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It is well known that the bilinear transform, or first order diagonal Padé approximation to the matrix exponential, preserves quadratic Lyapunov functions between continuous-time and corresponding discrete-time linear time invariant (LTI) systems, regardless of the sampling time. It is also well known that this mapping preserves common quadratic Lyapunov functions between continuous-time and discrete-time...
We establish a unified approach to stability and L2 gain analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for stability of all subsystems, then the...
We present a novel ultimate bound computation method for switched linear systems with disturbances and arbitrary switching. We consider both discrete-time and continuous-time systems. The proposed method relies on the existence of a transformation that takes all matrices of the switched linear system into a convenient form satisfying certain properties. The method provides ultimate bounds in the form...
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