Decentralized tracking control for a class of stochastic high-order time-delay nonlinear systems under arbitrary switchings

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

“…where Remark 3. We should point out that the time delays existed in the practical engineering systems are always bounded, therefore Assumption 2 is a reasonable assumption, and this assumption can also be found in the existing literature [23][24][25][26][27][28][29] on nonlinear time-delay systems.…”

“…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:…”

“…Nevertheless, we should note that all the aforementioned results 4‐16 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. Two Lyapunov–Krasovskii functionals were constructed in References 17 and 18 to demonstrate the stability of two switched nonlinear systems by adaptive neural network controllers.…”

“…Adaptive fault‐tolerant control method was developed in Reference 21 for a non‐affine nonlinear system to against its actuator faults and time delays. The studies for the stochastic nonlinear time delay systems were respectively proposed in References 22‐24 for the focused systems with Markovian jump and switching dynamics, respectively. Multi‐model approach was raised in Reference 25 for a multiple‐input signal‐output nonlinear time‐delay system.…”

“…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.…”