A Lyapunov Variable-Free KYP Lemma for SISO Continuous Systems

This technical note proposes a novel frequency-selective Kalman-Yakubovich-Popov (FS–KYP) lemma for analysis of single-input single-output (SISO) continuous systems. In contrast to existing approaches, the proposed method only uses a minimal number of variables due to the absence of Lyapunov variables in semidefinite programming (SDP) formulation. The SDP formulation is extended to polytopic uncertain systems also without any additional variable and yields an efficient method for computation of the $H_{\infty} $ gain for polytopic systems. The viability of the proposed method are demonstrated through several numerical examples.