A hierarchy of LMI inner approximations of the set of stable polynomials

Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMI) in the coefficients. As an application of these results, we derive a hierarchy of convex LMI inner approximations (affine sections of the cone of positive definite matrices of size $m$) of the nonconvex set of Schur stable polynomials of given degree $n < m$. It is shown that when $m$ tends to infinity the hierarchy converges to a lifted LMI approximation (projection of an LMI set defined in a lifted space of dimension quadratic in $n$) already studied in the technical literature

Positivity of discrete singular systems and their stability: An LP-based approach

In this paper we present an efficient approach to the analysis of discrete positive singular systems. One of our main objectives is to investigate the problem of characterizing positivity of such systems. Previously, this issue was not completely addressed. We provide easily checkable necessary and sufficient conditions for such problem to be solved. On the other hand, we study the stability of discrete positive singular systems. Note that this is not a trivial problem since the set of admissible initial conditions is not the whole space but it is represented by a special cone. All the conditions we provide are necessary and sufficient, and are based on a reliable computational approach via linear programming

Well-posedness and Attainability of Indefinite Stochastic Linear Quadratic Control in Infinite-time Horizon

This paper is concerned with a stochastic linear-quadratic (LQ) problem in an infinite time horizon with multiplicative noises both in the state and the control. A distinctive feature of the problem under consideration is that the cost weighting matrice

Positive infusion of propofol drug during induction

Non-opioid intravenous anesthetic agents, such as propofol, have been used in anesthesia since 1970’s for conscious sedation. In this paper, the study aims to regulate the syringe pump of propofol infusion during induction. The syringe pump is regulated by using a linear positive controller. The controller is designed so as to satisfy positivity in state. The control output is positive and bounded. Effect site concentration is used as a feedback to the controller. Simulation results show that the controller regulates propofol very well and the BIS responses of the patient are observed so that there is no overshoot or oscillation

Solvability and Asymptotic Behavior of Generalized Riccati equations arising in Indefinite Stochastic LQ Controls

The optimal control problem in a finite time horizon with an indefinite quadratic cost function for a linear system subject to multiplicative noise on both the state and control can be solved via a constrained matrix differential Riccati equation. In this paper, we provide general necessary and sufficient conditions for the solvability of this generalized differential Riccati equation. Furthermore, its asymptotic behavior is investigated along with its connection to the generalized algebraic Riccati equation associated with the linear quadratic control problem in infinite time horizon. Examples area presented to illustrate the results established