The Experts below are selected from a list of 1872 Experts worldwide ranked by ideXlab platform
Chienhua Lee - One of the best experts on this subject based on the ideXlab platform.
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upper and lower matrix bounds of the solution for the Discrete Lyapunov Equation
IEEE Transactions on Automatic Control, 1996Co-Authors: Chienhua LeeAbstract:New matrix bounds of the solution for the Discrete algebraic matrix Lyapunov Equation are established. The upper and lower eigenvalue bounds such as each eigenvalue including the extreme ones, the trace, and the determinant are also determined by these matrix bounds for the same solution. The present schemes are tighter as compared with the majority of existing results.
A Hmamed - One of the best experts on this subject based on the ideXlab platform.
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Discrete Lyapunov Equation simultaneous eigenvalue lower bounds
International Journal of Systems Science, 1991Co-Authors: A HmamedAbstract:Some lower bounds for the eigenvalues and certain sums and products of the eigenvalues of the solution of the Discrete Lyapunov matrix Equation are presented. These bounds are stronger than the majority of the relevant bounds shown in the literature. They complete some known bounds such as the extremal eigenvalues, the determinant and the trace of the solution of the above Equation.
Lorenzo Ntogramatzidis - One of the best experts on this subject based on the ideXlab platform.
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the generalised Discrete algebraic riccati Equation in linear quadratic optimal control
Automatica, 2013Co-Authors: Augusto Ferrante, Lorenzo NtogramatzidisAbstract:This paper investigates the properties of the solutions of the generalised Discrete algebraic Riccati Equation arising from the classic infinite-horizon linear quadratic (LQ) control problem. In particular, a geometric analysis is used to study the relationship existing between the solutions of the generalised Riccati Equation and the output-nulling subspaces of the underlying system and the corresponding reachability subspaces. This analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem, which is reflected in the generalised eigenstructure of the corresponding extended symplectic pencil. In establishing the main results of this paper, several ancillary problems on the Discrete Lyapunov Equation and spectral factorisation are also addressed and solved.
K S Riedel - One of the best experts on this subject based on the ideXlab platform.
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exponential condition number of solutions of the Discrete Lyapunov Equation
IEEE Transactions on Signal Processing, 2004Co-Authors: A P Mullhaupt, K S RiedelAbstract:The condition number of the n/spl times/n matrix P is examined, where P solves P-APA/sup */=BB/sup */, and B is a n/spl times/d matrix. Lower bounds on the condition number /spl kappa/ of P are given when A is normal, a single Jordan block, or in Frobenius form. The bounds show that the ill-conditioning of P grows as exp(n/d)/spl Gt/1. These bounds are related to the condition number of the transformation that takes A to input normal (IN) form. A simulation shows that P is typically ill-conditioned in the case of n/spl Gt/1 and d=1. When A/sub ij/ has an independent Gaussian distribution (subject to restrictions), we observe that /spl kappa/(P)/sup 1/n//spl sim/3.3. The effect of autocorrelated forcing on the conditioning on state space systems is examined.
Augusto Ferrante - One of the best experts on this subject based on the ideXlab platform.
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the generalised Discrete algebraic riccati Equation in linear quadratic optimal control
Automatica, 2013Co-Authors: Augusto Ferrante, Lorenzo NtogramatzidisAbstract:This paper investigates the properties of the solutions of the generalised Discrete algebraic Riccati Equation arising from the classic infinite-horizon linear quadratic (LQ) control problem. In particular, a geometric analysis is used to study the relationship existing between the solutions of the generalised Riccati Equation and the output-nulling subspaces of the underlying system and the corresponding reachability subspaces. This analysis reveals the presence of a subspace that plays an important role in the solution of the related optimal control problem, which is reflected in the generalised eigenstructure of the corresponding extended symplectic pencil. In establishing the main results of this paper, several ancillary problems on the Discrete Lyapunov Equation and spectral factorisation are also addressed and solved.