Induced Norm Analysis of Linear Systems for Nonnegative Input Signals

This paper is concerned with the analysis of the $L_p\ (p\in[1,\infty), p=\infty)$ induced norms of continuous-time linear systems where input signals are restricted to be nonnegative. This norm is referred to as the $L_{p+}$ induced norm in this paper. It has been shown recently that the $L_{2+}$ induced norm is effective for the stability analysis of nonlinear feedback systems where the nonlinearity returns only nonnegative signals. However, the exact computation of the $L_{2+}$ induced norm is essentially difficult. To get around this difficulty, in the first part of this paper, we provide a copositive-programming-based method for the upper bound computation by capturing the nonnegativity of the input signals by copositive multipliers. Then, in the second part of the paper, we derive uniform lower bounds of the $L_{p+}\ (p\in[1,\infty), p=\infty)$ induced norms with respect to the standard $L_{p}$ induced norms that are valid for all linear systems including infinite-dimensional ones. For each linear system, we finally derive a computation method of the lower bounds of the $L_{2+}$ induced norm that are larger than (or equal to) the uniform one. The effectiveness of the upper/lower bound computation methods are fully illustrated by numerical examples.Comment: 12 pages, 3 figures. A preliminary version of this paper was presented at ECC 2022 (arXiv:2401.03242) and IFAC WC 202

Postoperative assessment after AVR and TAVI

Background and aims : Severe aortic stenosis (AS) has been normally treated with surgical aortic valve replacement (AVR) whereas recently, transcatheter aortic valve implantation (TAVI) has been introduced as a minimally invasive operation for patients with high surgical risk and frailty. In this study, we have evaluated postoperative physical function and nutrition intake in the patients following AVR and TAVI. Methods : This prospective observational study involved 9 patients with surgical aortic valve replacement (AVR) and 7 patients with transcatheter aortic valve implantation (TAVI). Body composition was measured one day prior surgery, postoperative day (POD) 1, POD 3, POD 5 and POD 7. Hand grip strength, calf circumference and gait speed were measured one day before surgery and on the day of discharge. Results : Skeletal muscle was significantly decreased in AVR patients at postoperative day 3 and 7, while there was no change in TAVI patients. Patients with TAVI showed higher dietary intake after surgery compared to patients with AVR, and they maintained hand grip strength and calf circumference at discharge. Conclusions : In elderly patients with AS, TAVI can improve post-operative recovery maintaining nutritional status and physical function even

Initial state design for suppressing undesirable effects of controller switches

We propose a new initial state design procedure for a newly-activated controller at a controller switch.By minimizing the value of the state-dependent switching L2 gain presented in this paper, we can obtain the optimal initial state for suppressing the difference between the actuality that a controller switch occurs and the virtual situation where it does not occur

Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design

In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is non-convex. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library

Projection onto the Set of Rank-Constrained Structured Matrices for Reduced-Order Controller Design

In this paper, we propose an efficient numerical computation method of reduced-order controller design for linear time-invariant systems. The design problem is described by linear matrix inequalities (LMIs) with a rank constraint on a structured matrix, due to which the problem is non-convex. Instead of the heuristic method that approximates the matrix rank by the nuclear norm, we propose a numerical projection onto the rank-constrained set based on the alternating direction method of multipliers (ADMM). Then the controller is obtained by alternating projection between the rank-constrained set and the LMI set. We show the effectiveness of the proposed method compared with existing heuristic methods, by using 95 benchmark models from the COMPLeib library

L 2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming

International audienceThis paper is concerned with the analysis of the L2 induced norm of continuous-time LTI systems where the input signals are restricted to be nonnegative. This induced norm is referred to as the L2+ induced norm in this paper. It has been shown very recently that the L2+ induced norm is particularly useful for the stability analysis of nonlinear feedback systems constructed from linear systems and static nonlinearities where the nonlinear elements only provide nonnegative signals. For the upper bound computation of the L2+ induced norm, an approach with copositive programming has also been proposed. It is nonetheless true that this approach becomes effective only for multi-input systems, and for single-input systems this approach does not bring any improvement over the trivial upper bound, the standard L2 norm. To overcome this difficulty, we newly introduce positive filters to increase the number of positive signals. This enables us to enlarge the size of the copositive multipliers so that we can obtain better (smaller) upper bounds with copositive programming

L 2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming

International audienceThis paper is concerned with the analysis of the L2 induced norm of continuous-time LTI systems where the input signals are restricted to be nonnegative. This induced norm is referred to as the L2+ induced norm in this paper. It has been shown very recently that the L2+ induced norm is particularly useful for the stability analysis of nonlinear feedback systems constructed from linear systems and static nonlinearities where the nonlinear elements only provide nonnegative signals. For the upper bound computation of the L2+ induced norm, an approach with copositive programming has also been proposed. It is nonetheless true that this approach becomes effective only for multi-input systems, and for single-input systems this approach does not bring any improvement over the trivial upper bound, the standard L2 norm. To overcome this difficulty, we newly introduce positive filters to increase the number of positive signals. This enables us to enlarge the size of the copositive multipliers so that we can obtain better (smaller) upper bounds with copositive programming