Observer-based control for a class of polynomial systems with time delay

This paper investigates the problem of observer-based control for a class of polynomial systems. A polynomial observer to estimate unmeasurable states of polynomial systems is proposed. For the analysis of the global asymptotic stability, a design method is proposed. In this approach we adopt a polynomial Lyapunov krasovskii function with designed polynomial Lyapunov matrix. The design conditions in the proposed approach are represented in terms of Sum Of Squares (SOS) which can be numerically and symbolically solved via the recent developed SOSTOOLS and a Semi-Definite Program (SDP) solver. Finally, two numerical examples are introduced to show the validity and applicability of the proposed results.