Polynomial control design for polynomial systems: A non-iterative sum of squares approach

This paper proposes a non-iterative state feedback design approach for polynomial systems using polynomial Lyapunov function based on the sum of squares (SOS) decomposition. The polynomial Lyapunov matrix consists of states of the system leading to the non-convex problem. A lower bound on the time derivative of the Lyapunov matrix is considered to turn the non-convex problem into a convex one; and hence, the solutions are computed through semi-definite programming methods in a non-iterative fashion. Furthermore, we show that the proposed approach can be applied to a wide range of practical and industrial systems that their controller design is challenging, such as different chaotic systems, chemical continuous stirred tank reactor, and power permanent magnet synchronous machine. Finally, software-in-the-loop (SiL) real-time simulations are presented to prove the practical application of the proposed approach.