Abstract
The continuous coupled algebraic Riccati equation (CCARE) has wide applications in control theory and linear systems. In this paper, by a constructed positive semidefinite matrix, matrix inequalities, and matrix eigenvalue inequalities, we propose a new two-parameter-type upper solution bound of the CCARE. Next, we present an iterative algorithm for finding the tighter upper solution bound of CCARE, prove its boundedness, and analyse its monotonicity and convergence. Finally, corresponding numerical examples are given to illustrate the superiority and effectiveness of the derived results.
Highlights
Consider the following optimal control of jump linear system described by x_(t) A(r(t))x(t) + B(r(t))u(t), x t0 x0, (1)where x(t) ∈ Rn is the plant state and u(t) ∈ Rm is the control vector
A new two-parameter-type upper solution bound of the continuous coupled algebraic Riccati equation (CCARE) has been proposed
An iterative algorithm for finding the tighter upper solution bound of CCARE has been presented, and its boundedness, monotonicity, and convergence have been proved
Summary
Consider the following optimal control of jump linear system described by x_(t) A(r(t))x(t) + B(r(t))u(t), x t0 x0, (1). CCARE (4) is usually encountered in robust and optimal control [1,2,3,4,5,6,7,8], filter design [9], time-delay systems controller design [10], stability analysis [11,12,13,14,15,16], etc In these fields, it often suffices to estimate the tighter solution bounds of the algebraic Riccati equation rather than get the exact solution. A > 0(A ≥ 0) is used to denote that A is a symmetric positive definite (semidefinite) matrix. For any given positive semidefinite matrix A ∈ Rn×n and B ∈ Rn×n,. Let Wkk∈N ⊂ Rn×n be a given sequence of positive semidefinite matrices. Wkk∈N converges to a unique positive semidefinite W ∈ Rn×n
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