Periodic compensation of continuous‐time linear systems with norm‐bounded parametric uncertainties

Abstract

AbstractThis article employs a recently proposed high frequency, continuous‐time periodic controller to compensate single‐input‐single‐output linear plants with norm‐bounded time‐varying uncertainties. To this end, the design of periodic controller is converted into designing a linear time‐invariant (LTI) controller for a single‐input‐two‐output equivalent uncertain system, following averaging technique. To represent this equivalent uncertain system into a standard form of linear uncertain systems, where uncertainties appear in system matrix A and input matrix B, the observer canonical form description of the original uncertain plant is exploited. Using the relationship between quadratic stability and ‐norm minimization result available in literature, it is proved that the presence of virtual output with the periodic feedback introduces a feedforward action on the disturbance input of the generalized plant, unlike an LTI one. By virtue of this, the proposed periodic controller can tolerate more uncertainty bound in the input matrix B than its LTI counterpart, while keeping the bound on system matrix A the same. Finally, a linear matrix inequality‐based method is used to design the periodic controller to achieve quadratic stability along with robust linear quadratic performance. Suitable examples are considered to show the superiority of the periodic control as compared to LTI ones.