Positive Stabilization With Maximum Stability Radius for Continuous-Time Dynamic Systems

Positive systems have attracted much attention nowadays due to their numerous applications in modeling and control of physical, biological and economical systems. The state trajectory of such system remains in the nonnegative quadrant of the state space for any given nonnegative initial condition. This class of systems have nice stability and robustness properties. One can take advantage of these interesting properties to robustly stabilize general dynamic systems such that the closed-loop system becomes positive. One of the most important measures in robust control analysis is stability radius. This measure provides the amount of uncertainty that system can cope with before it becomes unstable. There are two types of stability radius defined; complex and real stability radius. Computation of real stability radius is more involved than its complex counterpart. Although the complex and real stability radius are different for a general LTI system, it has been found that they are equal for the class of positive system. In fact, a closed form expression can be obtained to find the stability radius of positive system. In this research, we try to positively stabilize a general uncertain system with the constraint of maximizing stability radius by using a state feedback control law. The necessary and sufficient conditions for the existence of controllers satisfying the positivity constraints are provided. This constrained stabilization problem will be formulated and solved using linear programming (LP) and linear matrix inequality (LMI). With the aid of bounded real lemma, the major contribution is to solve positive stabilization with maximum stability radius for both regular and time-delay systems.

Advisor: Bahram Shafai

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