Parameter Optimization of Linear Control System Based on Lyapunov Stability Theory

Abstract

Keywords: Lyapunov function, Optimal parameter, Lyapunov equation, Performance index. Abstract: This paper aims at optimizing the system parameter of the control system with adjustable parameter. The optimization performance index is represented as a Lyapunov function which is decided by a symmetrical positive definite matrix and system's initial conditions. This symmetrical positive definite matrix, which is dependent upon the adjustable system parameter, is derived by solving Lyapunov equation so that system's asymptotical stability can be guaranteed. By doing so, the system parameter optimization problem is changed to be the performance index function extremum problem. Then by solving the partial derivative equation, the extreme point, i.e. the optimal system parameter is determined. Application example indicates that system's adjustable parameter is optimally selected in the sense that the control system is asymptotically stable as well as the control system performance index is the minimum.