Saturated control of linear systems

✍ Scribed by Benhayoun, Mohamed; Benzaouia, Abdellah; Mesquine, Fouad

• Publisher: Springer
• Year: 2018
• Tongue: English
• Leaves: 257
• Series: Studies in systems decision and control 124
• Category: Library

✦ Synopsis

This book deals with a combination of two main problems for the first time. They are saturation on control and on the rate (or increment) of the control, and the solution of unsymmetrical saturation on the control by LMIs. It treats linear systems in state space form, in both the continuous- and discrete-time domains. Necessary and sufficient conditions are derived for autonomous linear systems with constrained state increment or rate, such that the system evolves respecting incremental or rate constraints if any. A pole assignment technique is then used to solve the problem, giving stabilizing state feedback controllers that respect non-symmetrical constraints on control alone or on both control and its increment or rate. Illustrative examples show the application of these methods on academic examples or on such real plant models as the double integrator system. This problem is then extended to various others including:

• systems with constraints and perturbations;
• singular systems with constrained control;
• systems with unsymmetrical saturations;
• saturated systems with delay, and
• 2-D systems with saturations.

The solutions obtained are of two types:

• necessary and sufficient conditions solved with linear programming techniques; and
• sufficient conditions under LMIs.

A new approach extends existing techniques for dealing with symmetrical saturations to take direct account of unsymmetrical saturations into account with LMIs. This tool enables the authors to obtain new results on continuous- and discrete-time systems. The book uses illustrative examples and figures and provides many comparisons with existing results.

Systems theoreticians interested in multidimensional systems and practitioners working with saturated and constrained controllers will find the research and background presented in Saturated Control of Linear Systems to be of considerable interest in helping them overcome problems with their plant and in stimulating further research.

✦ Table of Contents

Front Matter ....Pages i-xxxvii
Preliminary Results (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 1-22
Robust Constrained Linear Regulator Problem (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 23-42
Constrained Control and Rate or Increment for Linear Systems (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 43-68
Regulator Problem for Singular Linear Systems with Constrained Control (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 69-84
Observer-Based Constrained Control (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 85-104
Constrained Control and Rate or Increment: An LMI Approach (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 105-125
Output Feedback Stabilization for Constrained Control Systems (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 127-143
Stabilization of Unsymmetrical Saturated Control Systems (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 145-168
Delay Systems with Saturating Control (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 169-186
Stabilization of 2D Continuous Systems with Multi-delays and Saturated Control (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 187-199
Case Studies (Abdellah Benzaouia, Fouad Mesquine, Mohamed Benhayoun)....Pages 201-222
Back Matter ....Pages 223-226

✦ Subjects

Linear systems;Control theory