# zbMATH — the first resource for mathematics

Robust control and filtering for time-delay systems. (English) Zbl 0969.93002
Control Engineering (Boca Raton) 5. New York, NY: Marcel Dekker. 448 p. (2000).
The book is devoted to the problems of stability, stabilization, robust control design and filtering of linear continuous-time and discrete-time systems with time delays and both parametric and structural uncertainties. Some very special problems of nonlinear uncertain time-delay systems are also considered. The author presents a state-space approach to the analysis and design of uncertain systems. The methodology includes:
1) Lyapunov type and linear matrix inequality based techniques for analysis of delay-independent and delay-dependent stability of both continuous and discrete-time systems and the design of robustly stabilizing controllers for such systems using both state-feedback and dynamic output feedback.
2) $$H_\infty$$ methods for robust stability and robust performance analysis as well as robust control design.
3) Guaranteed cost control techniques including Lyapunov type methods and observer-based design.
4) Robust filtering of Kalman and $$H_\infty$$ type.
5) Large scale system and decentralized control techniques used to design control laws and filtering for interconnected time-delay systems.
All theoretical studies are appended by a number of simulation examples performed using MATLAB and LMI control software. The book is no difficult reading and could be advised for doctoral studies in control engineering and related topics.

##### MSC:
 93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory 93B51 Design techniques (robust design, computer-aided design, etc.) 93C23 Control/observation systems governed by functional-differential equations 93D09 Robust stability 93A15 Large-scale systems 93A14 Decentralized systems 93E11 Filtering in stochastic control theory 93D21 Adaptive or robust stabilization 93B36 $$H^\infty$$-control 93B07 Observability 15A39 Linear inequalities of matrices
Matlab