Abstract :
This work is motivated by some recent works on dilated LMI characterization (M.C. de Oliveira et al., 1999), (M.C. de Oliveira and R.E. Skelton, 2001), (D. Peaucelle et al., 2000) and sums-of-squares Lyapunov functions (J. Xu and L. Xie, 2005), (G. Chesi et al., 2003), as well as duality theory (R. Goebel et al., 2004), (A. Rantzer, 2001), (R. Goebel et al., 2005). The paper is divided into two parts. In the first part, we study the dilated LMI characterization, and show that many existing results can be derived under a unified framework. In the second part, we present a new stability result employing the dilated LMI characterization and sums-of-squares Lyapunov function, which can improve the stability analysis for polytopic uncertain systems compared with the existing works
Keywords :
Lyapunov matrix equations; duality (mathematics); linear matrix inequalities; linear systems; stability criteria; uncertain systems; dilated linear matrix inequality; duality theory; linear uncertain system; polytopic uncertain system; stability criterion; sums-of-squares Lyapunov function; Control system synthesis; Control systems; Filters; Linear matrix inequalities; Lyapunov method; Stability analysis; Stability criteria; Uncertain systems; Linear uncertain systems; dilated linear matrix inequality; duality; stability; sums of squares;
