Sliding sector control using new equivalent sector control

Abstract

ABSTRACTThis paper presents a variable structure control design method for linear and nonlinear continuous-time systems with a special type of sliding sector using a new equivalent sector control. The PR-sliding sector is the subset of state space in which the derivative of the square P-norm of the state, , is less than or equal to with a positive semi-definite matrix where is observable. The new equivalent sector control provides the derivative of being negative. The design method of and is proposed for the general linear single input system by using the Riccati equation. Under the proposed equivalent sector control, the state trajectory may jump at the particular uncontrollable states when , and the control is set zero. If becomes positive, the state is outside of the sector, and then the state shall be transferred to the inside of the sector by the discontinuous nonlinear control input. Numerical simulations show that the proposed method gives satisfactory results.