چكيده به لاتين
A nonlinear sample-data system with periodic or aperiodic sampling rates is an important part of control engineering with a wide range of applications. The structural complexity of these systems leads to less development than the linear sample-data systems and requires new methods for analysis and design.
In this thesis, the problem of using linear parameter variable systems for stability and performance analysis and design of a sample-data controller for nonlinear plants with aperiodic and multi-rate sampling period is presented. In this approach, nonlinear dynamical equations of the system are appropriately included in the parameter vector and the real nonlinear model of the system is transformed into a linear and variable-time structure that is suitable for controller design. The distance between the real parameters of the plant and the measured parameters of the controller is considered as the uncertainty. In the presence of these uncertainties, the stability and performance analysis of the nonlinear sample-data system was performed. For stability analysis, a modified form of the parameter and time-dependent Lyapunov Krasovskii functional is introduced in the framework of the time delay approach, which provides conditions for asymptotic and exponential stability of the closed-loop sampled-data LPV systems. Also, sufficient conditions were obtained to examine the effect of sampling period on system performance using L2-gain analysis criteria.
The results obtained in the stability and performance analysis utlized for the design of the sample-data linear parameter controller which in contrast to the existing methods guarantee the robust stability and performance. Also, in order to improve the behavior of the closed-loop system transient behavior, a novel pole placement method for nonlinear sampled-data systems has been developed. The conditions in this thesis are in the form of the parametrized linear and bilinear matrix inequalities which are the infinite dimensional problems. To solve these problems, various approaches such as grinding, convexity, and sum of squares have been used.
All the obtained results for the stability and performance analysis and design of the sampled-data linear parameter variable systems in presence of parameter uncertainty are confirmed through several numerical examples.
