Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in linear time-invariant descriptor systems are presented. These generalise in a natural way the known corresponding results for state-space systems. However, our arguments extend somewhat existing work on eigenstructure assignment by state feedback in descriptor systems. The main issue throughout the paper is closed-loop regularity, i.e. uniqueness of solutions of the initial value problem, which cannot be taken for granted. Introduction and main resultsWe shall study a linear time-invariant multivariable descriptor system with state and output equations:Here u(t), x(t) and y(t) are vector functions of time with m, n and p components, respectively, and A, B, C and E are real constant matrices of the appropriate sizes with E and A square and B and C of full rank. Usually E is singular, but in no case is this essential to our argument; we denote rank E by r.Descriptions of dynamical systems in the forms of eqns. 1 and 2 arise naturally when these systems are formed from interconnected subsystems. In fact, any system can generally be viewed as an interconnection of subsystems, and when the natural differential equations and algebraic constraints describing the system are first written down, they involve the internal variables of the subsystem in a description of the forms of eqns. 1 and 2, usually with a singular coefficient matrix E [12]. A list of references on descriptor systems, otherwise known as mixed differential algebraic systems or generalised statespace systems or singular systems, is provided by the review paper [11]. Closely related work on eigenstructure assignment itself has more recently appeared [9].If a constant output feedback: u= -Ky(3)is added to the system, eqns. 1 and 2, then the closed loop plant equation is:Paper 6105D (C8), first This paper is addressed to the problem of the modal control of the system, eqn. 4, which has two distinct aspects. It is fundamental to control that the system is regular, i.e., that the solution of the initial value problem is unique whenever it exists. This cannot be taken for granted, so the first objective of pole assignment is to ensure that this regularity condition is satisfied. Closely related to this is the dimension of the subspace of admissible initial conditions for the system, i.e., of initial conditions which lead to smooth solutions of eqn. 4. This dimension cannot exceed r = rank E but it can be less in particular cases; we shall seek conditions necessary and sufficient for there to be r linearly independent admissible initial conditions for eqn. 4. The second aspect of modal synthesis for the system is the requirement of pole assignment, familiar from state space systems. In order to avoid cumbersome phraseology let us say that annxn matrix M has eigenvalue \i if there exists a non-zero (right) eigenvector s such that Ms = fiEs or equivalently, a non-zero (left) eigenvector t so that t T M = nt T Ewhere E is the matrix in eqn. 1. If we need to refe...
A computational method for constructing individually acceptable diets by modifying a chosen diet to meet nutritional requirements is described. The effects on food quantities of imposing different nutrient requirements on a sample diet are demonstrated and techniques which can ensure the acceptability to the individual of the modified diet are described. The starting point in the calculation is the person's current dietary intake. This is modified using linear programming methods which make the smallest changes to the food quantities to meet specific targets. Sequential modification can be used to identify changes that are acceptable to the individual. The computer program has been developed in collaboration with practising dietitians and is in use in some leading UK hospitals.
Background The incidence of body dysmorphic disorder in cosmetic dermatology is high. Even though treating patients with this disorder may worsen symptoms and is fraught with potential complications, screening is low, due in part to lack of knowledge of the disorder, as well as inadequate screening tools. Objectives To verify the probability of body dysmorphic disorder in a nonsurgical esthetic setting and determine the effect of a multiphasic screening protocol on mitigating poor outcomes in high‐risk patients. Methods A multiphasic screening protocol for body dysmorphic disorder was distributed to a total of eight esthetic clinics in the United States. Practitioners administered an anonymous, cryptic prescreening form to all new, incoming patients aged ≥ 18 to ≤ 65 years from June 1, 2019, through September 1, 2019, followed by a second, more extensive screening questionnaire. Patients with suspected or subclinical body dysmorphic disorder could be refused treatment. Results A total of 734 initial screenings were recorded over 16 weeks. Of these, 4.2% (31/734) proceeded to the secondary screening phase; 29% (9/31) subsequently screened positive for body dysmorphic disorder. Practitioners refused to treat 77.8% (7/9) of positive screenings. Two patients out of seven who tested positive underwent a third screening and were subsequently treated with positive outcomes. Conclusions Use of a cryptic screening protocol enables identification of individuals at risk for BDD and encourages open and continuous communication between patient and provider.
For feedback control of linear systems in descriptor form it is essential that the closed-loop system be regular; that is, there should not be an infinity of solutions of the closed-loop differential equations for any initial condition. Closed-loop regularity cannot be taken for granted. In this paper a necessaryand sufficient condition for the existence of an output feedback giving closed-loop regularity is presented.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.