Abstract
In this paper, a time-varying gain design method is used to investigate the state feedback control problem of upper triangular nonlinear systems. Firstly, the nonlinear term recognizes an incremental rate relying on the unknown constant and the function with respect to time. Then, a time-varying gain design method is utilized to construct a state feedback controller. With the help of a suitable coordinate transformation and a Lyapunov function, one obtains that all the signals of the closed-loop system converge to zero. Finally, two numerical examples are presented to display the effectiveness of the time-varying gain design method.
Highlights
Many physical models can be described by nonlinear systems [1,2,3,4]. erefore, the control problem of these physical models can be transformed into the control problem of nonlinear systems [5]
Based on the coordinate transformation, the timevarying gain design method is an effective strategy for dealing with the uncertain parameter of upper triangular nonlinear systems [19]
By introducing a time-varying function in the controller, it can effectively deal with the nonlinear terms of upper triangular nonlinear systems [20]
Summary
Many physical models can be described by nonlinear systems [1,2,3,4]. erefore, the control problem of these physical models can be transformed into the control problem of nonlinear systems [5]. Based on the iterative design algorithm, these methods can effectively deal with strong nonlinearities, the design procedure is more complicated. In the past few decades, the gain design method is a very effective tool to deal with the control problem of upper triangular nonlinear systems [18]. Based on the coordinate transformation, the timevarying gain design method is an effective strategy for dealing with the uncertain parameter of upper triangular nonlinear systems [19]. By introducing a time-varying function in the controller, it can effectively deal with the nonlinear terms of upper triangular nonlinear systems [20]. Is paper uses the time-varying gain design method to study the control problem of upper triangular nonlinear systems. Us, a time-varying gain design method is introduced to achieve the control goals of the concerned system
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