LMI-based Controller Design for Leaky-integrator MIMO Systems - Deng, Hao; Stoica, Cristina; Chadli, Mohammed; Ossmann, Daniel (Applications of Modelling and Simulation, 2026)
Leaky-integrator systems have attracted attention due to their capability of capturing the gradual loss of the system states. Thanks to the advantages of taking into consideration the leaky effect on gradual loss of systems states, leaky-integrator systems have been applied in biological modeling and electronic circuit design. However, robust control design conditions for such systems are insufficiently developed. In the existing literature, global asymptotic stability analysis has been conducted on leaky-integrator systems, however, such analysis neglects the effects of the inputs and is based solely on single-input single-output systems. The stability analysis for leaky-integrator multi-input multi-output (MIMO) systems is yet to be developed. This paper proposes a controller design method based on Linear Matrix Inequality (LMI) for a class of leaky-integrator MIMO systems. Compared to the existing literature, controllers that guarantee incremental input-to-state stability for leaky-integrator systems are established. In this paper, a set of linear matrix inequalities regarding the controller design conditions is derived based on the incremental input-to-state stability. An observer structure for the considered leaky-integrator MIMO systems is also presented, along with the observer design conditions. A numerical simulation example showcases the effectiveness of the proposed approach. The simulation results demonstrate that the developed LMI conditions are applicable for a class of leaky-integrator MIMO systems. With the proposed controller and observer design conditions, the leaky-integrator MIMO system can be stabilized and achieve the control goal of trajectory tracking.