Stability and Stabilization of Linear Systems with Saturating Actuators

This monograph details basic concepts and tools fundamental for the analysis and synthesis of linear systems subject to actuator saturation and developments in recent research. The authors use a state-space approach and focus on stability analysis and the synthesis of stabilizing control laws in both local and global contexts. Different methods of modeling the saturation and behavior of the nonlinear closed-loop system are given special attention. Various kinds of Lyapunov functions are considered to present different stability conditions. Results arising from uncertain systems and treating performance in the presence of saturation are given. The text proposes methods and algorithms, based on the use of linear programming and linear matrix inequalities, for computing estimates of the basin of attraction and for designing control systems accounting for the control bounds and the possibility of saturation. They can be easily implemented with mathematical software packages.

It is well-known that actuator saturation is present in practically all control systems, the signal amplitude that an actuator can deliver usually being limited by physical or safety constraints. Neglect of these amplitude bounds and the consequent actuator saturation can be a source of performance degradation or even instability of the closed-loop system so an in-depth understanding of the phenomena caused by saturation is of importance in solving and avoiding problems in industrial control systems.

Stability and Stabilization of Linear Systems with Saturating Actuators details both basic concepts and tools fundamental for the analysis and synthesis of linear systems subject to actuator saturation and, in a formal though didactic fashion, developments in recent research. The authors consider a state-space approach and focus on the problems of stability analysis and the synthesis of stabilizing control laws in both local and global contexts. Different methods of modeling the saturation and behavior of the nonlinear closed-loop system are given special attention. Various kinds of Lyapunov functions, polyhedral, quadratic and Lure-type, for example, are considered in order to present different internal as well as external stability and stabilization conditions. Results arising from uncertain systems and treating performance in the presence of saturation are also given. Associated with the different theoretical results, the text proposes methods and algorithms for computing estimates of the basin of attraction and sets of admissible exogenous signals as well as for designing control systems taking into account, a priori, the control bounds and the possibility of saturation. In addition, the so-called anti-windup approach, which consists of adding anextra layer in the pre-designed control system specifically to tackle the undesirable effects of saturation, is presented.

These methods and algorithms are based on the use of linear programming and linear matrix inequalities and can be easily implemented with MATLAB^® and Scilab.

Stability and Stabilization of Linear Systems with Saturating Actuators is a valuable reference for electrical, mechanical, chemical and aeronautical engineers working on control applications, as well as graduate students and researchers interested in the development of new tools and theoretical results concerning systems with saturation.