact decoupling with preview, perfect tracking of previewed references, unknown-input state observation with fixed lag, and left inversion with fixed lag are considered from a unifying perspective where exact decoupling with preview is the basic problem. Necessary and sufficient constructive conditions for decoupling with finite preview are proved in the geometric framework. Structural and stabilizability conditions are considered separately and the use of self-bounded controlled invariant subspaces allows the dynamic compensator with the minimal unassignable dynamics to be straightforwardly derived. A steering along zeros technique is devised to guarantee decoupling with stability also in the presence of unstable unassignable dynamics of the minimal self-bounded controlled invariant.

SIGNAL DECOUPLING WITH PREVIEW: PERFECT SOLUTION FOR NONMINIMUM-PHASE SYSTEMS IN THE GEOMETRIC APPROACH CONTEXT

The problem of making the output insensitive to an exogenous input signal possibly known with preview is tackled in the geometric approach context. The definition of minimal preview for decoupling is introduced. Necessary and sufficient constructive conditions for decoupling with minimal preview are proved by means of simple geometric arguments. The structural and the stabilizability conditions are considered separately. The minimal complexity of the solution is guaranteed by using the minimal self-bounded controlled invariant subspace. In the presence of unstable dynamics of that subspace, a steering along zeros technique completely devised in the state-space allows the solution with internal stability to be nonetheless achieved. Implementation is obtained by resorting to finite impulse response systems.

Generalized Signal Decoupling Problem with Stability for Discrete-Time Systems

This paper deals with the decoupling problems of unknown, measurable, and previewed signals. First, well-known solutions of unknown and measurable disturbance decoupling problems are recalled. Then, new necessary and sufficient constructive conditions for the previewed signal decoupling problem are proposed. The discrete-time case is considered. In this domain, previewing a signal by p steps means that the kth sample of the signal to be decoupled is known p steps in advance. The main result is that the stability condition for the mentioned decoupling problems does not change; i.e., the resolving subspace to be stabilized is the same independently of the type of signal to be decoupled, no matter whether it is completely unknown, measured, or previewed. The problem has been studied through self-bounded controlled invariants, thus minimizing the dimension of the resolving subspace which corresponds to the infimum of a lattice. The reduced dimension of the resolving controlled invariant subspace reduces the order of the controller units.

Complete Sets of Mutually Orthogonal Hypercubes and Their Connections to Affine Resolvable Designs

Recently, Laywine and Mullen proved several generalizations of Bose's equivalence between the existence of complete sets of mutually orthogonal Latin squares of order n and the existence of affine planes of order n. Laywine further investigated the relationship between sets of orthogonal frequency squares and affine resolvable balanced incomplete block designs. In this paper we generalize several of Laywine's results that were derived for frequency squares. We provide sufficient conditions for construction of an affine resolvable design from a complete set of mutually orthogonal Youden frequency hypercubes; we also show that, starting with a complete set of mutually equiorthogonal frequency hypercubes, an analogous construction can always be done. In addition, we give conditions under which an affine resolvable design can be converted to a complete set of mutually orthogonal Youden frequency hypercubes or a complete set of mutually equiorthogonal frequency hypercubes.

Sliding block encoders that are rho-bar continuous functions of their input (Corresp.)

Sliding block encoders operating within a statistically contaminated source environment are considered. Stationary analog sources are studied using the rho-bar distance as the measure of contamination. Sufficient constructive conditions are developed for the design of sliding block encoders that guarantee rho-bar stability of their output when operating within a statistically contaminated source environment. The relationship of this stability to the robustness of the encoding scheme is discussed, where robustness is a local stability property applied on the output entropy and the average distortion.

A frequency domain approach to minimal-order observer design for several linear functions of the state

A design procedure for minimal-order observers which is applicable to linear, observable, time-invariant systems is developed based on certain polynomial matrices associated with the transfer functions of the plant. The approach is to select the observer dynamics so that the feedback control law is satisfied with a minimal-order system. The method is a frequency domain technique but is significantly different from earlier results. Necessary and sufficient conditions for construction of a minimal-order observer to observe several linear functions of the state are given.

Sufficient Conditions for Construction of the Character System of a Finite Group

Necessary and sufficient conditions for the construction of the character table of a finite group from its multiplication table are discussed. It is pointed out that the technique most commonly used to evaluate the characters is inadequate. A rigorous method is described and its utility is discussed.