Total controllability results for a class of time‐varying switched dynamical systems with impulses on time scales
Vipin Kumar, Mohamed Djemaï, Michaël Defoort, Muslim Malik
Abstract
Abstract In this paper, we establish some necessary and sufficient conditions of the controllability results for a class of impulsive switched systems with non‐instantaneous jumps on time scales. Firstly, we define the solution of the considered problem by using the parameter variation method. We also define some Gramian matrices to establish the controllability results. Moreover, we give some conditions under which the time invariant impulsive switched system is totally controllable. At the end, we provide one numerical example for different time scales to validate the obtained analytical results.
Topics & Concepts
ControllabilityControllability GramianControl theory (sociology)Class (philosophy)LTI system theoryMathematicsGramian matrixApplied mathematicsComputer scienceTopology (electrical circuits)Mathematical analysisLinear systemControl (management)Eigenvalues and eigenvectorsPhysicsArtificial intelligenceQuantum mechanicsCombinatoricsNonlinear Differential Equations AnalysisStability and Controllability of Differential EquationsAdvanced Differential Equations and Dynamical Systems