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We consider the stability of the feedback connection of a stable linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program (QP). We establish quadratic constraints from the Karush-Kuhn-Tucker (KKT) conditions that may be used to construct a piecewise quadratic Lyapunov function via the S-procedure. The approach is based on existing results in the...
Based on multiple Lyapunov functions methodology, we study disturbance attenuation of discrete-time switched linear systems. A bilinear matrix inequalities (BMIs) based condition is derived to stabilize the switched system with a prescribed disturbance attenuation level Upsi when only switching can be utilized in the control of systems. This condition can be dealt with as linear matrix inequalities...
This note addresses the problems of stability analysis and stabilization of systems presenting nested saturations. Depending on the open-loop stability assumption, the global stability analysis and stabilization problems are considered. In the (local) analysis problem, the objective is the determination of estimates of the basin of attraction of the system. Considering the stabilization problem, the...
This paper deals with the class of singular continuous systems. By decomposing the singular linear system with time-delay into slow and fast subsystems, LMI-based delay-dependent stability and stabilization conditions are established, and an LMI-based algorithm to design a memoryless state feedback control that stabilizes the system is provided. Two numerical examples are worked out to show the usefulness...
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