Robust H∞ performance for lineardelay-differential systems with time-varying uncertainties

The present paper concerns robust H∞ performance for linear delay-differential systems which involve an uncertain time delay and time-varying norm-bounded parameter uncertainties. Based on the Lyapunov functional, a simple criterion is proposed which assures the pseudo-quadratic stability as a well as an H_∞-norm bound. The criterion is given in the form of a linear matrix inequality which is affine or convex in additional scalar parameters. A simple criterion is presented to evaluate the extent of the performance robustness     

State difference feedback for stabilizing uncertain steady states of non-linear systems

Supposing a non-linear system is subjected to parametric uncertainties, the present paper aims at stabilizing its unstable steady states. A distinctive feature of the problem is that exact information about the steady state is unavailable. To cope with the difficulty, we have examined the applicability of the state difference feedback which uses the difference between the present state x(t) and the past state x(t-T). A rigorous stability analysis has been executed for the case where state deviations are controllable by a single input variable. The stability analysis has led to a favourable conclusion that if the number of unstable modes is just two, and if they are not associated with the origin in the complex plane, we are always able to find a controller which stabilizes the deviations from the unknown steady state. Design process is illustrated by using two kinds of pendulum systems.     

A Kharitonov-like theorem for interval polynomial matrices

As an extension of Kharitonov's theorem, robust stability of interval polynomial matrices is studied. Here a polynomial matrix is said to be stable if its determinant has all roots with negative real parts. The present paper shows that the robust stability of interval polynomial matrices is equivalent to that of the subclasses where each row (column) has only one element that involves Kharitonov edge polynomials and all the other elements take on one of the four Kharitonov vertex polynomials.     

A root distribution criterion for interval polynomials

The problem of finding the conditions under which an interval polynomial has a given number of roots in the open left-half plane and the other roots in the open right-half plane, irrespective of the values of its coefficients, is considered. A simple criterion is provided to test interval polynomials for the root distribution invariance, viewed as an extension of Kharitonov's theorem. The goal is to provide an alternative theorem and then give an efficient means of checking the root distribution invariance     

An exact quadratic stability condition of uncertain linear systems

It is pointed out that in order to check the quadratic stability of a family of linear systems with a stable nominal system, the positive definiteness constraint can be dropped from the quadratic Lyapunov function     

Comments on “On the robust Popov criterion for interval Lur'esystems”

This paper supplements the remarks made in a paper by Dahleh et al. (IEEE Trans. Automat. Contr. vol.38, p.1400-5 (1993)) regarding the Popov sector of Lur'e systems with interval plants. A numerical example is provided to show that strict inequalities hold among three sectors: those obtained by the theorem of the paper, by applying Popov theorem to each member system, and by applying that to each of the systems with Kharitonov plants. This counterexample negates a tempting conjecture on “strong” robust Popov criterion     

Reduced order model predictive control with disturbance attenuation

This paper deals with model predictive control (MPC) with disturbance attenuation. By introducing a decomposition method for a quadratic objective function, an MPC law is obtained from a reduced order optimization problem. The effectiveness of the proposed MPC law is demonstrated by numerical simulation. IEEJ Trans 2010 DOI: 10.1002/tee.20613     

Activation of thrombin-activable fibrinolysis inhibitor requires epidermal growth factor-like domain 3 of thrombomodulin and is inhibited competitively by protein C

Thrombomodulin is a cofactor protein on vascular endothelial cells that inhibits the procoagulant functions of thrombin and enhances thrombin-catalyzed activation of anticoagulant protein C. Thrombomodulin also accelerates the proteolytic activation of a plasma procarboxypeptidase referred to as thrombin-activable fibrinolysis inhibitor (TAFI). In this study, we describe structures on recombinant membrane-bound thrombomodulin that are required for human TAFI activation. Deletion of the N-terminal lectin-like domain and epidermal growth factor (EGF)-like domains 1 and 2 had no effect on TAFI or protein C activation, whereas deletions including EGF-like domain 3 selectively abolished thrombomodulin cofactor activity for TAFI activation. Provided that thrombomodulin EGF-like domain 3 was present, TAFI competitively inhibited protein C activation catalyzed by the thrombin-thrombomodulin complex. A thrombomodulin construct lacking EGF-like domain 3 functioned normally as a cofactor for protein C activation but was insensitive to inhibition by TAFI. Thus, the anticoagulant and antifibrinolytic cofactor activities of thrombomodulin have distinct structural requirements: protein C binding to the thrombin-thrombomodulin complex requires EGF-like domain 4, whereas TAFI binding also requires EGF-like domain 3.     

Common Lyapunov function approach to matrix root clustering

This paper proposes an alternative route to the matrix root clustering problem, which enables to use a result on the common Lyapunov function for solving the problem efficiently. A necessary and sufficient condition is obtained in terms of the existence of a common positive definite solution to a set of Lyapunov inequalities for eigenvalues of a matrix to lie in a prescribed subregion of the complex plane. Applications to root clustering in sector regions are shown for illustration.