Stability and stabilization for singularly perturbed systems with Markovian jumps
Guoliang Wang, Lei Xu
Abstract
Summary This article focuses on the stability and stabilization problems of singularly perturbed jump systems. Here, the singularly perturbed parameter (SPP) is also with Markov switching and satisfies any with positive bound predefined. First, stability conditions expressed ϵ i ‐free but involving its bound are developed by constructing an ϵ i ‐dependent Lyapunov function. Then, a method for state feedback stabilization controller depending on SPP is proposed, whose conditions are given in terms of linear matrix inequalities. Moreover, some special cases about deterministic SPP are considered too. Finally, two practical examples are used to demonstrate the effectiveness and superiorities of the proposed methods.
Topics & Concepts
Control theory (sociology)Stability (learning theory)Lyapunov functionController (irrigation)Upper and lower boundsMathematicsState (computer science)Matrix (chemical analysis)Markov processExponential stabilityFunction (biology)Applied mathematicsComputer scienceControl (management)Mathematical analysisNonlinear systemPhysicsAlgorithmMaterials scienceBiologyStatisticsEvolutionary biologyArtificial intelligenceQuantum mechanicsComposite materialMachine learningAgronomyStability and Control of Uncertain SystemsControl and Stability of Dynamical SystemsMatrix Theory and Algorithms