On ℓ2–ℓ∞ output-feedback control scheduled by stochastic communication protocol for two-dimensional switched systems

This paper is concerned with the $ \ell _{2} $ ℓ2– $ \ell _{\infty } $ ℓ∞ output-feedback control problem for a class of two-dimensional (2-D) switched systems described by the general Fornasini–Marchesini second model under the stochastic communication protocol (SCP). In a networked 2-D switched control system, the sensors and the controller are typically connected through a shared communication network of limited bandwidth, which is likely to result in data collision problem. To circumvent this network-induced problem, a new SCP is dedicatedly put forward for the 2-D switched system in order to orchestrate the transmission order of sensor nodes, under which only one sensor node obtains the privilege to access the network at each transmission instant. Then, based on the nominal system information compensation, a set of new mode-dependent output-feedback controllers is designed for 2-D switched systems subject to SCP and external disturbances. Moreover, using the average dwell-time approach, sufficient conditions are established to ensure the existence of the desired controllers that guarantee both the exponential mean-square stability and the $ \ell _{2} $ ℓ2– $ \ell _{\infty } $ ℓ∞ performance. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed controller design method.