Output-feedback sliding-mode control of multivariable systems with uncertain time-varying state delays and unmatched non-linearities

• Published in: IET control theory & applications 2013-08, Vol.7 (12), p.1616-1623
• Main Authors: Coutinho, Camila Lobo, Oliveira, Tiago Roux, Cunha, José Paulo V. S
• Format: Article
• Language: English
• Subjects: control nonlinearities; control signal amplitude; Control systems; Convergence; Delay; delays; feedback; finite‐time convergence; global stability properties; high‐frequency gain matrix; matrix algebra; mild Hurwitz condition; model‐reference unit vector control; Multivariable; multivariable control systems; multivariable uncertain systems; Nonlinearity; norm observer design; Norms; Observers; output‐feedback sliding‐mode controller; output‐tracking error; polynomial nonlinearities; Polynomials; stability; system output‐dependent nonlinearities; time‐varying systems; uncertain systems; uncertain time‐varying state delays; unknown time‐varying state delays; unmatched nonlinearities; unmeasurable state‐dependent nonlinearities
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2013.0388

An output-feedback sliding-mode controller is proposed for multivariable uncertain systems with unknown time-varying state delays and unmatched non-linear terms. The non-linearities are allowed to depend not only on the system output, but also on its unmeasurable state, and can be polynomial. This scheme is based on model-reference unit vector control under a mild Hurwitz condition for the high-frequency gain matrix. To achieve global stability properties, the amplitude of the control signal is given by a norm observer for the unmeasured state. For the first time, the design of norm observers is applied to a class of time-delay systems. This approach guarantees finite-time convergence of the output-tracking error to zero. Simulation results illustrate the application of the developed control scheme.