Existence and comparison theorems for algebraic Riccati equations and Riccati differential and difference equations

DOI10.1007/BF02254701zbMath0979.93091MaRDI QIDQ1972729

Gerhard Freiling, Gerhard Jank

Publication date: 13 April 2000

Published in: Journal of Dynamical and Control Systems (Search for Journal in Brave)

zbMATH Keywords

comparison theoremgeneralized Riccati differential equationsRiccati difference equationsintervals of existence of solutions

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Matrix equations and identities (15A24) Existence theories for optimal control problems involving ordinary differential equations (49J15)

Related Items (16)

On Riccati matrix differential equations ⋮ Perturbation Theory for Linearly Perturbed Algebraic Riccati Equations ⋮ On the dependence of the solutions of algebraic and differential game Riccati equations on the parameter \(\mu\) ⋮ Convergence and existence results for continuous- and discrete-time Riccati equations ⋮ Systems of matrix rational differential equations arising in connection with linear stochastic systems with Markovian jumping. ⋮ On a class of rational matrix differential equations arising in stochastic control. ⋮ Existence and comparison theorems for algebraic Riccati equations and Riccati differential and difference equations ⋮ Disturbance attenuating output-feedback control of nonlinear systems with local optimality ⋮ ℋ_∞stabilisation of switched linear stochastic systems under dwell time constraints ⋮ Generalized Riccati equations arising in stochastic games ⋮ Existence and uniqueness of open-loop Stackelberg equilibria in linear-quadratic differential games ⋮ Properties of the solutions of rational matrix difference equations ⋮ Time-varying discrete Riccati equation: Some monotonicity results ⋮ Invariant manifolds and projective combinations of solutions of the Riccati differential equation ⋮ Upper and lower bounds for the solution of the general matrix Riccati differential equation on a time scale ⋮ A survey of nonsymmetric Riccati equations

Cites Work

• Unnamed Item
• Unnamed Item
• On the existence of maximal solution for generalized algebraic Riccati equations arising in stochastic control
• Monotonicity of maximal solutions of algebraic Riccati equations
• Existence and comparison theorems for algebraic Riccati equations for continuous- and discrete-time systems
• Maximal solution of a certain class of periodic Riccati differential equations
• A comparison theorem for matrix Riccati difference equations
• The general nonstrict algebraic Riccati inequality
• Non-symmetric matrix Riccati equations
• On the solution of discrete-time Markovian jump linear quadratic control problems
• On the dependence of the solutions of algebraic and differential game Riccati equations on the parameter \(\mu\)
• Existence and comparison theorems for algebraic Riccati equations and Riccati differential and difference equations
• An existence and monotonicity theorem for the discrete algebraic matrix Riccati equation
• On stabilizing properties of solutions of the Riccati difference equation
• On Hermitian Solutions of the Symmetric Algebraic Riccati Equation
• Robust-controller design for systems with large parameter variations
• Existence of positive-definite and semidefinite solutions of discrete-time algebraic Riccati equations
• Solution and asymptotic behavior of coupled Riccati equations in jump linear systems
• On a Matrix Riccati Equation of Stochastic Control
• On the discrete time matrix Riccati equation of optimal control†

This page was built for publication: Existence and comparison theorems for algebraic Riccati equations and Riccati differential and difference equations