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This paper investigates the linear quadratic regulator (LQR) problem for continuous-time linear systems with redundant control inputs. The LQR control problem has been widely studied, but due to technical difficulties, there is little advance in the study of adding input redundancies. To address this problem, a convergent matrix series, the limit of a monotonically decreasing sequence, is first presented as an upper bound of the symmetric positive definite solution of a class of continuous algebraic Riccati equations (CAREs). Compared with the existing studies on this topic, the obtained bounds are more precise. Moreover, by utilising these upper bounds in the LQR problem of adding input redundancies, a class of sufficient conditions is presented to decrease the quadratic performance index. Finally, the corresponding numerical examples are given to illustrate the effectiveness of our results and compare them with the existing results. Meanwhile, some simulation experiments show that systems with redundant control inputs have good control performance. [ABSTRACT FROM AUTHOR]

Stability is important for control systems. In this paper, using the transformation of the matrix equations and some significant properties of the matrix inequality, we derived new upper solution bounds of the continuous coupled algebraic Riccati equation (CCARE). The new bounds are more precise than those proposed in some existing works on this topic numerically. Next, a condition for the stability of multi-agent systems with time-delay in the state is presented according to the upper solution bound of the CCARE. Finally, corresponding numerical examples are provided to illustrate the superior and effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

Infective endocarditis (IE)-associated rapidly progressive glomerulonephritis (RPGN) is rarely reported. Sporadic case reports have noted the diagnostic and therapeutic challenge in IE-associated glomerulonephritis because it may masquerade as idiopathic vasculitis. Patients with clinical diagnosis of IE-related RPGN in a tertiary hospital in China between January 2004 and May 2021 were identified and retrospectively reviewed. Twenty-four patients with IE-associated RPGN were identified. All patients presented with fever and multiorgan system involvement on top of heart and kidneys, spleen (79%, 19/24), skin (63%, 15/24), lung (33%, 8/24) and nervous system (17%, 4/24). Six of the 24 patients (25%) were initially suspected to have ANCA-associated or IgA vasculitis. Forty-five percent of patients are seropositive for ANCA. Renal histology showed mesangial and/or endocapillary hypercellularity with extensive crescents in most patients. C3-dominant deposition was the predominant pattern on immunofluorescence and pauci-immune necrotising crescentic glomerulonephritis was observed in one case. All patients received antibiotics with or without surgery. Six patients received immunosuppressive therapy before antibiotics due to misdiagnosis and seven patients received immunosuppressive therapy after antibiotics due to persistence of renal failure. Three of the 24 patients died due to severe infection. All the surviving patients had partial or complete recovery of renal function. IE-associated RPGN is rare and the differential diagnosis from idiopathic vasculitis can be challenging due to overlaps in clinical manifestations, ANCA positivity and absence of typical presentations of IE. The prognosis is generally good if antibiotics and surgery are not delayed. The decision on introducing immunoruppressive treatment should be made carefully on a case by case basis when kidney function does not improve appropriately after proper anti-infective therapy. Infective endocarditis associated RPGN is rare and differentiating it from idiopathic vasculitis can be challenging due to overlap in clinical manifestations, ANCA positivity and occasional absence of typical manifestations of infective endocarditis. Kidney function usually responds to antibiotic therapy alone. Immunosuppressive therapy may be beneficial in carefully selected patients whose kidney function does not improve with antibiotics alone. [ABSTRACT FROM AUTHOR]

In this paper, we first show a class relation between the eigenvalue of functional matrix derivative and the derivative of function matrix eigenvalue. Applying the relation, we transform the time-varying linear matrix differential equation into eigenvalue differential equation. Furthermore, by using singular value decomposition and majorisation inequalities, we derive upper and lower bounds on eigenvalue summation of the solution for the Lyapunov matrix differential equation, which improve the recent results. As an application in control and optimisation, we show that our bounds could be used to discuss the stability of a class time-varying nonlinear system. Finally, we give a corresponding numerical example to show the superiority and effectiveness of the derived bounds. [ABSTRACT FROM AUTHOR]

