Finding the LQR Weights to Ensure the Associated Riccati Equations Admit a Common Solution

This paper addresses the problem of finding linear quadratic regulator (LQR) weights such that associated discrete-time algebraic Riccati equations admit a common optimal stabilising solution. Solving is key to designing LQR controllers stabilise switched systems under arbitrary switching, or polytopic (e.g., Takagi-Sugeno fuzzy and parameter varying systems) in entire operating region. To ensure tractability reduce searching space, this proposes an efficient framework only state based on given input weights. Linear matrix inequality conditions are derived conveniently check feasibility problem. An iterative algorithm with convergence low computational complexity developed solve Efficacy proposed method illustrated through numerical simulations various sizes.