Infinite horizon H2/H∞ control for discrete-time time-varying Markov jump systems with multiplicative noise

Exact detectability of linear discrete-time time-varying stochastic systems

“…Such a counterexample can be easily constructed. K ∞ -exact detectability implies that all k ∞ 0 -unobservable initial state ξ leads to an exponentially stable trajectory for any k 0 ≥ 0, which does not require a constant feedback gain K in time-invariant case or a matrix sequence {K k } k∈N0 in time-varying case such that (12) …”

Mixed H 2 / H ∞ control of time‐varying stochastic discrete‐time systems under uniform detectability

“…In system (13), if the disturbance input v k ∈ l 2 (N ; R nv ) and the output y k ∈ l 2 (N ; R ny ), then a linear perturbed operator (14)) that is,…”

“…In [13], Ma et al solved the second problem, and dealt with the first and the third difficulties under the condition of stochastic detectability. In this paper, it is proved that uniform detectability is weaker than stochastic detectability (see Lemma 3).…”

Finite horizonH2/H∞control of time‐varying stochastic systems with Markov jumps and (x,u,v)‐dependent noise

“…On the other hand, many physical systems may experience abrupt changes in their structures, and such systems can be adequately described by hybrid systems driven by continuous-time Markov chains [4,5]. Consequently, stochastic systems with Markov jumps and multiplicative noises have received considerable attention, and many important issues have been studied for this kind of system, such as stability and stabilisation [6][7][8][9][10], observability and detectability [11], linear quadratic (LQ) control [12,13], H ∞ control [14,15] and H 2 /H ∞ control [16][17][18] and so on.…”