H_∞ state feedback for linear systems with decentralized control inputs

This paper considers state feedback with decentralized structure for interconnected systems. The connection between subsystems is described by a directed graph. To design a decentralized controller, we use the information from its own subsystem and other subsystems based on the interconnection. Decentralized controller is defined as a solution of bilinear matrix inequality (BMI) problem, which is then solved by using the homotopy approach. Two numerical examples are performed to show validity of the design procedure

New exponential stability criterion for switched linear systems with average dwell time

In this article, the partition of state space is investigated based on the average dwell time theory, and a novel switching condition is proposed. Under the switching condition and strategy, a switched system where all subsystems are unstable is globally exponentially stabilized. Compared with the existing literature, the conclusion is less conservative and more general. Consequently, the conditions appropriate for this exponential stability issue are derived and a computational procedure to solve the bilinear matrix inequality problems and admissible average dwell time is provided. Finally, two numerical examples are used to show the validity and effectiveness of the proposed methods.

Stability analysis and observer design for one-sided Lipschitz descriptor systems with time-varying delay

This paper investigates the problem of stability analysis and observer design for nonlinear descriptor systems with time-varying delay. In the systems, the nonlinear function satisfies the one-sided Lipschitz condition and the quadratic internal boundary condition. The disturbance is considered in both the state and the output equation. Using one-sided Lipschitz condition, the quadratic internal boundary condition, and the generalized Lyapunov method, we establish the non-strict bilinear matrix inequality (BMI)-based condition. We change the condition into strict bilinear matrix inequality (BMI) condition. Furthermore, we give the linear matrix inequality-based condition to ensure the gradual convergence of state estimation error and to accomplish robustness against L2 norm bounded disturbances by utilizing change of variables for straight forward computation of the observer gain matrix. Finally, a numerical example is given to verify the effectiveness of the observer design scheme.