A New Design of Asynchronous Observer-Based Output-Feedback Control for Piecewise-Affine Systems

This letter is devoted to the asynchronous observer-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$ {\mathscr {H}}_{\infty }$ </tex-math></inline-formula> output-feedback control problem for continuous-time piecewise-affine systems via continuous piecewise Lyapunov functions. More precisely, by a system state-input augmentation, the traditional observer-based closed-loop control system is initially re-organized into a descriptor form of the piecewise-affine system. With the construction of a continuous asynchronous piecewise Lyapunov function, a new <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathscr {H}}_{\infty }$ </tex-math></inline-formula> performance analysis condition is then presented. Thanks to the special structure of the descriptor format, the asynchronous observer-based control design can be carried out by virtue of a convex program. An illustrative example is finally given to show the efficacy of the proposed scheme.