Sliding Mode Control for Lipschitz Nonlinear Systems in Reciprocal State Space: Synthesis and Experimental Validation

State and output feedback control for Lipschitz nonlinear systems in reciprocal state space: synthesis and real-time validation

“…In these examples, Arduino I/O mode is chosen where all technical implementation details are given in [12]. In a similar way to the implementation conditions given in [27], the same noise signals are considered whose amplitudes and frequencies are variable from 7 to 80 Hz and (±0.35𝑉) respectively. In this section, we present the variation of the different variables in the closed-loop mode to show the stability offered by the proposed approach.…”

“…A condition has been proposed by [27] in order to ensure the optimization of the criterion 𝐽 ̄ in the case where the system has non-zero initial conditions as follows: Introduce a decision variable 𝑌 ̄∈ ℝ 𝑛×𝑝 𝑌 ̄− 𝐼 𝑛 𝑋 ̄−1 𝐼 𝑛 > 0: Then, minimize 𝑡𝑟𝑎𝑐𝑒 (𝑌 ̄) the subject to minimize the cost function𝐽 ̄.…”

“…Similarly, for the case of nonlinear systems, recent works dealing with several control methods based on Lyapunov stability have been synthesized, such as H∞ fuzzy state feedback [14]; adaptive stabilization and tracking control [19]; state feedback stabilization of one-sided Lipschitz systems [26]; and sliding mode control for Lipschitz systems [27].…”