Control Design for System with Lipschitz Nonlinearity of State Derivative Variables in Reciprocal State Space Form

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

“…Next, according to the same steps presented in the previous section: i) use a slack variable 𝑋 ̄= 𝑋 ̄𝑇 = 𝑃 −1 and pre and post multiply ( 18) by [ 𝑋 ̄0 0 𝐼 ]; ii) apply the Schur complement [25]. Moreover, by applying them to (18), 𝛩 ̄𝑦it becomes:…”

“…Despite the important literature on approaches proposed in SSS (using state variables), many limitations exist. Effectively, many engineering systems and applications give measurements and data covering their basic physical phenomena or their operating principles according to derivatives state: photovoltaic systems [14]; mobile robots [15]; active suspension systems [16], [17]; and electronic impulse systems [18], [19]. This leads to the state derivatives being easily obtained in some engineering systems.…”

“…Moreover, the studies on the derivative Lipschitz nonlinearity [18], [19] are few in control design problems. As well as for the case of control by output feedback in the RSS and treating the Lipschitz nonlinear systems is not treated to the authors' knowledge.…”