Continuous‐time stable and unstable system modelling with orthonormal basis functions

In this paper, model sets for linear time‐invariant continuous‐time systems which are spanned by fixed‐pole orthonormal bases are investigated. The obtained model sets are shown to be complete in the Lebesque spaces L_p (1<p<∞) and in C, the space of complex‐valued functions that are continuous on the extended imaginary axis. The L_p norm error bounds for estimating systems in L_p by the partial sums of the Fourier series formed by the orthonormal functions are computed for the case 1<p<∞. Some inequalities on the 𝓁_p means of the Fourier coefficients are also derived. These results have application in estimation and model reduction of stable and unstable continuous‐time linear time‐invariant systems. A numerical example illustrates the use of the basis functions for the approximation of unstable infinite‐dimensional dynamics. Copyright © 2000 John Wiley & Sons, Ltd.     

DISCRETIZING CONTINUOUS‐TIME CONTROLLERS WITH FUZZY LOGIC SYSTEMS AND ITS STABILITY ANALYSIS

In this paper, a new method, applying the fuzzy logic system, is proposed to discretize the continuous‐time controller in computer‐controlled systems. All the continuous‐time controllers can be reconstructed by the proposed method under the Sampling Theorem. That is, the fuzzy logic systems are used to add nonlinearity and to approximate smooth functions. Hence, the proposed controller is a new smooth controller that can replace the original controller, independent of the sampling time under the Sampling Theorem. Consequently, the proposed controller not only can discretize the continuous‐time controllers, but also can tolerate a wider range of sampling time uncertainty. Besides, the input‐output stability is proposed for discretizing the continuous‐time controller of the fuzzy logic systems. Finally, computer simulation shows that the proposed method can easily reconstructthe continuous‐time controller and has very good robustness for different sampling times.     

DELAY‐DEPENDENT ROBUST CONTROL OF DESCRIPTOR SYSTEMS WITH TIME DELAY

This paper deals with the problem of stability and robust control for both certain and uncertain continuous‐time singular systems with state delay. Systems with norm‐bounded parameter uncertainties are considered. Robust delay‐dependent stability criteria and linear memoryless state feedback controllers based on linear matrix inequality are obtained. By choosing some Lyapunov‐Krasovskii functionals, neither model transformation nor bounding for cross terms is required in the derivation of our delay‐dependent results. Finally, numerical example is provided to illustrate the effectiveness of the proposed method.