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49
On the Global Existence of Solutions for Game Riccati Differential Equations ∗
"... symplectic transformations, global existence of solutions, H ∞ control. For the symplectic H∞type matrix Riccati differential equation we derive sufficient conditions ensuring the global existence of the solutions of the corresponding initial and/or terminal value problems. 1 ..."
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symplectic transformations, global existence of solutions, H ∞ control. For the symplectic H∞type matrix Riccati differential equation we derive sufficient conditions ensuring the global existence of the solutions of the corresponding initial and/or terminal value problems. 1
A Linear Matrix Inequality Approach to H∞ Control
 INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
, 1994
"... The continuous and discretetime H∞ control problems are solved via elementary manipulations on linear matrix inequalities (LMI). Two interesting new features emerge through this approach: solvability conditions valid for both regular and singular problems, and an LMIbased parametrization of all H ..."
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Cited by 155 (11 self)
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H∞suboptimal controllers, including reducedorder controllers. The solvability conditions involve Riccati inequalities rather than the usual indefinite Riccati equations. Alternatively, these conditions can be expressed as a system of three LMI's. Efficient convex optimization techniques
Hamiltonian structure of the Algebraic Riccati Equation and its Infinitesimal VStability
"... We will investigate the stability behavior of quadratic maps in higher dimensions. To check stability, we will use infinitesimal Vstability of critical points of the map; since the infinitesimal Vstability of a map at all of its critical points is equivalent to the stability of the map. We will es ..."
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will establish the connection between infinitesimal Vstability of solutions to the Algebraic Riccati Equations, and the Hamiltonian eigenstructure of the solutions, by investigating the stability behavior of the corresponding Riccati map. Infinitesimal Vstability of critical points of the Riccati map
Solving algebraic Riccati equations with SLICOT
 in CDROM Proc. of The 11th Mediterranean Conference on Control and Automation MED’03, June 18–20 2003, Rhodes, Greece, 2003, invited session IV01, Paper IV0101
"... Abstract — The numerical solution of algebraic Riccati equations is a central issue in computeraided control systems design. It is the key step in many computational methods for model reduction, filtering, and controller design for linear control systems. We discuss recent advances in the solvers f ..."
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Cited by 4 (1 self)
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Abstract — The numerical solution of algebraic Riccati equations is a central issue in computeraided control systems design. It is the key step in many computational methods for model reduction, filtering, and controller design for linear control systems. We discuss recent advances in the solvers
Newton's Method with Exact Line Search for Solving the Algebraic Riccati Equation
, 1995
"... This paper studies Newton's method for solving the algebraic Riccati equation combined with an exact line search. Based on these considerations we present a Newtonlike method for solving algebraic Riccati equations. This method can improve the sometimes erratic convergence behavior of Newton& ..."
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Cited by 3 (0 self)
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p\Thetap , C 2 IR p\Thetan , and S 2 IR p\Thetam . This equation arises frequently in control problems. We will assume that E and R are nonsingular and Q S S T R 0, where M 0 denotes positive semidefinite matrices M . Often, the desired solution X is stabilizing in the sense
A Cyclic Reduction Method for Solving Algebraic Riccati Equations
, 2006
"... A new iterative method for solving algebraic Riccati equations is presented. The algorithm is based on the transformation of the Riccati equation into an equation of the form AX2 +BX +C = 0 which is e±ciently solved via the Cayley transform and cyclic reduction. The algorithm is quadratically conv ..."
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A new iterative method for solving algebraic Riccati equations is presented. The algorithm is based on the transformation of the Riccati equation into an equation of the form AX2 +BX +C = 0 which is e±ciently solved via the Cayley transform and cyclic reduction. The algorithm is quadratically
Disk Functions And Their Relationship To The Matrix Sign Function
, 1997
"... This short paper investigates a generalization of the matrix sign function to matrix pencils. 1 Introduction The problem of extracting an invariant subspace of a matrix or a deflating subspace of a matrix pencil arises in many control computations including solving Lyapunov, Sylvester, and Riccati ..."
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Cited by 10 (7 self)
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less common) definitions is the following. The sign of a matrix A 2 R n\Thetan is the antistabilizing solution S = sign(A) to the (nonsymmetric) algebraic Riccati equation A \Gamma SAS = 0; (1) i.e., the solution for which the eigenvalues of AS lie in the open right half plane. (Equation (1
ForwardIntegration RiccatiBased OutputFeedback Control of Linear TimeVarying Systems
 Proc. Amer. Conf. Contr
, 2012
"... Abstract — In applications involving timevarying systems, the state dynamics matrix is often not known in advance. To address this problem, this paper investigates the effectiveness of a forwardintime Riccatibased control law. This approach is motivated by the fact that the optimal state estimat ..."
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Cited by 1 (1 self)
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estimator is based on a forwardintime Riccatibased solution that does not require advance knowledge of the system dynamics. In this paper we show that a forwardintime Riccatibased control law stabilizes the system if the dynamics of the quasidual system are asymptotically stable. This property holds
Computation of L_2Induced Norms of Switched Linear Systems
"... In this paper we compute the L2induced norm of a switched linear system when the interval between consecutive switchings is large. The motivation for this problem is the application of robust stability tools to the analysis of hybrid systems. The algorithm proposed is based on the fact that a giv ..."
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given constant # provides an upper bound on the L2induced norm whenever there is a separation between the stabilizing and the antistabilizing solutions to a set of algebraic Riccati equations. 1
Efficient algorithms for generalized algebraic Bernoulli equations based on the matrix sign function
 Numer. Algor.
, 2007
"... ..."
Results 1  10
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