Simultaneous Stabilization using Set Stabilizing Gain Generation - Deshmukh, Venkatesh S. (Discontinuity, Nonlinearity, and Complexity, 2026)
A set stabilizing gain generator (SSGG) framework is developed along with dynamic controllers and observers to regulate and estimate the state trajectories of an arbitrary set of three or more open loop unstable linear time invariant dynamic system models of variable dimensions in the state space form. The individual systems in the set are assumed to be controllable and observable. An algorithm is suggested for Single Input (SI) simultaneous stabilization and Single Output (SO) simultaneous observation. This is then extended to a set of Multiple Input (MI) and Multiple Output (MO) models. A dynamic observer based dynamic controller is also formulated for SISO and MIMO systems. The algorithm is then extended to accommodate simultaneous stabilization and observation of system models of variable dimensions. It is finally shown that the dynamic controllers and observers guarantee a certain stability radius against bounded time-varying uncertainty for the entire set which their static counterparts fail to assign. Suitable SI, SO, SISO and MI, MO, MIMO examples are provided.