Lyapunov Equations with Positive Definite Solutions for Continuous- and Discrete-time Descriptor Systems

Lyapunov equations with positive definite solutions are presented to guarantee the asymptotic stability for continuous-and discrete-time descriptor systems. They hold without impulse free assumption for continuous-time descriptor system and causal assumption for discrete-time descriptor systems. The solutions of proposed Lyapunov equations can be obtained by Matlab directly.