Sampled-data control of a class of uncertain nonlinear systems based on direct method

Sampled‐data output feedback stabilization for a class of upper‐triangular nonlinear systems with input delay

“…With the increasing requirement of the control accuracy for the modern industrial systems, the electronic computer is necessary to be introduced for many engineering systems to reach the high-precision control requirement, such as the high-precision control for the aircraft system, 1 underwater vehicle system, 2 and multi-robot system, 3 which leads the mismatched control theory of the electronic computer control, that is, sampled-data control, has become a research topic in recent years. [4][5][6][7][8][9][10][11][12][13][14][15][16] Global sampled-data output feedback stabilization and tracking are respectively investigated in References 4-6 for uncertain non-strict feedback nonlinear systems with linear growth condition, and such sampled-data stabilization was respectively extended to the nonlinear systems considered in References 7 and 8 with uncertain time-varying control coefficients and output functions. Two global sampled-data output feedback stabilization were reached in References 9 and 10 for nonlinear systems with nonminimum-phase and linearly uncontrollable, unobservable dynamics, respectively.…”

“…Nevertheless, we should note that all the aforementioned results [4][5][6][7][8][9][10][11][12][13][14][15][16] all neglect the time delay existed in systems, actually, time delay is a commonly phenomenon existed in many engineering systems, if the adverse effects of the time delay cannot be restricted timely, then the performance of such engineering systems may become worse. For a few past years, some researches on nonlinear systems against time delay were proposed in References 17-29.…”

“…Overall, although the sampled-data stabilization for the lower-triangular nonlinear systems, [4][5][6][7][8][9][10][11][12][13][14][15][16] and the stabilization studies for the nonlinear time-delay systems [17][18][19][20][21][22][23][24][25][26][27][28][29] have draw enough attention, there exists few result focus on the sampled-data output feedback stabilization for the upper-triangular nonlinear systems with time delay, [33][34][35] in which, a global sampled-data output feedback stabilization result was given in Reference 33 for a upper-triangular nonlinear system with transmission delay, and two observer-based sampled-data stabilization methods were proposed in References 33-35 for the nonlinear time-delay systems with upper-triangular structure. However, in those previous literature, [33][34][35] they only consider the upper-triangular systems whose nonlinearities satisfy the linear growth conditions, and the input delay which is commonly existed in the engineering systems was all ignored in those focused systems, which naturally causes some following open problems:…”

“…Two global sampled‐data output feedback stabilization were reached in References 9 and 10 for nonlinear systems with nonminimum‐phase and linearly uncontrollable, unobservable dynamics, respectively. By following References 4‐6, two nonlinear systems with more general $$$ p $$$‐normal and pure‐feedback structures were deeply considered in References 11 and 12 respectively to solve the corresponding sampled‐data stabilization problems. Global sampled‐data stabilization was respectively discussed in References 13 and 14 for large‐scale nonlinear systems with inherent nonlinearities and stochastic factors.…”

“…Furthermore, it should be noticed that all the aforementioned results 4‐29 only focus the tracking or stabilization problems of the nonlinear systems with lower‐triangular structure, for some engineering nonlinear systems, such as inverted pendulum system, they cannot be described as low‐triangular nonlinear systems but can only be described as upper‐triangular nonlinear systems, which brings strong research significance for the upper‐triangular nonlinear systems 30‐32 . A global stabilization result for a upper‐triangular cascaded nonlinear system was given in Reference 30, the sampled‐data output feedback stabilization was analyzed in Reference 31 for a upper‐triangular nonlinear system to guarantee the global stability and robustness against uncertainties of the resulting closed‐loop system.…”