A new approach to simultaneous stabilisation with D stability and its application to control of antilock braking systems

The simultaneous stabilisation problem (SSP) and strong simultaneous stabilisation problem (SSSP) with the simple Hurwitz stability requirement are challenging in the control community. In this paper a new approach to these two problems is presented, with the extension to the general D stability requirement rather than simply the Hurwitz stability requirement. The advantages of this approach include: 1. the desired D stability region can be of any form and be connected or disjoint. This leads to a unified treatment of continuous and discrete systems, and consequently encompasses the Hurwitz and Schur stability regions as special cases; 2. the size of the family of plants may be more than three, which is the upper bound with the existing approaches; 3. both the SSPs and the SSSPs can be dealt with in a unified way, although a SSSP is more complicated than a SSP. 4. the traditional PID controller tuning problem can be treated within this general framework. Examples harder than the previous results are provided to show the merits of this synthesis approach. Application of the approach to Anti-lock Braking System (ABS) controller design is also presented.