The Robust Control Of The Delta Domain Systems

The discrete sampled systems have been developing rapidly because of the computer technology. But when sampling rates are high, most- traditional digital signal processing and control algorithms are inherently ill-conditioned. Considerable recent progress toward ameliorating such as ill-conditicning problems has been made through the use of a divided-difference operator, rather than the conventional shift operator, to represent the dynamics of sampled data. Up to now, Robust control theory which can conveniently deal with uncertainty has been improved greatly. The merger of Delta operator theory and robust control theory that is a new theme is significant for practical control systems, especially for high speed sampled systemsWe investigate initially the robust control of Delta domain systems as follows.For the Delta domain systems with uncertainty including structured and non-structured uncertainty, we study the robust stability of it and give the bounds of it. It results in that with the sampling periods decreasing the bounds of the system stability is increasing and the system is stable all the same.We analyze and design the Hx controllers of the Delta domain systems with structured uncertainty using Lyapunov stability theory and LMI. It shows that when sampling period is decreasing the system is stable all the same while the performance of the discrete-time system is approaching the continuous-time system.We assign the poles of the closed-loop systems described by the Delta operator models in the specified stable region of the complex plane while optimizing the LQ cost function which make the poles in the specified region when the sampling periods is becoming lessWe solved the Hx filter problem of the Delta operator systems, which is significant for the anti-disturbance of the high speed sampled systems. The gain matrix of the estimator of the Delta domain systems is approaching that of the continuous-time systems when the sampling periods is approaching zeroIwhich not only guarantees the stability and the performance of the systems but also avoids the defects the Z domain...