Design of Variable Structure Control System With Nonlinear Time-Varying Sliding Sector

• Published in: IEEE transactions on automatic control Vol. 54; no. 8; pp. 1981 - 1986
• Main Authors: Yaodong Pan, Kumar, K.D., Guangjun Liu, Furuta, K.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Computer science; control theory; systems; Control systems; Control theory. Systems; Design engineering; Differential equations; Differential Riccati equations; Exact sciences and technology; Lyapunov functions; Lyapunov method; Mathematical analysis; Nonlinear control systems; Nonlinear equations; nonlinear system; Nonlinear systems; Nonlinearity; Riccati equations; Sliding; Sliding mode control; Stability; State-space methods; Time varying systems; Variable structure control; variable structure system; Variable structure control; Differential equation; Linear form; Sliding mode; Non linear control; Control synthesis; Linear time; State space; State space method; nonlinear system; Non linear system; variable structure system; Time dependence; Time varying system; State dependence; Riccati equation; Lyapunov function; Differential Riccati equations
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2009.2023965

A variable structure control (VSC) algorithm is proposed with a nonlinear time-varying (NTV) sliding sector for a class of nonlinear time-variant systems represented in a state-dependent linear time-variant form. The NTV sliding sector, a subset of the state space is designed by the state-dependent differential Riccati equation (SDDRE). A VSC law is designed such that the system enters the sliding sector in finite time and a Lyapunov function candidate decreases inside the NTV sliding sector. An NTV control and a sliding mode control algorithms are proposed based on the solution of the SDDRE as well.