Linear matrix inequality-based analysis of the discrete-continuous nonlinear multivariable systems

The E. M. Fridman method for analysis of the hybrid linear systems by passing to a system with sawtoothed delay and using the nonstationary Lyapunov–Krasovskii functionals and descriptor variables was extended to the nonlinear multivariable Lur'e systems. Consideration was given to the discrete control in the form of a feedback with bounded above variable step of discretization. At that, in the system equations the control function was multiplied by a bounded scalar nonlinear function. This case corresponds to numerous oscillators such as the “pendulum on cart” system. On the basis of the classical results obtained by V. A. Yakubovich on losslessness of the S-procedure, the problem of estimating the upper boundary of the discretization step comes to analyzing the system of linear matrix inequalities for solvability.