By Vasile Dragan, Toader Morozan, Adrian-Mihail Stoica

In this monograph the authors increase a thought for the strong regulate of discrete-time stochastic platforms, subjected to either self reliant random perturbations and to Markov chains. Such platforms are prevalent to supply mathematical versions for actual strategies in fields akin to aerospace engineering, communications, production, finance and economic climate. the speculation is a continuation of the authors’ paintings offered of their earlier booklet entitled "Mathematical equipment in strong keep watch over of Linear Stochastic platforms" released by means of Springer in 2006.

Key features:

- offers a standard unifying framework for discrete-time stochastic structures corrupted with either self sufficient random perturbations and with Markovian jumps that are often taken care of individually within the keep watch over literature

- Covers initial fabric on likelihood thought, self reliant random variables, conditional expectation and Markov chains

- Proposes new numerical algorithms to resolve coupled matrix algebraic Riccati equations

- Leads the reader in a traditional option to the unique effects via a scientific presentation

- offers new theoretical effects with targeted numerical examples

The monograph is geared to researchers and graduate scholars in complicated regulate engineering, utilized arithmetic, mathematical platforms conception and finance. it's also obtainable to undergraduate scholars with a basic wisdom within the idea of stochastic systems.

**Read or Download Mathematical methods in robust control of discrete-time linear stochastic systems PDF**

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**Additional info for Mathematical methods in robust control of discrete-time linear stochastic systems**

**Example text**

26) deﬁned by a sequence of linear bounded and positive operators the exponential stability is equivalent to the boundedness of the solution with the zero initial value of the forward aﬃne equation xk+1 = Lk xk + ξ. We recall that in the general case of a discrete-time linear equation if we want to use Perron’s theorem to characterize the exponential stability we have to check the boundedness of the solution with zero initial value of the forward aﬃne equation xk+1 = Lk xk + fk for arbitrary bounded sequence {fk }k≥0 ⊂ X .

3 it follows that | · |ξ is a norm on X . 8). Hence (X , | · |ξ ) is a Banach space. 2 Discrete-time equations deﬁned by positive operators 29 P1 . If x, y, x ∈ X are such that y ≤ x ≤ z then |x|ξ ≤ max{|y|ξ , |z|ξ }. 11) P2 . 12) and |ξ|ξ = 1. If Y is a Banach space, T : Y → Y is a linear bounded operator, and | · | is a norm on Y, then T = sup|x|≤1 |T x| is the corresponding operator norm. 2 (a) Because |·|ξ and |·|2 are equivalent, then · ξ and · 2 are also equivalent. This means that there are two positive constants c1 and c2 such that c1 T ξ ≤ T 2 ≤ c2 T ξ for all linear bounded operators T : X → X .

If x ∈ ∞ (Z, X ) we denote |x| = supk∈Z |xk |ξ . Let ∞ (Z, X + ) ⊂ ∞ (Z, X ) be the subset of bounded sequences {xk }k∈Z ⊂ + X . It can be checked that ∞ (Z, X + ) is a solid, closed, convex cone. 11 in [30] are fulﬁlled. Now we are in position to prove the following. 8 Let {Lk }k∈Z , {Gk }k∈Z be sequences of positive linear bounded operators such that {Gk }k∈Z is a bounded sequence. Under these conditions the following are equivalent. 49) l=−∞ T (k, l) being the linear evolution operator on X deﬁned by the sequence {Lk }k∈Z .