Robust H∞ Control for Non‐Minimum Phase Switched Cascade Systems with Time Delay

The H_∞ control of a class of the uncertain switched nonlinear cascaded systems with time delay is explored in this paper via the multiple Lyapunov functions. The considered systems are assumed to comprise an inherently nonlinear and a linearizable nonlinear dynamic system that may be non‐minimum phase. A group of partial differential inequalities containing adjustable functions are used in the control design task. The state feedback controllers and a suitable switching law are designed simultaneously so as to achieve the desired disturbance attenuation while preserving asymptotic stability for all admissible uncertainties. The partial differential inequalities are of lower dimension than general Hamilton–Jacobi inequalities, and therefore the solving process is feasible. This particular technique is applicable even if no subsystem is asymptotically stable. The non‐minimum phase property is compensated for by means of an appropriate switching mechanism. A robust H_∞ control for non‐switched cascade system with time delay is obtained in addition. An illustrative example is given to demonstrate the efficiency of the proposed design method.