2024/02/14 by Ignacio Huerta, Huerta, Ignacio, Pablo Monzón +3 · 3 citations
Engineering · #34D05 #34D09 #93B05 #93D15 #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #Spectral Theory (math.SP) #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2402.08870
openalex publication_date 2024/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a new controllability property for linear time varying control systems in finite dimension: the nonuniform complete controllability, which is halfway between the classical Kalman's properties of complete controllability and uniform complete controllability. This new concept is described in terms of two gramian inequalities, which have a strong relation; as we prove in our first result; with the property of nonuniform bounded growth for the corresponding plant, also called uncontrolled part. On the other hand, the second result proves that if a control system is nonuniformly completely controllable and its plant has the property of nonuniform bounded growth, then there exist a linear feedback control leading to a nonuniformly exponentially stable closed--loop system.