Parameter dependent stability and stabilization of uncertain time-delay systems

861 structure, the behavior of the curve is extremely complicated. The numbers written inside each region indicate the respective number of RHP roots. The shaded region indicates the set of controller parameters that stabilizes the given plant (i.e., number of RHP roots = 0). Fig. 3 depicts the three dimensional stability region in the controller parameter space. The two-dimensional sections of the region are for 01:25 x3 1:375. The figure shows that the region gets smaller as x 3 approaches +1.375 and 01.25. An effective computational procedure to determine all first-order controllers that stabilize a given discrete-time LTI system is described in this note. The determination of the complete set requires fixing x 3 , obtaining the stabilizing set in the x1 0x2 plane and repeating this solution by sweeping over all x 3. In practice, the range of x 3 may be predetermined based on other design considerations and a method involving sweeping over only one parameter is quite practical, given the available computational power. As in [4], the result can also be extended to simultaneous stabilization, maximal delay tolerance and maximally deadbeat designs. A control scheme that optimizes a given optimality criteria and the attainment of other performance criteria over these sets is currently under investigation. We anticipate the parameter plane techniques developed in [11] to be useful in this context.based structure and covariance bounds, " IEEE Trans. The optimal projection equations with Petersen-Hollot bounds: robust stability and performance via fixed-order dynamic compensation for systems with structured real-valued parameter uncertainty, " IEEE Trans. Abstract—A new robust delay dependent stability test is introduced that determines the asymptotic stability of linear systems with state delays. The parameters of the system are not exactly given. They are known to reside in a given polytope. The test provides an efficient sufficient condition for the stability of the system over the uncertainty polytope. This condition is parameter dependent and it therefore improves previous results that were derived using a single Lyapunov–Krasovskii functional. The stability test is readily extended to provide a criterion for robust stabilization via state-feedback.