The discrete algebraic Riccati equation and linear matrix inequality

DOI10.1016/S0024-3795(97)00365-0zbMath0899.93023MaRDI QIDQ1386508

Ali Saberi, Anton A. Stoorvogel

Publication date: 17 November 1998

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

discrete algebraic Riccati equationrank-minimizing solutions to a linear matrix inequality

Mathematics Subject Classification ID

Linear inequalities of matrices (15A39) Discrete-time control/observation systems (93C55)

Related Items (18)

On discrete algebraic Riccati equations: a rank characterization of solutions ⋮ New upper and lower bounds, the iteration algorithm for the solution of the discrete algebraic Riccati equation ⋮ Continuous-time singular linear-quadratic control: necessary and sufficient conditions for the existence of regular solutions ⋮ A new approach to the cheap LQ regulator exploiting the geometric properties of the Hamiltonian system ⋮ Identification of ARX systems with non-stationary inputs -- asymptotic analysis with application to adaptive input design ⋮ A reduction technique for discrete generalized algebraic and difference Riccati equations ⋮ The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation ⋮ Existence of a Mean-Square Stabilizing Solution to a Modified Algebraic Riccati Equation ⋮ A separation theorem for guaranteed \(H_2\) performance through matrix inequalities ⋮ The generalized continuous algebraic Riccati equation and impulse-free continuous-time LQ optimal control ⋮ Finding the strongly rank-minimizing solution to the linear matrix inequality ⋮ Implications of dissipativity on stability of economic model predictive control -- The indefinite linear quadratic case ⋮ Newton's method for a rational matrix equation occurring in stochastic control ⋮ The geometry of the generalized algebraic Riccati equation and of the singular Hamiltonian system ⋮ On the reduction of the continuous-time generalized algebraic Riccati equation: an effective procedure for solving the singular LQ problem with smooth solutions ⋮ Solving the infinite-dimensional discrete-time algebraic Riccati equation using the extended symplectic pencil ⋮ MAX-plus fundamental solution semigroups for a class of difference Riccati equations ⋮ A note on finite-horizon LQ problems with indefinite cost

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