Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems

Stochastic H<inf>&#x221E;</inf> Static output-feedback control of state-multiplicative discrete-time systems with delay

“…In this paper, we address the problem of H ∞ static output-feedback control of state-delayed, discrete-time, state-multiplicative linear systems via the input-output approach based on the Bounded Real Lemma (BRL) of these systems, which was developed in [1]. In our systems, a (different) white noise sequence multiplies both the delayed and the non delayed states of the system.…”

“…In [1], this method was applied to the latter systems where, based on a stability condition, a BRL condition was introduced followed by a solution of the state-feedback control problem and a solution of the filtering problem. In the continuous-time setting [8], the input-output approach have been shown to achieve better results, over other solution methods.…”

“…Here, we continue to adopt the input-output approach, applied in [1], for the solution of the stochastic static outputfeedback control problem. This approach is based on the representation of the system's delay action by linear operators, with no delay, which in turn allows one to replace the underlying system with an equivalent one which possesses a norm-bounded uncertainty, and therefore may be treated by the theory of norm bounded uncertain, non-retarded systems with state-multiplicative noise [14].…”

“…This approach is based on the representation of the system's delay action by linear operators, with no delay, which in turn allows one to replace the underlying system with an equivalent one which possesses a norm-bounded uncertainty, and therefore may be treated by the theory of norm bounded uncertain, non-retarded systems with state-multiplicative noise [14]. Similarly to the systems treated in [1], in our systems we allow for a time-varying delay where the uncertain stochastic parameters multiply both the delayed and the non delayed states in the state space model of the systems. This paper is organized as follows: We first bring the previously published stability and BRL results [1] for both nominal and uncertain systems.…”

Robust stabilisation of discrete-time time-varying linear systems with Markovian switching and nonlinear parametric uncertainties

“…Such kind of modelling of the uncertainties has found many applications in engineering, signal processing and network communication (Gershon & Shaked, 2013;Gershon, Shaked, & Yaesh, 2005;Pan, Wang, Gao, Li, & Du, 2010;Wei, Wang, & Shen, 2010).…”