Yet Another Computation-Oriented Necessary and Sufficient Condition for Stabilizability of Switched Linear Systems
Mirko Fiacchini
Abstract
This article presents a computational method to test the stabilizability of discrete-time switched linear systems. The existence of a conic cover of the space on whose elements a convex condition holds is proved to be necessary and sufficient for stabilizability. An algorithm for computing a conic partition that satisfies the new necessary and sufficient condition is given. The algorithm, which allows us to determine bounds on the exponential convergence rate, is proved to overcome the conservatism of conditions equivalent to periodic stabilizability and is applied to a 4-D system.
Topics & Concepts
Conic sectionMathematicsPartition (number theory)Linear systemConvergence (economics)Cover (algebra)ComputationRegular polygonApplied mathematicsControl theory (sociology)Computer scienceAlgorithmControl (management)Mathematical analysisCombinatoricsEconomic growthEconomicsMechanical engineeringEngineeringArtificial intelligenceGeometryStability and Control of Uncertain SystemsControl and Stability of Dynamical SystemsNetwork Time Synchronization Technologies