Efficient Positive Real Balanced Truncation of SISO Systems Via Cross-Riccati Equations

Abstract

This paper presents a highly efficient approach for performing positive real balanced truncation (PRBT) of single-input single-output (SISO) systems. The solution of two dual algebraic Riccati equations (AREs), whose high computational cost baffles conventional PRBT, is replaced with the solution of a cross-Riccati equation (CRE). The cross-Riccatian nature of the solution then allows simple construction of the projection matrices in PRBT. Application examples confirm the effectiveness of the proposed PRBT method over conventional schemes