Stability analysis for switched discrete-time linear singular systems
Pham Ky Anh, Pham Thi Thuy Linh, Do Duc Thuan, Stephan Trenn
Abstract
The stability of arbitrarily switched discrete-time linear singular (SDLS) systems is studied. Our analysis builds on the recently introduced one-step-map for SDLS systems of index-1. We first provide a sufficient stability condition in terms of Lyapunov functions. Furthermore, we generalize the notion of joint spectral radius of a finite set of matrix pairs, which allows us to fully characterize exponential stability.
Topics & Concepts
MathematicsStability (learning theory)Lyapunov functionLinear systemSpectral radiusDiscrete time and continuous timeExponential stabilitySet (abstract data type)Applied mathematicsSingular valueMatrix (chemical analysis)Control theory (sociology)Mathematical analysisComputer scienceEigenvalues and eigenvectorsNonlinear systemPhysicsControl (management)Artificial intelligenceMachine learningComposite materialProgramming languageMaterials scienceStatisticsQuantum mechanicsStability and Control of Uncertain SystemsControl and Stability of Dynamical SystemsMatrix Theory and Algorithms