Riccati equation

About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.

Competitive and Cooperative Tridiagonal Systems of Differential Equations

Abstract: A vector field in $\mathbb{R}^n $ determines a competitive (or cooperative) system of differential equations provided all the off-diagonal terms of the Jacobian matrix are nonpositive (or nonnegati...

Upper and lower bounds on the solution of the algebraic Riccati equation

Abstract: Given an algebraic matrix Riccati equation A'K+ KA - KBB'K + Q =0 , the fundamental inequalities which are satisfied by the extremal eigenvalues of the positive definite solution K , are established. It Is illustrated that these resultant estimations appear to be considerably tighter than previously available results in many cases. Similar results are obtained for the discrete algebraic matrix Riccati equation.

Robust stabilization for uncertain time-delay systems containing saturating actuators

Abstract: A class of uncertain time-delay systems containing a saturating actuator is considered. These systems are characterized by delayed state equations (including a saturating actuator) with norm-bounded parameter uncertainty (possibly time varying) in the state and input matrices. The delay is assumed to be constant bounded but unknown. Using a Razumikhin approach for the stability of functional differential equations, upper bounds on the time delay are given such that the considered uncertain system is robustly stabilizable, in the case of constrained input, via memoryless state feedback control laws. These bounds are given in terms of solutions of appropriate finite dimensional Riccati equations.

Stability and stabilization of fuzzy large-scale systems

Abstract: This paper investigates the stability and stabilization problems for the fuzzy large-scale system in which the system is composed of a number of Takagi-Sugeno fuzzy model subsystems with interconnections. The stability criterion of the fuzzy large-scale system without control is derived first. Instead of fuzzy parallel distributed compensation design, linear state feedback control is used in the stabilization work. Each local control is obtained from Riccati equation of the corresponding subsystem and the interconnection terms are used to determine the local feedback gain determination. Based on Lyapunov criterion, some conditions are derived under which the whole fuzzy large-scale system is stabilized asymptotically. A numerical example is given to illustrate the control design procedure and its effectiveness.