This paper focuses on studying the interval continuous-time algebraic Riccati equation A∗X + XA + Q − XGX = 0, both from the theoretical aspects and the computational ones. In theoretical parts, we show that Shary’s results for interval linear systems can only be partially generalized to this interval Riccati matrix equation. We then derive an efficient technique for enclosing the united stable...

Upper bounds for eigenvalues of a solution to continuous time coupled algebraic Riccati equation (CCARE) and discrete time coupled algebraic Riccati equation (DCARE) are developed as special cases of bounds for the uni...ed coupled algebraic Riccati equation (UCARE). They include bounds of the maximal eigenvalues, the sums of the eigenvalues and the trace.

The continuity of various types of Riccati equations has been considered in various contexts in the last decade. In (Czornik, 1996; 2000; Delchamps, 1980; Faibusovich, 1986; Lancaster and Rodman, 1995; Rodman, 1980), the authors examine the continuity of continuous-time algebraic Riccati equations under different conditions. Czornik and Sragovich (1995) consider the situation when the coefficie...

in this paper, the optimal adaptive leader-follower consensus of linear continuous time multi-agent systems is considered. the error dynamics of each player depends on its neighbors’ information. detailed analysis of online optimal leader-follower consensus under known and unknown dynamics is presented. the introduced reinforcement learning-based algorithms learn online the approximate solution...

In this paper, the optimal adaptive leader-follower consensus of linear continuous time multi-agent systems is considered. The error dynamics of each player depends on its neighbors’ information. Detailed analysis of online optimal leader-follower consensus under known and unknown dynamics is presented. The introduced reinforcement learning-based algorithms learn online the approximate solution...

The algebraic regulator and filter Riccati equations of weakly coupled dticrere-rime stochastic linear control systems are completely and exactly decomposed into reduced-order continuous-time algebraic Riccati equations corresponding to the subsystems. That is, the exact solution of the global discrete algebraic Riccati equation is found in terms of the reduced-order subsystem nonsymmetric cont...

A method for H∞ observer design for linear time-delay systems based on the algebraic Riccati equation is proposed. A ”weak” sufficient condition for the existence of such an observer is given.

In this paper, by constructing the equivalent form of the continuous algebraic Riccati equation (CARE) and applying some matrix inequalities, a new lower bounds solution of the CARE is proposed. Finally, corresponding numerical examples are provided to illustrate the effectiveness of the results.