... matricesSt(j)=Pt−j,t/tCtT−δ0,jHtRtCt−1(j = 0, 1, ···, L − 1), (82)65New Smoothers for Discrete- time Linear Stochastic Systems with Unknown Disturbances DiscreteTime Systems 52 Chang, K. C.; Tian, Z. & Saha, R. ... filter reaches its steady state. In this case, the EC Pis given by (13). Now,74 Discrete Time Systems DiscreteTime Systems 50 This completes the proof of Theorem 2. Proof of Theorem 3 a., ... matrix.55New Smoothers for Discrete- time Linear Stochastic Systems with Unknown DisturbancesThis chapter investigates the behavior of the Kalman filter for discrete- time linear systemswhose output...
... asPk+1|k=P11,k+1|kP12,k+1|kPT12,k+1|kP22,k+1|k, (50)101Kalman Filtering for DiscreteTime Uncertain SystemsKalman Filtering for DiscreteTime Uncertain Systems 15above its error variance prediction, i.e., ... concentration of a given medicine in his patient. Kalman Filtering for Discrete Time Uncertain Systems 612 DiscreteTime SystemsUsing (74), we can simplify the expressions for Φ∗k, K∗kand ... Ee(j)i,k2, (81)Ee(j)i,k≈1NN∑j=1e(j)i,k, (82)104 Discrete Time SystemsKalman Filtering for DiscreteTime Uncertain Systems 13Step 0 (Initial conditions):x0|−1= x0and...
... the discretetime Riccati equation (7), then it also is a stabilizing solution to the discrete time Riccati inequality (6). According to the concept of stabilizing solution of discrete time ... will consider two discretetime mixed LQR/ H∞control problems. One is the discrete time state feedback mixed LQR/H∞control problem, another is the non-fragile discrete time state feedback ... Feedback Control of Discrete- time LTI Systems: Scaling LMI Approaches DiscreteTime Systems 140 Fig. 1. Responses of the system for nonlinear descriptor system in discretetime 7. References...
... a discretetime Riccati equation, we derive the simple approach to discretetime state feedback mixed LQR/H∞ control problem by combining the Lyapunov method for proving the discretetime ... for uncertain discrete- time systems with time- varying delays have given in the literature.In this paper, we consider the stabilization for a nominal discrete- time system with time- varying delay ... todelay-dependent H∞control of discrete- time systems with time- varying delay,International Journal of Robust and Nonlinear Control, Vol.18, 630-647.194 Discrete Time Systemsa Lyapunov function...
... continuous time dynamicsof the system into a discrete- time model. The ODEs in (1)-(2) can be described in a compactform by˙v= M−1p[η,v]+ M−1τ (10)˙η= q[η,v], (11)258 Discrete Time Systems5.6 ... consensus problemsfor discrete- time multi-agent systems with switching topology and time- varying delays havebeen presented by using matrix theories. In Moreau (2005), a discrete- time network modelof ... insequences, in matrices or sample -time points. In time sequences, one will distinguish betweena prediction xn+1at time tnfrom a sample x[tn]=xtnat sample time tn. Often we apply thenotation...
... Hence, the grey discretetime system (1) is asymptotically stable by Lemma 2.1. 3. Grey discretetime systems with time- delay Considering the grey discretetime system with a time- delay as follows: ... the grey discretetime time-delay systems. The proposed examples clearly demonstrate that the criteria presented in this paper for the stability of grey discrete time systems with time- delay ... Lemma 2.1, the grey discretetime with a time- delay system (13) is asymptotically stable. 4. llustrative examples Example 4.1 Consider the stability of grey discretetime system (1) as follows:...
... assets. Their initial prices at time t =0 areknown, theirfuture pricesat timet = 1 aredescribed asrandom variables onsomeprobability space. Trading takes place at time t = 0. Already in this simple ... one-period model, theseassets are priced at the initial time t = 0 and at the final time t = 1. We assume thatthe ithasset is available at time 0 for a price πi≥ 0. The collectionπ = (π0,π1, ... investor at time t = 0 will also depend on the informationavailable at time 0. Thus, we assume thatξ = (ξ0,ξ1, ,ξd)is an F0-measurable random vector. The asset prices observed at time t...
... Trong miền tần số: phương pháp Fourier Transform. - Trong miền thời gian và tần số: STFT( Short TimeFourier Transform). 2.4.1. Phương pháp Fourier: 2.4.1.1. Biến đổi Fourier: Cho một hàm f(t) ... kết thúc của sự kiện thì Fourier không phát hiện được. 2.4.2. Phương pháp STFT: Để đạt được một biến đổi Fourier cục bộ, chúng ta có thể định nghĩa một biến đổi Fourier cửa sổ. Tín hiệu đầu ... đổi Fourier của nó được định nghĩa: () () ()tfedtetfFtitj,ωωω ==∫∞∞−− (2.14) Biến đổi Fourier ngược là: () ()∫∞∞−= ωωπωdeFtftj21 (2.15) Giả sử rằng biến đổi Fourier...