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Adaptive finite-time fault-tolerant control scheme of UAV against combined faults. [PDF]

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Yan X, Li T, Tian Y.
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The Periodic Lyapunov Equation

SIAM Journal on Matrix Analysis and Applications, 1988
Necessary and sufficient conditions for the existence and uniqueness of (positive semidefinite) T-periodic solutions of T-periodic Lyapunov equations in discrete- and continuous-time are given. The proofs are based on the equivalence of these problems to those for certain algebraic Lyapunov equations. Also inertia theorems are included.
BOLZERN, PAOLO GIUSEPPE EMILIO, COLANERI, PATRIZIO   +1 more
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Numerical solution of singular Lyapunov equations

Numerical Linear Algebra with Applications, 2021
AbstractWe consider the numerical solution of large scale singular (continuous‐time) Lyapunov equations of the formAX + XA⊤ + BB⊤ = 0, whereAis semistable, that is, its spectrum is contained in the left half plane, with the exception of a few semisimple eigenvalues at zero. We also consider the case of a few semisimple eigenvalues on the imaginary axis.
Eric K.‐W. Chu, Daniel B. Szyld, Jieyong Zhou   +2 more
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Low Rank Solution of Lyapunov Equations

SIAM Journal on Matrix Analysis and Applications, 2002
The Cholesky factor-alternating direction implicit algorithm is presented to compute a low rank approximation to the solution \(X\) of the Lyapunov equation \(AX+XA^T=-BB^T\) with large matrix \(A\) and right hand side of low rank. The algorithm requires only matrix-vector products and linear solvers.
Li, Jing-Rebecca, White, Jacob
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Solving Lyapunov equations symbolically

Proceedings of Joint Conference on Control Applications Intelligent Control and Computer Aided Control System Design, 2002
Symbolic manipulation is an indispensable tool in control design and in system analysis. While numeric computational languages and algorithms have been exhaustively used, symbolic manipulation methods have been barely used at all. In this study, we developed a Maple language procedure to solve continuous Lapunov equations symbolically in conjunction ...
M. Abdalla, R. Wang, R. McLauchlan
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Parallel Solution of Large Lyapunov Equations

SIAM Journal on Matrix Analysis and Applications, 1992
The solution of large-order (\(100\leq n\leq 1000\)) Lyapunov equations \(AX+XA^ T+Q=0\) is considered. A parallel version of the Hammarling algorithm [cf. \textit{S. J. Hammerling}, IMA J. Numer. Anal. 2, 303-323 (1982; Zbl 0492.65017)] for large and dense \(A\) and a novel iterative parallel algorithm, called full-rank perturbed iteration (FRPI), for
Hodel, A. Scottedward, Poolla, Kameshwar
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Solution of the Discrete Lyapunov Equation

SIAM Journal on Algebraic Discrete Methods, 1985
Consider the discrete Lyapunov equation \(P=A^ TPA+Q\) with given \(n\times n\) matrices A,Q and symmetric, positive definite Q. A unique symmetric, positive solution P exists when \(\rho (A)
Fu, Sheauwei, Sawan, Mahmoud E.
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Hyperbolic operator semigroups and Lyapunov’s equation

Mathematical Notes, 2011
The authors consider a complex Hilbert space \({\mathcal H}\) and the Banach algebra of linear bounded operators acting on \({\mathcal H}\), \(\operatorname{End} {\mathcal H}\). The authors extend Krein's results to the generators of strongly continuous groups of operators and to the generators of certain classes of semigroups of operators.
Baskakov, A. G., Vorob'ev, A. A., Romanova, M. Yu.   +2 more
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