Some Upper Matrix Bounds for the Solution of the Continuous Algebraic Riccati Matrix Equation

Abstract

We propose diverse upper bounds for the solution matrix of the continuous algebraic Riccati matrix equation (CARE) by building the equivalent form of the CARE and using some matrix inequalities and linear algebraic techniques. Finally, numerical example is given to demonstrate the effectiveness of the obtained results in this work as compared with some existing results in the literature. These new bounds are less restrictive and provide more efficient results in some cases.

Control Techniques for a Class of Fractional Order Systems

“…Ref. [29] For matrix P R nxn , P = P T 0, the following inequality holds: λ min(P) I P λ max(P) I Consider the fractional order system…”

“…is a Hurwitz matrix and P is the solution of the Lyapunov equation, A * P + PA * = −qq T = −Q and P < λ max(P) < ζ(Q), ζ represents the upper matrix bound of P [29].…”

“…A matrix Q = qq T = diag(0.1 0.1 0.1 0.1] is used for Lyapunov Equation (22). The upper matrix bound λ max(P) = ζ(Q) = 96.8 is evaluated [29]. The matrix…”

“…Stability criteria are formulated in the form of algebraic criteria [22][23][24] or are derived by analytical techniques derived from the Lyapunov method [25][26][27][28]. The control of multi-system architectures defined by FOS models is discussed in [29][30][31]. Frequency criteria for the control of Linear FOS are presented in [32][33][34].…”