Bilinear matrix inequality‐based nonquadratic controller design for polytopic‐linear parameter varying systems
Hamidreza Javanmardi, Maryam Dehghani, Mohsen Mohammadi, Navid Vafamand
Abstract
Summary This article proposes relaxed sufficient bilinear matrix inequality (BMI) conditions to design a gain‐scheduling controller for nonlinear systems described by polytopic‐linear parameter varying (LPV) representations. The obtained conditions are derived based on a nonquadratic Lyapunov function and a parallel distributed compensator scheme. The controller design procedure involves some novel null terms and leads to a BMI problem, which hardly has been solved in previous researches. Furthermore, to effectively solve the BMI conditions, a novel sequential approach is proposed which convert the overall BMI problem into linear matrix inequality (LMI) constraints and some simpler BMI conditions with fewer dimensions than the original one. Initially, the LMI conditions are solved as a convex optimization problem. Second, the BMI terms are iteratively linearized near the feasible solutions of the LMIs and each solution candidates for the BMI constraints. Finally, the linearized condition is solved as an eigenvalue problem. To show the merits of the proposed approach, several numerical comparisons and simulations are provided.