The interval Lyapunov matrix equation: analytical results and an efficient numerical technique for outer estimation of the united solution set

DOI10.1016/j.mcm.2011.08.036zbMath1255.15002OpenAlexW2044499328MaRDI QIDQ1930971

Behnam Hashemi, Mehdi Dehghan

Publication date: 24 January 2013

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2011.08.036

zbMATH Keywords

interval analysisLyapunov matrix equationunited solution setAE-solution sets

Mathematics Subject Classification ID

Related Items (13)

Parametric AE-solution sets to the parametric linear systems with multiple right-hand sides and parametric matrix equation \(A(p)X=B(p)\) ⋮ Generalized solution sets of the interval generalized Sylvester matrix equation \(\sum_{i=1}^p\mathbf A_iX_i+\sum_{j=1}^qY_j\mathbf B_j=\mathbf C\) and some approaches for inner and outer estimations ⋮ Fast enclosing the solution set of the parametric Sylvester matrix equations ⋮ On the iterative method for the system of nonlinear matrix equations ⋮ New sufficient conditions for robust stability analysis of interval matrices ⋮ A Newton iterative method for coupled Lyapunov matrix equations ⋮ Efficient approaches for enclosing the united solution set of the interval generalized Sylvester matrix equations ⋮ Sufficient conditions for the solvability of a Sylvester-like absolute value matrix equation ⋮ The united stable solution set of interval continuous-time algebraic Riccati equation and veri ed numerical computation of its outer estimation ⋮ New sufficient conditions for the unique solution of a square Sylvester-like absolute value equation ⋮ Kalman state filtering based least squares iterative parameter estimation for observer canonical state space systems using decomposition ⋮ Unnamed Item ⋮ Enclosing the solution set of the parametric generalised Sylvester matrix equation A(p)XB(p) + C(p)XD(p) = F(p)

Uses Software

• INTLAB
• ParLinSys
• Algorithm 432

Cites Work

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• Results concerning interval linear systems with multiple right-hand sides and the interval matrix equation \(AX=B\)
• Scientific computing with automatic result verification
• Inner and outer bounds for the solution set of parametric linear systems
• Derived eigenvalues of symmetric matrices, with applications to distance geometry
• Controllable solution set to interval static systems
• A note on epsilon-inflation
• The interval Sylvester equation
• Enclosing solutions of linear interval equations is NP-hard
• Computational complexity and feasibility of data processing and interval computations
• Robust assignment of poles in large-scale interval systems
• A new technique in systems analysis under interval uncertainty and ambiguity
• Numerical solution of the Lyapunov equation by approximate power iteration
• Algebraic approach to the interval linear static identification, tolerance, and control problems, or one more application of Kaucher arithmetic
• Verified Computation of Square Roots of a Matrix
• Introduction to Interval Analysis
• A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
• Rigorous solution of linear programming problems with uncertain data
• Quality of the Solution Sets of Parameter-Dependent Interval Linear Systems
• Computing Exact Componentwise Bounds on Solutions of Lineary Systems with Interval Data is NP-Hard
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Approximation of Large-Scale Dynamical Systems

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