The discrete coupled algebraic Riccati equation (DCARE) has wide applications in control theory and linear system. In general, for the DCARE, one discusses every term of the coupled term, respectively. In this paper, we consider the coupled term as a whole, which is different from the recent results. When applying eigenvalue inequalities to discuss the coupled term, our method has less error. In terms of the properties of special matrices and eigenvalue inequalities, we propose several upper and lower matrix bounds for the solution of DCARE. Further, we discuss the iterative algorithms for the solution of the DCARE. In the fixed point iterative algorithms, the scope of Lipschitz factor is wider than the recent results. Finally, we offer corresponding numerical examples to illustrate the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

In the paper, basing on the structure of Nekrasov matrices, the authors first obtain several practical criteria for judgingH-matrices, then provide some criteria for identifying that a given matrix is not anH-matrix. The effectiveness of the proposed results is illustrated by numerical examples. [ABSTRACT FROM PUBLISHER]

In this paper, combining the equivalent form of the unified coupled algebraic Riccati equation (UCARE) with the eigenvalue inequalities of a matrix's sum and product, using the properties of an M-matrix and its inverse matrix, we offer new lower and upper matrix bounds for the solution of the UCARE. Furthermore, applying the derived lower and upper matrix bounds and a fixed-point theorem, an existence uniqueness condition of the solution of the UCARE is proposed. Then, we propose a new fixed-point iterative algorithm for the solution of the UCARE. Finally, we present a corresponding numerical example to demonstrate the effectiveness of our results. [ABSTRACT FROM PUBLISHER]

By using singular value decomposition and majorisation inequalities, we propose new upper and lower bounds for summations of eigenvalues (including the trace) of the solution of the continuous algebraic Riccati equation. These bounds improve and extend some of the previous results. Finally, we give corresponding numerical examples to illustrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this article, applying the properties of M-matrix and non-negative matrix, utilising eigenvalue inequalities of matrix's sum and product, we firstly develop new upper and lower matrix bounds of the solution for discrete coupled algebraic Riccati equation (DCARE). Secondly, we discuss the solution existence uniqueness condition of the DCARE using the developed upper and lower matrix bounds and a fixed point theorem. Thirdly, a new fixed iterative algorithm of the solution for the DCARE is shown. Finally, the corresponding numerical examples are given to illustrate the effectiveness of the developed results. [ABSTRACT FROM AUTHOR]

Some well-known characterizations of nonnegative k-potent matrices have been obtained by Flor [P. Flor, On groups of nonnegative matrices, Compositio Math. 21 (1969), pp. 376-382.] and Jeter and Pye [M. Jeter and W. Pye, Nonnegative (s, t)-potent matrices, Linear Algebra Appl. 45 (1982), pp. 109-121.]. In this article, we obtain a structural characterization of a real k-potent matrix A, provided that (sgn(A))k+1 is unambiguously defined, regardless of whether A is nonnegative or not. [ABSTRACT FROM AUTHOR]

In this article, by using some matrix identities, we construct the equivalent form of the continuous coupled algebraic Riccati equation (CCARE). Further, with the aid of the eigenvalue inequalities of matrix's product, by solving the linear inequalities utilising the properties of M-matrix and its inverse matrix, new upper matrix bounds for the solutions of the CCARE are established, which improve and extend some of the recent results. Finally, a corresponding numerical example is proposed to illustrate the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

Recently, some iterative characterizations of H-matrices have been proposed. These methods can have less computational complexity than the direct ones, but as they are all designed for a sequential computer, they may be not so effective for large scalar matrices. In this paper, based on the previous and new ideas, we discuss about the parallel characterization of H-matrices on the distributed-memory multiprocessor machines, and propose two new algorithms which need fewer number of iterations and less computational time than the earlier ones. Several numerical examples to show the effectiveness of the proposed algorithms are provided. [ABSTRACT FROM AUTHOR]

In this paper we provide several new criteria for generalized diagonally dominant matrices (GDDMs) by making use of elements of matrices only, and also propose two corresponding non-parameter algorithms to test GDDMs. Numerical examples for the effectiveness of the methods are presented. [ABSTRACT FROM AUTHOR]