Control of uncertain piecewise discrete-time linear systems via state and output feedback

Abstract

Based on piecewise quadratic Lyapunov function techniques, this paper first provides a stability condition for the uncertain piecewise discrete-time linear system, which is a feasibility problem of linear matrix inequalities. Then the control methods for uncertain piecewise discrete-time linear systems via state feedback and output feedback controllers are proposed. It is shown that both the state feedback and output feedback controllers can be obtained by solving a set of bilinear matrix inequalities. A numerical example is given to illustrate the effectiveness of the developed methods

Adaptive state estimation for cyber physical systems under sparse attacks

“…Proof: (1) As we know, the equilibrium point x e = 0 is the stability condition for the discrete control system. Based on Zhang et al (2012), x ( k ) = ( A + BG ) k x 0 are the solutions of the closed-loop system (28), and the solutions satisfy the following condition…”

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“…More recently, Zhang and Tang extended the PQLF technique to the output feedback control of PWS with admissible uncertainties and disturbances, and bilinear matrix inequality (BMI)‐based results were shown to design controller and observer gains, which can be solved by the mixed algorithm proposed by Zhang and Tang. On the other side, Tao et al.…”