On the Structure of the Solutions of Discrete-Time Algebraic Riccati Equation With Singular Closed-Loop Matrix

2004 ◽  
Vol 49 (11) ◽  
pp. 2049-2054 ◽  
Author(s):  
A. Ferrante
Keyword(s):  
Riccati Equation ◽  
Discrete Time ◽  
Closed Loop ◽  
Algebraic Riccati Equation ◽  
Loop Matrix

Robust H∞ State Feedback Control With Regional Pole Constraints: An Algebraic Riccati Equation Approach

1998 ◽  
Vol 120 (2) ◽  
pp. 289-292 ◽  
Author(s):  
Zidong Wang
Keyword(s):  
Riccati Equation ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
State Feedback Control ◽  
Algebraic Riccati Equation ◽  
Equation Approach ◽  
Parameter Uncertainties ◽  
Realization Problem ◽  
Loop Matrix

This paper focuses on the controller design for uncertain linear continuous-time systems with H∞ norm and circular pole constraints and addresses the following multiobjective simultaneous realization problem: designing a state feedback controller such that the closed-loop system, for all admissible parameter uncertainties, simultaneously satisfies the prespecified H∞ norm constraint on the transfer function from disturbance input to output and the prespecified circular pole constraint on the closed-loop matrix. An effective, algebraic, modified Riccati equation approach is developed to solve this problem. The existence conditions, as well as the analytical expression of desired controllers, are derived. A numerical example is provided to show the directness and effectiveness of the present approach.

scholarly journals Indefinite LQ Control for Discrete-Time Stochastic Systems via Semidefinite Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Shaowei Zhou ◽  
Weihai Zhang
Keyword(s):  
Semidefinite Programming ◽  
Riccati Equation ◽  
Discrete Time ◽  
Time Horizon ◽  
Stochastic Systems ◽  
Positive Semidefinite ◽  
Algebraic Riccati Equation ◽  
Infinite Time ◽  
Lq Problem ◽  
Lq Control

This paper is concerned with a discrete-time indefinite stochastic LQ problem in an infinite-time horizon. A generalized stochastic algebraic Riccati equation (GSARE) that involves the Moore-Penrose inverse of a matrix and a positive semidefinite constraint is introduced. We mainly use a semidefinite-programming- (SDP-) based approach to study corresponding problems. Several relations among SDP complementary duality, the GSARE, and the optimality of LQ problem are established.

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