Design and analysis of discrete-time Q-dissipative control systems: stability margin perspective

This paper studies discrete-time dissipative control systems from a stability margin perspective. The paper first introduces the concept of discrete-time control systems whose loop transfer systems, not necessarily stable, satisfy a dissipativity condition specified by a weighting matrix Q. Next, it proposes a design method taking suitable Q so that the control system is robustly stable against a prespecified range of perturbations inserted in the feedback loop. This robustness includes the well-known gain and phase margins as a special case. A design example is given to illustrate the proposed method. Finally, the discrete-time dissipativity is discussed in relation to LQ control and positive realness.