**A Formula for the Stability Radius of Time Varying Systems**

stability radius of a time-invariant system (i.e., A(t)#A, B(t)#B and ... that it contains all perturbations given by a time-varying linear system. In this situation we will prove that the stability radius equals ... formula and not only a lower bound. Additionally, we get that the real and complex stability radius coincide. Some of the results ...

**Stability of Dynamical Systems George Mason University**

transfer function for a continuous-time system must all lie strictly in the left half of the complex s-plane. The poles must all have strictly negative real parts. For a discrete-time system to be stable, the poles of the transfer function must lie in the interior of a circle of unit radius centered

**Stability Radii for Positive Linear Time Invariant Systems ...**

Stability Radii for Positive Linear Time-Invariant Systems on Time Scales ... the diﬀerences between the complex and the real stability radius can be found in [3]. The complex stability radius is more easily analysed and computed ... continuous-time systems yields that system (3) is positive if and only if A is Metzler. Case 2: T contains ...

**On the robustness of stable discrete time linear systems**

On the robustness of stable discrete time linear systems ... tation of the complex stability radius is presented. ... complex stability radius — besides being a lower bound for the real one ...

**On the marginal instability of linear switched systems**

Stability properties for continuous-time linear switched systems are at ﬁrst deter-mined by the (largest) Lyapunov exponent associated with the system, which is the analogous of the joint spectral radius for the discrete-time case. The purpose of this paper is to provide a characterization of marginally unstable systems, i.e., systems for

**Stability of Discrete Linear Systems with Periodic ...**

destroying stability or more precisely we are looking for the largest bound r such that stability is preserved for all perturbations )Δ(n of norm strictly less than r in a given normed perturbation set. This largest bound is called the stability radius. First time the problem was formally formulated for the continuous time invariant system in the

**STABILITY AND PERFORMANCE ANALYSIS IN THE PRESENCE OF ...**

stability radius was gradually increased by changing the original controller. Horisberger and Belanger (1976) posed the stability problem, in the presence of magnitude bounded real uncertainty entering the "A" matrix of the closed loop system linearly, as the existence of a matrix P=P'0O that simultaneously satisfies a set of