Guaranteed control of switched control systems using model order reduction and state-space bisection

This paper considers discrete-time linear systems controlled by a quantized law, i.e., a piecewise constant time function taking a finite set of values. We show how to generate the control by, first, applying model reduction to the original system, then using a “state-space bisection” method for synthesizing a control at the reduced-order level, and finally computing an upper bound to the deviations between the controlled output trajectories of the reduced-order model and those of the original model. The effectiveness of our approach is illustrated on several examples of the literature. 1998 ACM Subject Classification B.1.2 Control Structure Performance Analysis and Design Aids, B.1.3 Control Structure Reliability, Testing, and Fault-Tolerance, B.2.3 Reliability, Testing, and Fault-Tolerance